Rotating Stars in Relativity

Numerical Equilibrium Configurations and Quadrupole Moments of Post-Merger Differentially Rotating Relativistic Stars

Numerical simulations of binary neutron star mergers invariably show that, when a long-lived remnant forms, its rotation profile is never a simple decaying function of the radius but rather exhibits a maximum rotation rate shifted away from the center. This is in contrast to the usual differential rotation profile employed for the numerical modeling of axisymmetric equilibria of relativistic stars. Two families of rotation rate functions that mimic post-merger profiles were proposed by Uryū et al. (2017). In this work we implement Uryū’s profiles into the XNS code by Bucciantini and Del Zanna (2011) and we present novel equilibrium sequences of differentially rotating neutron stars. These are constructed by using three different equations of state, in order to study the dependence of mass, radius, angular momentum, and other important physical quantities, especially the quadrupole deformation and metric quadrupole moment, from the rotation properties.

Quark Stars in Massive Brans–Dicke Gravity with Tolman–Kuchowicz Spacetime

In this paper, we construct anisotropic model representing salient features of strange stars in the framework of massive Brans–Dicke gravity. We formulate the field equations for Tolman–Kuchowicz ansatz by incorporating the MIT bag model. Junction conditions are applied on the boundary of the stellar model to evaluate the unknown constants in terms of mass and radius of the star. The radius of the strange star candidate PSR J1614-2230 is predicted by assuming maximum anisotropy at the surface of the star for different values of the coupling parameter, mass of the scalar field and bag constant. We examine various properties as well as the viability and stability of the anisotropic sphere. We conclude that the astrophysical model agrees with the essential criteria of a physically realistic model for higher values of the coupling parameter as well as mass of the scalar field.

The Erez–Rosen Solution Versus the Hartle–Thorne Solution

In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez–Rosen and the Hartle–Thorne solutions are particular solutions of a more general solution, the Zipoy–Voorhees transformation is applied to the exact Erez–Rosen metric in order to obtain a generalized solution in terms of the Zipoy–Voorhees parameter δ = 1 + s q . The Geroch–Hansen multipole moments of the generalized Erez–Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass m, quadrupole q and Zipoy–Voorhees δ parameters. The coordinate transformations between the metrics are found in the approximation of ∼q. It is shown that the Zipoy–Voorhees parameter is equal to δ = 1 - q with s = - 1 . This result is in agreement with previous results in the literature.

Numerical relativity of compact binaries in the 21st century

We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star-neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible (Pretorius 2005 Phys. Rev. Lett. 95 121101, Campanelli et al 2006 Phys. Rev. Lett. 96 111101, Baker et al 2006 Phys. Rev. Lett. 96 111102). Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star-neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.

Rotating stars in relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f-modes and r-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

Binary neutron star mergers: a review of Einstein's richest laboratory

In a single process, the merger of binary neutron star systems combines extreme gravity, the copious emission of gravitational waves, complex microphysics and electromagnetic processes, which can lead to astrophysical signatures observable at the largest redshifts. We review here the recent progress in understanding what could be considered Einstein's richest laboratory, highlighting in particular the numerous significant advances of the last decade. Although special attention is paid to the status of models, techniques and results for fully general-relativistic dynamical simulations, a review is also offered on the initial data and advanced simulations with approximate treatments of gravity. Finally, we review the considerable amount of work carried out on the post-merger phase, including black-hole formation, torus accretion onto the merged compact object, the connection with gamma-ray burst engines, ejected material, and its nucleosynthesis.

The initial value problem as it relates to numerical relativity

Spacetime is foliated by spatial hypersurfaces in the 3+1 split of general relativity. The initial value problem then consists of specifying initial data for all fields on one such a spatial hypersurface, such that the subsequent evolution forward in time is fully determined. On each hypersurface the 3-metric and extrinsic curvature describe the geometry. Together with matter fields such as fluid velocity, energy density and rest mass density, the 3-metric and extrinsic curvature then constitute the initial data. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of general relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium, which essentially assumes that time derivatives are negligible in corotating coordinates for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.

Exploring New Physics Frontiers Through Numerical Relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

Bridging the gap by squeezing superfluid matter

Cooper pairing between fermions in dense matter leads to the formation of a gap in the fermionic excitation spectrum and typically exponentially suppresses transport properties. However, we show here that reactions involving conversion between different fermion species, such as Urca reactions in nuclear matter, become strongly enhanced and approach their ungapped level when the matter undergoes density oscillations of sufficiently large amplitude. We study both the neutrino emissivity and the bulk viscosity due to direct Urca processes in hadronic, hyperonic, and quark matter and discuss different superfluid and superconducting pairing patterns.

Spectral Methods for Numerical Relativity

Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.