Gravity Probe B: final results of a space experiment to test general relativity

Self-calibrated atom-interferometer gyroscope by modulating atomic velocities

Atom-interferometer gyroscopes have attracted much attention for their long-term stability and extremely low drift. For such high-precision instruments, self-calibration to achieve an absolute rotation measurement is critical. In this work, we propose and demonstrate the self-calibration of an atom-interferometer gyroscope. This calibration is realized by using the detuning of the laser frequency to control the atomic velocity, thus modulating the scale factor of the gyroscope. The modulation determines the order and the initial phase of the interference stripe, thus eliminating the ambiguity caused by the periodicity of the interferometric signal. This self-calibration method is validated through a measurement of the Earth's rotation rate, and a relative uncertainty of 162 ppm is achieved. Long-term stable and self-calibrated atom-interferometer gyroscopes have important applications in the fields of fundamental physics, geophysics, and long-time navigation.

Sensor Head Temperature Distribution Reconstruction of High-Precision Gravitational Reference Sensors with Machine Learning

Temperature fluctuations affect the performance of high-precision gravitational reference sensors. Due to the limited space and the complex interrelations among sensors, it is not feasible to directly measure the temperatures of sensor heads using temperature sensors. Hence, a high-accuracy interpolation method is essential for reconstructing the surface temperature of sensor heads. In this study, we utilized XGBoost-LSTM for sensor head temperature reconstruction, and we analyzed the performance of this method under two simulation scenarios: ground-based and on-orbit. The findings demonstrate that our method achieves a precision that is two orders of magnitude higher than that of conventional interpolation methods and one order of magnitude higher than that of a BP neural network. Additionally, it exhibits remarkable stability and robustness. The reconstruction accuracy of this method meets the requirements for the key payload temperature control precision specified by the Taiji Program, providing data support for subsequent tasks in thermal noise modeling and subtraction.

Measuring gravity with milligram levitated masses

Gravity differs from all other known fundamental forces because it is best described as a curvature of space-time. For that reason, it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here, we show gravitational coupling between a levitated submillimeter-scale magnetic particle inside a type I superconducting trap and kilogram source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors.

High-Precision Inertial Sensor Charge Management Based on Ultraviolet Discharge: A Comprehensive Review

The charge accumulation caused by cosmic rays and solar energetic particles poses a significant challenge as a source of noise for inertial sensors used in space gravitational wave detection. To address this issue, the implementation of charge management systems based on ultraviolet discharge becomes crucial. This paper focuses on elucidating the principles and methods of using ultraviolet discharge for charge management in high-precision inertial sensors. Furthermore, it presents the design and implementation of relevant payloads. Through an analysis of the charge accumulation effect and its impact on noise, key considerations regarding coatings, light sources, and optical paths are explored, and some current and valuable insights into the future development of charge management systems are also summarized. The conclusions drawn from this research also provide guidance for the advancement of higher precision ultraviolet discharge technology and the design of charge management systems.

A high precision surface potential imaging torsion pendulum facility to investigate physical mechanism of patch effect

The physical mechanism of the patch effect is still an open question. Thus, a high-precision surface potential mapping facility based on a specially designed electrostatically-controlled torsion pendulum is proposed in this paper. The facility not only features high sensitivity and a two-dimensional mapping function but also adapts to various measurement requirements for centimeter-sized samples. The sensitivity of the torsion pendulum reaches about 2.0 × 10^-14 N m/Hz^1/2 in a frequency range of 1-8 mHz. The temporal variation of the surface potential can be detected at a level of 30 μV/Hz^1/2 with a probe whose surface area is 7 mm². The potential spatial distribution resolution comes to 0.1 mm² at a level of 40 μV with 1 h integration time.

A Third Angular Momentum of Photons

Photons that acquire orbital angular momentum move in a helical path and are observed as a light ring. During helical motion, if a force is applied perpendicular to the direction of motion, an additional radial angular momentum is introduced, and alternate dark spots appear on the light ring. Here, a third, centrifugal angular momentum has been added by twisting the helical path further according to the three-step hierarchical assembly of helical organic nanowires. Attaining a third angular momentum is the theoretical limit for a photon. The additional angular momentum converts the dimensionless photon to a hollow spherical photon condensate with interactive dark regions. A stream of these photon condensates can interfere like a wave or disintegrate like matter, similar to the behavior of electrons.

Generation of Entanglement from Mechanical Rotation

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a superposition of two different spacetimes. We predict the generation of genuine entanglement even at low rotation frequencies and show how these effects could be observed even due to the Earth's rotation. These predictions provide an accessible platform in which to study the role of the underlying spacetime in the generation of entanglement.

Dipole moment background measurement and suppression for levitated charge sensors

Optically levitated macroscopic objects are a powerful tool in the field of force sensing, owing to high sensitivity, absolute force calibration, environmental isolation, and the advanced degree of control over their dynamics that have been achieved. However, limitations arise from the spurious forces caused by electrical polarization effects that, even for nominally neutral objects, affect the force sensing because of the interaction of dipole moments with gradients of external electric fields. Here, we introduce a technique to measure, model, and eliminate dipole moment interactions, limiting the performance of sensors using levitated objects. This process leads to a noise-limited measurement with a sensitivity of 3.3 × 10^-5 e. As a demonstration, this is applied to the search for unknown charges of a magnitude much below that of an electron or for exceedingly small unbalances between electron and proton charges.

Precision improvement of patch potential measurement in a scanning probe equipped torsion pendulum

Patch effect is important for ultra-sensitive experiments involving closely spaced conducting surfaces. A scanning probe equipped torsion pendulum is an experimental apparatus for measuring spatial resolved patch potential on conductive surfaces. An effective approach to improve its measurement precision is by the optimization on the amplitude and frequency of the injected signal in the probe. In this paper, a method based on single- and double-frequency signal injection modes is proposed. The analysis results demonstrate that the potential resolution could achieve the level of 2-4 μV/Hz^1/2. In the same integration time, the surface potential precision in the double-frequency mode is twice better than that in the single-frequency mode. In addition, when achieving the same measurement precision, the double-frequency mode takes less time than the single-frequency mode, which improves the measuring efficiency.

Towards an Acoustic Geometry in Slightly Viscous Fluids

We explore the behaviour of barotropic and irrotational fluids with a small viscosity under the effect of first-order acoustic perturbations. We discuss, following the extant literature, the difficulties in gleaning an acoustic geometry in the presence of viscosity. In order to obviate various technical encumbrances, when viscosity is present, for an extraction of a possible acoustic geometry, we adopted a method of double perturbations, whereby dynamical quantities such as the velocity field and potential undergo a perturbation both in viscosity and in an external acoustic stimulus. The resulting perturbation equations yield a solution which can be interpreted in terms of a generalised acoustic geometry, over and above the one known for inviscid fluids.

Spin Precession in the Gravity Wave Analogue Black Hole Spacetime

It was predicted that the spin precession frequency of a stationary gyroscope shows various anomalies in the strong gravity regime if its orbit shrinks, and eventually, its precession frequency becomes arbitrarily high very close to the horizon of a rotating black hole. Considering the gravity waves of a flowing fluid with a vortex in a shallow basin, which acts as a rotating analogue black hole, one can observe the predicted strong gravity effect on the spin precession in the laboratory. Attaching a thread with the buoyant particles and anchoring it to the bottom of the fluid container with a short-length miniature chain, one can construct a simple local test gyroscope to measure the spin precession frequency in the vicinity of the gravity wave analogue black hole. The thread acts as the axis of the gyroscope. By regulating the orbital frequency of the test gyroscope, one can also measure the strong gravity Lense–Thirring effect and geodetic/de-Sitter effect with this experimental set-up as the special cases. For example, to measure the Lense–Thirring effect, the length of the miniature chain can be set to zero, so that the gyroscope becomes static. One can also measure the geodetic precession with this system by orbiting the test gyroscope in the so-called Keplerian frequency around the non-rotating analogue black hole that can be constructed by making the rotation of the fluid/vortex negligible compared to its radial velocity.

A signature invariant geometric algebra framework for spacetime physics and its applications in relativistic dynamics of a massive particle and gyroscopic precession

A signature invariant geometric algebra framework for spacetime physics is formulated. By following the original idea of David Hestenes in the spacetime algebra of signature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(+,-,-,-)$$\end{document}(+,-,-,-), the techniques related to relative vector and spacetime split are built up in the spacetime algebra of signature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-,+,+,+)$$\end{document}(-,+,+,+). The even subalgebras of the spacetime algebras of signatures \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pm ,\mp ,\mp ,\mp )$$\end{document}(±,∓,∓,∓) share the same operation rules, so that they could be treated as one algebraic formalism, in which spacetime physics is described in a signature invariant form. Based on the two spacetime algebras and their “common” even subalgebra, rotor techniques on Lorentz transformation and relativistic dynamics of a massive particle in curved spacetime are constructed. A signature invariant treatment of the general Lorentz boost with velocity in an arbitrary direction and the general spatial rotation in an arbitrary plane is presented. For a massive particle, the spacetime splits of the velocity, acceleration, momentum, and force four-vectors with the normalized four-velocity of the fiducial observer, at rest in the coordinate system of the spacetime metric, are given, where the proper time of the fiducial observer is identified, and the contribution of the bivector connection is considered, and with these results, a three-dimensional analogue of Newton’s second law for this particle in curved spacetime is achieved. Finally, as a comprehensive application of the techniques constructed in this paper, a geometric algebra approach to gyroscopic precession is provided, where for a gyroscope moving in the Lense-Thirring spacetime, the precessional angular velocity of its spin is derived in a signature invariant manner.

Optimization of beam shaping for ultrasensitive inertial measurement using a phase-only spatial light modulator

This study proposes an approach to generate a uniform flat-top beam with a liquid crystal spatial light modulator (LC-SLM) to optimize ultrasensitive inertial measurement. The random incomplete Gaussian beam is modulated into a flat-top beam by uploading a beam shaping optimization algorithm on an LC-SLM. Simulation results verify the effectiveness of the proposed method. The beam obtained from the experimental results with the 4f filter system optimization also conforms to the properties of the generated flat-top beam. Compared to existing beam shaping algorithms for simulation and experimental analysis, the beam shaping design based on the LC-SLM to optimize the ultrasensitive inertial measurement is realized. This method has also been verified to be effective in beam shaping in various beam situations. The application of this method in ultrahigh-sensitivity inertial measurement should prove significant.

Frame-Dragging: Meaning, Myths, and Misconceptions

Originally introduced in connection with general relativistic Coriolis forces, the term frame-dragging is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type “body-dragging”) are debunked. Applications considered include rotating cylinders (Lewis–Weyl metrics), Kerr, Kerr–Newman and Kerr–dS spacetimes, black holes surrounded by disks/rings, and binary systems.

Multi-loop atomic Sagnac interferometry

The sensitivity of light and matter-wave interferometers to rotations is based on the Sagnac effect and increases with the area enclosed by the interferometer. In the case of light, the latter can be enlarged by forming multiple fibre loops, whereas the equivalent for matter-wave interferometers remains an experimental challenge. We present a concept for a multi-loop atom interferometer with a scalable area formed by light pulses. Our method will offer sensitivities as high as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 10^{-11}$$\end{document}2×10-11 rad/s at 1 s in combination with the respective long-term stability as required for Earth rotation monitoring.

Gravitomagnetic Stern-Gerlach Force

A heuristic description of the spin-rotation-gravity coupling is presented and the implications of the corresponding gravitomagnetic Stern-Gerlach force are briefly mentioned. It is shown, within the framework of linearized general relativity, that the gravitomagnetic Stern-Gerlach force reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

Prototype of a monolithic cavity-based ultrastable optical reference for space applications

We present a compact, monolithic optical reference for the frequency stabilized laser of future inter-satellite laser interferometer missions. A prototype based on the integration of a high-finesse cavity and associate optics has been designed to be space compatible while maintaining sufficient stability. The prototype has then been developed with a space-qualified bonding technique, and an in situ multi-degree-of-freedom alignment method. The performances of the optical reference have been studied by beat note analysis with another frequency stabilized laser, and the preliminary results are in agreement with the potential requirements of future space missions.

Einstein’s Geometrical versus Feynman’s Quantum-Field Approaches to Gravity Physics: Testing by Modern Multimessenger Astronomy

Modern multimessenger astronomy delivers unique opportunity for performing crucial observations that allow for testing the physics of the gravitational interaction. These tests include detection of gravitational waves by advanced LIGO-Virgo antennas, Event Horizon Telescope observations of central relativistic compact objects (RCO) in active galactic nuclei (AGN), X-ray spectroscopic observations of Fe Kα line in AGN, Galactic X-ray sources measurement of masses and radiuses of neutron stars, quark stars, and other RCO. A very important task of observational cosmology is to perform large surveys of galactic distances independent on cosmological redshifts for testing the nature of the Hubble law and peculiar velocities. Forthcoming multimessenger astronomy, while using such facilities as advanced LIGO-Virgo, Event Horizon Telescope (EHT), ALMA, WALLABY, JWST, EUCLID, and THESEUS, can elucidate the relation between Einstein’s geometrical and Feynman’s quantum-field approaches to gravity physics and deliver a new possibilities for unification of gravitation with other fundamental quantum physical interactions.

Gravity Tests with Radio Pulsars

The discovery of the first binary pulsar in 1974 has opened up a completely new field of experimental gravity. In numerous important ways, pulsars have taken precision gravity tests quantitatively and qualitatively beyond the weak-field slow-motion regime of the Solar System. Apart from the first verification of the existence of gravitational waves, binary pulsars for the first time gave us the possibility to study the dynamics of strongly self-gravitating bodies with high precision. To date there are several radio pulsars known which can be utilized for precision tests of gravity. Depending on their orbital properties and the nature of their companion, these pulsars probe various different predictions of general relativity and its alternatives in the mildly relativistic strong-field regime. In many aspects, pulsar tests are complementary to other present and upcoming gravity experiments, like gravitational-wave observatories or the Event Horizon Telescope. This review gives an introduction to gravity tests with radio pulsars and its theoretical foundations, highlights some of the most important results, and gives a brief outlook into the future of this important field of experimental gravity.

Exact Solution for Relativistic Trajectories Using Modal Transseries

In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form e−nθ, n=1, 2, …, where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions.

Reconstruction of the Instantaneous Earth Rotation Vector with Sub-Arcsecond Resolution Using a Large Scale Ring Laser Array

Absolute rotation rate sensing with extreme sensitivity requires a combination of several large scale gyroscopes in order to obtain the full vector of rotation. We report on the construction and operation of a four-component, tetrahedral laser gyroscope array as large as a five story building and situated in a near surface, underground laboratory. It is demonstrated that reconstruction of the full Earth rotation vector can be achieved with sub-arcsecond resolution over more than six weeks.

Gravitational Spin-Orbit Coupling through Third-Subleading Post-Newtonian Order: From First-Order Self-Force to Arbitrary Mass Ratios

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

Gravitomagnetism characterizes phenomena in the weak-field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theories of gravity may have an important impact on these effects which may constrain potential models within these theories.

A radiating Kerr black hole and Hawking radiation

This study proposes an axisymmetric generalization of the Vaidya metric, namely the Vaidya–Kerr metric, to describe a radiating rotating black hole, and presents its Hawking radiation temperature. This study is an improved version of our previous research via ellipsoid coordinate transformation, and the Einstein field equations are solved concisely and intuitively by an orthogonal ansatz. The results demonstrate that the energy–momentum tensor of the derived radiating Kerr metric satisfies the energy-conservation law and is classified as a Petrov type II fluid, whereas the stationary Kerr metric is a Petrov type IV vacuum. The inner and outer event-horizon radii, the ergosphere radii, as well as the angular velocity at the event horizon are solved, and then, surface gravity, entropy, and Hawking radiation are derived. We estimate the Hawking-radiation temperature of the black holes with the angular momentum and the same mass of Pluto and the sun, as well as the supermassive black hole in the core of the M87 galaxy to be 9.42K, 6.08×10−8K, and 8.78×10−18K, respectively. Only the value of the rotating Pluto-mass black hole is slightly greater than the 3K cosmic microwave background radiation and may be detected by high-resolution tools in the future.

Lense-Thirring frame dragging induced by a fast-rotating white dwarf in a binary pulsar system

Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141-6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observed a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring (LT) precession of the orbit resulting from rapid rotation of the WD. LT precession, an effect of relativistic frame dragging, is a prediction of general relativity. This detection is consistent with an evolutionary scenario in which the WD accreted matter from the pulsar progenitor, spinning up the WD to a period of <200 seconds.

Fundamental Physics Implications for Higher-Curvature Theories from Binary Black Hole Signals in the LIGO-Virgo Catalog GWTC-1

Gravitational-wave astronomy offers not only new vistas into the realm of astrophysics, but it also opens an avenue for probing, for the first time, general relativity in its strong-field, nonlinear, and dynamical regime, where the theory's predictions manifest themselves in their full glory. We present a study of whether the gravitational-wave events detected so far by the LIGO-Virgo scientific collaborations can be used to probe higher-curvature corrections to general relativity. In particular, we focus on two examples: Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons gravity. We find that the two events with a low-mass m≈7  M_{⊙} BH (GW151226 and GW170608) place stringent constraints on Einstein-dilaton-Gauss-Bonnet gravity, α_{EDGB}^{1/2}≲5.6  km, whereas dynamical Chern-Simons gravity remains unconstrained by the gravitational-wave observations analyzed.

Sensing Earth rotation with a helium-neon laser operating on three transitions in the visible region

We demonstrate an active Sagnac ring interferometer that operates on the previously unexploited 3s₂→2p₆ (611.8 nm), 3s₂→2p₇ (604.6 nm), and 3s₂→2p₈ (593.9 nm) neon transitions, in a helium-neon gain medium. The cavity was constructed using state-of-the-art ion-beam sputtered, ultralow-loss supermirrors designed to yield greater transmission loss at lower optical frequency, which partially compensates for the gain differential across the three transitions. For an optimized cavity fill of 0.3 mbar partial pressure of neon (50% Ne20 and 50% Ne22) and a total gas pressure of 2 mbar, for laser operation at 611.8 nm, the cavity Q is 1.2×10¹¹, having a cold cavity ringdown time of 38 μs. The laser yielded a stable Sagnac frequency of 117.4 Hz due to the Earth's rotation. The usable gyroscopic sensitivity is determined to be 8.8×10^-9  rad/s for a measurement time of 128 s.

Nonlocal Gravitomagnetism

We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocalgeneralization of Einstein’s theory of gravitation based on a certain analogy with the nonlocalelectrodynamics of media. Nonlocal gravity thus involves integro-differential field equationsand a causal constitutive kernel that should ultimately be determined from observational data.We consider the stationary gravitational field of an isolated rotating astronomical source in the linearapproximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG,we describe the gravitomagnetic field associated with the rotating source and compare our resultswith gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we brieflystudy the energy-momentum content of the GEM field in nonlocal gravity.

Rotation Sensing Lasers in General Relativity: Some Technical Notes and Current Advances

We review the current status of large ring laser gyroscopes having the potential to contributeto terrestrial measurements of general relativistic precessions. At this point in time, although thesedevices possess the raw sensitivity for such a measurement, they remain limited by long-term geometricinstability, detection noise and imperfections in the physical models required to isolate geophysicaleffects. Furthermore, minute non-reciprocal biases provide a null-shift error and therefore no currentlyconstructed laser system meets the requirement of absolute rotation rate sensing. Nevertheless, we are ofthe view that these are surmountable problems and the ability of ring laser gyroscopes to measure lowfrequency to DC signals has vastly increased in the last decade.

General Relativity Measurements in the Field of Earth with Laser-Ranged Satellites: State of the Art and Perspectives

Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a 0.5 % precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Gravitational Qubits

We report on the behavior of two-level quantum systems, or qubits, in the background of rotating and non-rotating metrics and provide a method to derive the related spin currents and motions. The calculations are performed in the external field approximation.

Self-force and radiation reaction in general relativity

The detection of gravitational waves from binary black-hole mergers by the LIGO-Virgo Collaboration marks the dawn of an era when general-relativistic dynamics in its most extreme manifestation is directly accessible to observation. In the future, planned (space-based) observatories operating in the millihertz band will detect the intricate gravitational-wave signals from the inspiral of compact objects into massive black holes residing in galactic centers. Such inspiral events are extremely effective probes of black-hole geometries, offering unparalleled precision tests of general relativity in its most extreme regime. This prospect has in the past two decades motivated a programme to obtain an accurate theoretical model of the strong-field radiative dynamics in a two-body system with a small mass ratio. The problem naturally lends itself to a perturbative treatment based on a systematic expansion of the field equations in the small mass ratio. At leading order one has a pointlike particle moving in a geodesic orbit around the large black hole. At subsequent orders, interaction of the particle with its own gravitational perturbation gives rise to an effective 'self-force', which drives the radiative evolution of the orbit, and whose effects can be accounted for order by order in the mass ratio. This review surveys the theory of gravitational self-force in curved spacetime and its application to the astrophysical inspiral problem. We first lay the relevant formal foundation, describing the rigorous derivation of the equation of self-forced motion using matched asymptotic expansions and other ideas. We then review the progress that has been achieved in numerically calculating the self-force and its physical effects in astrophysically realistic inspiral scenarios. We highlight the way in which, nowadays, self-force calculations make a fruitful contact with other approaches to the two-body problem and help inform an accurate universal model of binary black hole inspirals, valid across all mass ratios. We conclude with a summary of the state of the art, open problems and prospects. Our review is aimed at non-specialist readers and is for the most part self-contained and non-technical; only elementary-level acquaintance with general relativity is assumed. Where useful, we draw on analogies with familiar concepts from Newtonian gravity or classical electrodynamics.

Reply to "A comment on "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model, by I. Ciufolini et al.""

In 2016, we published "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth's gravity model. Measurement of Earth's dragging of inertial frames [1]", a measurement of frame-dragging, a fundamental prediction of Einstein's theory of General Relativity, using the laser-ranged satellites LARES, LAGEOS and LAGEOS 2. The formal error, or precision, of our test was about 0.2% of frame-dragging, whereas the systematic error was estimated to be about 5%. In the 2017 paper "A comment on "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth's gravity model by I. Ciufolini et al."" by L. Iorio [2] (called I2017 in the following), it was incorrectly claimed that, when comparing different Earth's gravity field models, the systematic error in our test due to the Earth's even zonal harmonics of degree 6, 8, 10 could be as large as 15%, 6% and 36%, respectively. Furthermore, I2017 contains other, also incorrect, claims about the number of necessary significant decimal digits of the coefficients used in our test (claimed to be nine), in order to eliminate the largest uncertainties in the even zonals of degree 2 and 4, and about the non-repeatability of our test. Here we analyze and rebut those claims in I2017.

Automated precision alignment of optical components for hydroxide catalysis bonding

We describe an interferometric system that can measure the alignment and separation of a polished face of a optical component and an adjacent polished surface. Accuracies achieved are ∼ 1μrad for the relative angles in two orthogonal directions and ∼ 30μm in separation. We describe the use of this readout system to automate the process of hydroxide catalysis bonding of a fused-silica component to a fused-silica baseplate. The complete alignment and bonding sequence was typically achieved in a timescale of a few minutes, followed by an initial cure of 10 minutes. A series of bonds were performed using two fluids - a simple sodium hydroxide solution and a sodium hydroxide solution with some sodium silicate solution added. In each case we achieved final bonded component angular alignment within 10 μrad and position in the critical direction within 4 μm of the planned targets. The small movements of the component during the initial bonding and curing phases were monitored. The bonds made using the sodium silicate mixture achieved their final bonded alignment over a period of ∼ 15 hours. Bonds using the simple sodium hydroxide solution achieved their final alignment in a much shorter time of a few minutes. The automated system promises to speed the manufacture of precision-aligned assemblies using hydroxide catalysis bonding by more than an order of magnitude over the more manual approach used to build the optical interferometer at the heart of the recent ESA LISA Pathfinder technology demonstrator mission. This novel approach will be key to the time-efficient and low-risk manufacture of the complex optical systems needed for the forthcoming ESA spaceborne gravitational waves observatory mission, provisionally named LISA.

Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission

The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter η = (−6.6 ± 7.2) × 10⁻⁵. By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter β = 1 + (−1.6 ± 1.8) × 10⁻⁵ and the Sun’s gravitational oblateness, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{J}}_{2 \odot }$$\end{document}J2⊙ = (2.246 ± 0.022) × 10⁻⁷. Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{{G} {{M}}_ \odot} {\mathrm{/}}{{G}}{{M}}_ \odot$$\end{document}GM⊙°∕GM⊙ = (−6.13 ± 1.47) × 10⁻¹⁴, which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| {{\dot{ G}}} \right|{\mathrm{/}}{{G}}$$\end{document}G°∕G to be <4 × 10⁻¹⁴ per year.

The NASA MESSENGER mission collected a rich dataset enabling determination of Mercury’s ephemeris. Here, the authors analyse MESSENGER data obtained over an extended period of time to quantify parameters related to General Relativity.

Fabrication of ultrahigh-precision hemispherical mirrors for quantum-optics applications

High precision, high numerical aperture mirrors are desirable for mediating strong atom-light coupling in quantum optics applications and can also serve as important reference surfaces for optical metrology. In this work we demonstrate the fabrication of highly-precise hemispheric mirrors with numerical aperture NA = 0.996. The mirrors were fabricated from aluminum by single-point diamond turning using a stable ultra-precision lathe calibrated with an in-situ white-light interferometer. Our mirrors have a diameter of 25 mm and were characterized using a combination of wide-angle single-shot and small-angle stitched multi-shot interferometry. The measurements show root-mean-square (RMS) form errors consistently below 25 nm. The smoothest of our mirrors has a RMS error of 14 nm and a peak-to-valley (PV) error of 88 nm, which corresponds to a form accuracy of λ/50 for visible optics.

Differential optical shadow sensor for sub-nanometer displacement measurement and its application to drag-free satellites

We present a method for 3D sub-nanometer displacement measurement using a set of differential optical shadow sensors. It is based on using pairs of collimated beams on opposite sides of an object that are partially blocked by it. Applied to a sphere, our 3-axis sensor module consists of 8 parallel beam-detector sets for redundancy. The sphere blocks half of each beam's power in the nominal centered position, and any displacement can be measured by the differential optical power changes amongst the pairs of detectors. We have experimentally demonstrated a displacement sensitivity of 0.87nm/Hz at 1 Hz and 0.39nm/Hz at 10 Hz. We describe the application of the module to the inertial sensor of a drag-free satellite, which can potentially be used for navigation, geodesy and fundamental science experiments as well as ground based applications.

Impact of Next-to-Leading Order Contributions to Cosmic Microwave Background Lensing

In this Letter we study the impact on cosmological parameter estimation, from present and future surveys, due to lensing corrections on cosmic microwave background temperature and polarization anisotropies beyond leading order. In particular, we show how post-Born corrections, large-scale structure effects, and the correction due to the change in the polarization direction between the emission at the source and the detection at the observer are non-negligible in the determination of the polarization spectra. They have to be taken into account for an accurate estimation of cosmological parameters sensitive to or even based on these spectra. We study in detail the impact of higher order lensing on the determination of the tensor-to-scalar ratio r and on the estimation of the effective number of relativistic species N_{eff}. We find that neglecting higher order lensing terms can lead to misinterpreting these corrections as a primordial tensor-to-scalar ratio of about O(10^{-3}). Furthermore, it leads to a shift of the parameter N_{eff} by nearly 2σ considering the level of accuracy aimed by future S4 surveys.

Gravitational waves and electrodynamics: new perspectives

Given the recent direct measurement of gravitational waves (GWs) by the LIGO-VIRGO collaboration, the coupling between electromagnetic fields and gravity have a special relevance since it opens new perspectives for future GW detectors and also potentially provides information on the physics of highly energetic GW sources. We explore such couplings using the field equations of electrodynamics on (pseudo) Riemann manifolds and apply it to the background of a GW, seen as a linear perturbation of Minkowski geometry. Electric and magnetic oscillations are induced that propagate as electromagnetic waves and contain information as regards the GW which generates them. The most relevant results are the presence of longitudinal modes and dynamical polarization patterns of electromagnetic radiation induced by GWs. These effects might be amplified using appropriate resonators, effectively improving the signal to noise ratio around a specific frequency. We also briefly address the generation of charge density fluctuations induced by GWs and the implications for astrophysics.