Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.

Why Reichenbach wasn't entirely wrong, and Poincaré was almost right, about geometric conventionalism

The present paper revisits conventionalism about the geometry of classical and relativistic spacetimes. By means of critically examining a recent evaluation of conventionalism, we clarify key themes of, and rectify common misunderstandings about, conventionalism. Reichenbach's variant is demarcated from conventionalism simpliciter, associated primarily with Poincaré. We carefully outline the latter's core tenets-as a selective anti-realist response to a particular form of theory underdetermination. A subsequent double defence of geometric conventionalism is proffered: one line of defence employs (and thereby, to some extent, rehabilitates) a plausible reading of Reichenbach's idea of universal forces; another consists in independent support for conventionalism, unrelated to Reichenbach. Conventionalism, we maintain, remains a live option in contemporary philosophy of spacetime physics, worthy of serious consideration.

The Singularity Theorems of General Relativity and Their Low Regularity Extensions

On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent extension to Lorentzian metrics of low regularity. The latter is motivated by the quest to explore the nature of the singularities predicted by the classical theorems. Aiming at the more mathematically minded reader, we give a pedagogical introduction to the classical theorems with an emphasis on the analytical side of the arguments. We especially concentrate on focusing results for causal geodesics under appropriate geometric and initial conditions, in the smooth and in the low regularity case. The latter comprise the main technical advance that leads to the proofs of C 1 -singularity theorems via a regularisation approach that allows to deal with the distributional curvature. We close with an overview on related lines of research and a future outlook.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

The effect of mission duration on LISA science objectives

The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of ≈ 0.75 , which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended.

The general-relativistic case for super-substantivalism

Super-substantivalism (of the type we'll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier "on top of" spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism's tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics.

Careful with those scissors, Eugene! Against the observational indistinguishability of spacetimes

We discuss Manchak (2009a)'s result that there are locally (but not globally) isometric universes observationally indistinguishable from our own. This theorem makes the epistemic predicament of modern cosmology particularly problematic and the prospects of ever gaining knowledge of the global structure of the universe rather unlikely in the context of general relativity. We argue however that this conclusion is too quick; indeed, Manchak's theorem deploys spacetimes which are not physically reasonable, since they have features which are not the product of any physical process. This ultimately rests on the fact that local isometry between two spacetimes is not sufficient to guarantee that they are both physically reasonable. We propose an additional condition to properly define when a spacetime is physically reasonable, and we show that Manchak's spacetimes do not satisfy this further demand.

Is the EHT black hole experiment a new experiment in the guise of an old experiment?

This paper analyzes the experiment presented in 2019 by the Event Horizon Telescope (EHT) Collaboration that unveiled the first image of the supermassive black hole at the center of galaxy M87. The intended aim of the paper is to assess whether the EHT Collaboration has made an "inference to the best explanation" (IBE) to conclude that the data effectively confirm the hypothesis that the object at the center of M87 is in fact a supermassive Kerr rotating black hole. I demonstrate that the EHT Collaboration has applied an IBE. It is shown that the hypothesis that at the center of M87 there is a supermassive Kerr rotating black hole was already the best explanation at the time in which the 2017 EHT experiment was conducted. My analysis is intertwined with considerations on realist and empiricist interpretations of IBE, which are used to assess whether the conclusion that the object at the center of M87 is a Kerr rotating black hole implies holding a realist commitment with respect to such object.

Coincidence and reproducibility in the EHT black hole experiment

This paper discusses some philosophical aspects related to the recent publication of the experimental results of the 2017 black hole experiment, namely the first image of the supermassive black hole at the center of galaxy M87. In this paper I present a philosophical analysis of the 2017 Event Horizon Telescope (EHT) black hole experiment. I first present Hacking's philosophy of experimentation. Hacking gives his taxonomy of elements of laboratory science and distinguishes a list of elements. I show that the EHT experiment conforms to major elements from Hacking's list. I then describe with the help of Galison's Philosophy of the Shadow how the EHT Collaboration created the famous black hole image. Galison outlines three stages for the reconstruction of the black hole image: Socio-Epistemology, Mechanical Objectivity, after which there is an additional Socio-Epistemology stage. I subsequently present my own interpretation of the reconstruction of the black hole image and I discuss model fitting to data. I suggest that the main method used by the EHT Collaboration to assure trust in the results of the EHT experiment is what philosophers call the Argument from Coincidence. I show that using this method for the above purpose is problematic. I present two versions of the Argument from Coincidence: Hacking's Coincidence and Cartwright's Reproducibility by which I analyse the EHT experiment. The same estimation of the mass of the black hole is reproduced in four different procedures. The EHT Collaboration concludes: the value we have converged upon is robust. I analyse the mass measurements of the black hole with the help of Cartwright's notion of robustness. I show that the EHT Collaboration construe Coincidence/Reproducibility as Technological Agnosticism and I contrast this interpretation with van Fraassen's scientific agnosticism.

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.

Time dilation and acceleration in depression

BACKGROUND

A recent meta-analysis left open a significant question regarding altered time perception in depression: Why do depressed people overproduce short durations and under-produce longer durations if their present experience is that time flows slowly? Experience and judgement of time do not seem to accord with one another.

ANALYSIS

By excluding two of the six studies on methodological grounds from a previous meta-analysis of medium-length interval productions, and re-analysing the remaining four studies, the present paper finds that subjective time accelerates from initial dilation within present experience (approximately 1 s duration) to subsequent acceleration within working memory (approximately 30 s duration) when depressed.

PROPOSALS

It is proposed that depressive time dilation and acceleration refer to the default mode and central executive networks, respectively. The acceleration effect is suggested to occur due to mood congruency between long intervals, boredom, and depression. This mood congruency leads to the automatic recall of intrusive, negative, and non-specific autobiographical long-term memories used to judge intervals from previous experience. Acceleration in working memory then occurs according to the contextual change model of duration estimation.

LIMITATIONS

The meta-analysis is limited to four studies only, but provides a potential link between time experience and judgement within the same explanatory model.

CONCLUSIONS

Similarities between psychological time dilation/acceleration and physical time dilation/acceleration are discussed.

Boundedness and Decay for the Teukolsky Equation on Kerr Spacetimes I: The Case | a | ≪ M

We prove boundedness and polynomial decay statements for solutions of the spin ± 2 Teukolsky equation on a Kerr exterior background with parameters satisfying | a | ≪ M . The bounds are obtained by introducing generalisations of the higher order quantities P and P _ used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters | a | < M . As in the Schwarzschild case, these bounds provide the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.

Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries

Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Configurations are treated where the absolute values of the spin vectors can be considered constant. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to d-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up. The conservative spin-dependent dynamics finds explicit presentation in Hamiltonian form through next-to-next-to-leading-order spin-orbit and spin1-spin2 couplings and to leading-order in the cubic and quartic in spin interactions. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin-orbit and spin1-spin2 couplings. The most important historical issues get pointed out.

Computer algebra in gravity research

The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR's requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.

Black holes, hidden symmetries, and complete integrability

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Massive Gravity

We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.

The Hole Argument and Some Physical and Philosophical Implications

This is a historical-critical study of the hole argument, concentrating on the interface between historical, philosophical and physical issues. Although it includes a review of its history, its primary aim is a discussion of the contemporary implications of the hole argument for physical theories based on dynamical, background-independent space-time structures. The historical review includes Einstein's formulations of the hole argument, Kretschmann's critique, as well as Hilbert's reformulation and Darmois' formulation of the general-relativistic Cauchy problem. The 1970s saw a revival of interest in the hole argument, growing out of attempts to answer the question: Why did three years elapse between Einstein's adoption of the metric tensor to represent the gravitational field and his adoption of the Einstein field equations? The main part presents some modern mathematical versions of the hole argument, including both coordinate-dependent and coordinate-independent definitions of covariance and general covariance; and the fiber bundle formulation of both natural and gauge natural theories. By abstraction from continuity and differentiability, these formulations can be extended from differentiable manifolds to any set; and the concepts of permutability and general permutability applied to theories based on relations between the elements of a set, such as elementary particle theories. We are closing with an overview of current discussions of philosophical and physical implications of the hole argument.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.