Starting with the conceptual foundation of general relativity (GR) - equivalence principle, space-time geometry and special relativity, I train cross hairs on two characteristic predictions of GR - black holes and gravitational waves. These two consequences of GR have played a significant role in relativistic astrophysics, e.g. compact X-ray sources, GRBs, quasars, blazars, coalescing binary pulsars, etc.
With quantum theory wedded to GR, particle production from vacuum becomes a generic feature whenever event horizons are present. In this paper, I shall briefly discuss the fate of a `black hole atom' when Hawking radiation is taken into account. In the context of gravitational waves, I shall focus on the possible consequences of gravitational and electromagnetic radiation from highly magnetized and rapidly spinning white dwarfs. The discovery of RX J0648.0-4418 system - a WD in a binary with mass slightly over 1.2 $ M_{\odot}$, and rotating with spin period as short as 13.2 s, provides an impetus to revisit the problem of WD spin evolution due to energy loss.
We describe the first numerical Tolman-Oppenheimer-Volkoff solutions of compact objects in entangled relativity, which is an alternative to the framework of general relativity that does not have any additional free parameter. Assuming a simple polytropic equation of state and the conservation of the rest-mass density, we notably show that, for any given density, compact objects are always heavier (up to $\sim 8\%$) in entangled relativity than in general relativity -- for any given central density within the usual range of neutron stars' central densities, or for a given radius of the resultin…
We study a flat spacetime with a compact spatial dimension and dispute the claim of Bansal, Laing, and Sriharan that a local experiment can determine whether or not an inertial observer is "privileged" in this spacetime.
A charged compact star models have been determined for anisotropic fluid distribution. We have solved the Einstein's- Maxwell field equations to construct the charged compact star models by using radial pressure, metric function $e^λ$ and electric charge function. The generic charged anisotropic solution is verified by exploring different physical conditions like, causality condition, mass-radius relation and stability of the solution (via. adiabatic index, TOV equations and Herrera cracking concept). It is observed that the present charged anisotropic compact star is compatible with the star …
Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor associated with the gyroscope and uses only its exterior field for its characterization. The resulting equations of motion differ from those of previous derivations.
The theory of general relativity, which is extremely well verified by classic tests in the solar system as well as by the radiation of the binary pulsar, is one of the fundamental tools of nowadays astrophysics. It permits the computation of the gravitational wave form emitted during the inspiral phase of binary systems of neutron stars and black holes. Based on the so-called post-Newtonian approximation (developped to high order), the prediction of general relativity is used as a "template" for searching and analysing the signals in the network of gravitational-wave detectors VIRGO/LIGO.
We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo and KAGRA, for mass ratio 7 and total mass as low as $45.5\,M_\odot$. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral wavef…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
We have developed a new numerical scheme to obtain quasiequilibrium structures of nonaxisymmetric compact stars such as binary neutron star systems as well as the spacetime around those systems in general relativity. Concerning quasiequilibrium states of binary systems in general relativity, several investigations have been already carried out by assuming conformal flatness of the spatial part of the metric. However, the validity of the conformally flat treatment has not been fully analyzed except for axisymmetric configurations. Therefore it is desirable to solve quasiequilibrium states by de…
Durgapal's fifth isotropic solution describing spherically symmetric and static matter distribution is extended to an anisotropic scenario. To do so we employ the gravitational decoupling through the minimal geometric deformation scheme. This approach allows to split Einstein's field equations in two simply set of equations, one corresponding to the isotropic sector and other to the anisotropic sector described by an extra gravitational source. The isotropic sector is solved by the Dugarpal's model and the anisotropic sector is solved once a suitable election on the minimal geometric deformati…
We numerically calculate equilibrium configurations of uniformly rotating and charged neutron stars, in the case of insulating material and neglecting the electromagnetic forces acting on the equilibrium of the fluid. This allows us to study the behaviour of the gyromagnetic ratio for those objects, when varying rotation rate and equation of state for the matter. Under the assumption of low charge and incompressible fluid, we find that the gyromagnetic ratio is directly proportional to the compaction parameter M/R of the star, and very little dependent on its angular velocity. Nevertheless, it…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for realistic anisotropic neutron stars was obtained using the general theory of relativity. Assuming a physically acceptable non-singular form of one metric potential and radial pressure containing the curvature parameter $R$, the constant $k$, and the radius $r$, analytical solutions to Einstein's field equations for anisotropic matter distribution were obtained. Taki…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (1/c^6 beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO-type experiments.
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, wit…
In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman-Oppenheimer-Volkoff framework. Analytical and numerical solutions match perfectly well outside spherical compact objects, therefore validating both types of solutions at the same time. The analytical external (hairy) solutions -- which depend on two parameters only -- may be used in order to easily compute observables -- such as X-ray pusle profiles -- without having to rely on an unknown equation of state for matter inside the compact obj…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that none of the standard models obtained by using Fock's method can be used as an interior source for the approximate exterior Kerr solution. We then use Fock's method to derive a generalized interior solution, and also an exterior solution that turns out to be equivalent to the exterior Hartle-Thorne approximate solution that, in turn, is equivalent to an approxi…
The second generation of gravitational-wave detectors is scheduled to start operations in 2015. Gravitational-wave signatures of compact binary coalescences could be used to accurately test the strong-field dynamical predictions of general relativity. Computationally expensive data analysis pipelines, including TIGER, have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from general relativity can be detected, Cornish et al. and Vallisneri recently proposed an approximate scheme to compute the Bayes factor between a general-relativity gravita…
The gravitational-wave energy flux produced during the head-on infall and collision of two compact objects is calculated using two approaches: (i) a post-Newtonian method, carried to second post-Newtonian order beyond the quadrupole formula, valid for systems of arbitrary masses; and (ii) a black-hole perturbation method, valid for a test-body falling radially toward a black hole. In the test-body case, the methods are compared. The post-Newtonian method is shown to converge to the ``exact'' perturbation result more slowly than expected {\it a priori\/}. A surprisingly good approximation to th…
Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave (GW) astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on NR simulations than first- and second-generation ground-based detectors. We discuss the issues facing compact-object simulations over the next decade, with an emphasis on estimating where the accuracy and parameter space coverage will be sufficient for ET and where significant work is needed.
Inspiraling compact binaries are expected to be the strongest sources of gravitational waves for VIRGO, LIGO and other laser interferometers. We present the first computations of quasi-equilibrium sequences of compact binaries containing two strange quark stars (which are currently considered as a possible alternative to neutron stars). We study a precoalescing stage in the conformal flatness approximation of general relativity using a multidomain spectral method. A hydrodynamical treatment is performed under the assumption that the flow is irrotational.
We present a physically plausible solution representing Einstein's cluster mimicking the behaviors of compact star in the context of teleparallel equivalent of general relativity. The Teleparallel gravity (TEGR) is an alternative formulation of gravity which uses tetrads as the dynamical variables. We focus on two particularly interesting scenarios. First, we develop the Einstein clusters in TEGR field equations using effective energy-momentum tensor for diagonal as well as off-diagonal tetrad. We then study the clusters in modified $f(T)-$gravity for anisotropic fluid distribution. Based on t…
The parameterized post-Einsteinian framework modifies inspiral waveform models to incorporate effects beyond General Relativity. We extend the existing model into the merger-ringdown regime. The modification introduced here adds a single degree of freedom that corresponds to a change in the binary coalescence time. Other merger properties remain as predicted by GR. We discuss parameter estimation with this model, and how it can be used to extract information from beyond-GR waveforms.
We consider two most popular definitions of velocities of remote objects in General Relativity. Our work has two motivations. From a research point of view, we generalize the formula connecting these two velocities in FRW metrics found by Chodorowski to arbitrary synchronous spherically symmetric metrics. From a methodological point of view, our goal is to outline certain counter-intuitive properties of the definitions in question, which would allow to use them when it is reasonable and to avoid incorrect statements, based on inappropriate use of intuition.
Second generation interferometric gravitational wave detectors, such as Advanced LIGO and Advanced Virgo, are expected to begin operation by 2015. Such instruments plan to reach sensitivities that will offer the unique possibility to test General Relativity in the dynamical, strong field regime and investigate departures from its predictions, in particular using the signal from coalescing binary systems. We introduce a statistical framework based on Bayesian model selection in which the Bayes factor between two competing hypotheses measures which theory is favored by the data. Probability dens…
We demonstrate that there are theories that exhibit spontaneous scalarization in the strong gravity regime while having General Relativity with a constant scalar as a cosmological attractor. We identify the minimal model that has this property and discuss its extensions.
Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution. The generalisation involves the addition of anisotropic pressures and electric charge to the density profile. Of these new solutions three are found to obey all the necessary conditions of physical acceptability, including linear stability under radial perturbations, and causality of the speed of pressure waves inside the object. Additionally an equation of…
We investigate the production of gravitational waves during the inspiral of compact binaries close to their merger in the context of a conformal gravity model. The model incorporates five massive polarization degrees of freedom, besides the two massless gravitational wave polarizations of general relativity. For small graviton mass, we find that the amplitude of the gravitational waves is strongly suppressed as compared to general relativity and decreases as coalescence is approached, which contradicts the observational fact. We conclude that this model with small graviton mass, including a re…
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations are then obtained in covariant form for the anisotropic case. These equations are used to obtain new exact solutions using direct resolution and reconstruction techniques. Finally, we show that three of the generating theorems known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.
Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future detection by gravitational wave observatories. In this article we review numerical relativity approaches to modeling compact binaries. Starting with a brief introduction to the 3+1 decomposition of Einstein's equations, we discuss important components of numerical relativity, including the initial data problem, reformulations of Einstein's equations, coordinate …
Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we have applied the recently developed Extended General Relativistic theory to calculate the lower limit for the size of some relevant galaxies: the Milky Way, Andromeda and M87. Our results are in very good agreement with observations.
We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial parameters by comparing the inspiral with post-Newtonian calculations. Our method is the first to be applied directly to the gravitational-wave (GW) signal, rather than the orbital motion. The GW signal is in general less contaminated by gauge effects, which, in moving-puncture simulations, limit orbital-motion-based measurements of the eccentricity to an uncertai…
We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum tensor for the objects and derive equations of motion from it. As a result, we reproduce the Papapetrou equations for a spinning particle. Furthermore, we will show that we can obtain more simple equations than the Papapetrou equations by changing the center-of-mass.
We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state $ P=-ρ/5$. These geometries depend on up to four parameters and are static and spherically symmetric. They describe compact spaces with naked central singularities.
We describe a general framework for analyzing orbits of systems containing compact objects (neutron stars or black holes) in a class of Lagrangian-based alternative theories of gravity that also admit a global preferred reference frame. The framework is based on a modified Einstein-Infeld-Hoffmann (EIH) formalism developed by Eardley and by Will, generalized to include the possibility of Lorentz-violating, preferred-frame effects. It uses a post-Newtonian $N$-body Lagrangian with arbitrary parameters that depend on the theory of gravity and on "sensitivities" that encode the effects of the bod…
General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO and eLISA will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present progress in the calculation of second post-Newtonian (2PN) gravitational waveforms for inspiraling compact binaries in a general class of scalar-tensor theories. The waveforms are constructed using a stand…
In this paper we elaborate on earlier work by the same authors in which a novel Bayesian inference framework for testing the strong-field dynamics of General Relativity using coalescing compact binaries was proposed. Unlike methods that were used previously, our technique addresses the question whether one or more 'testing coefficients' (e.g. in the phase) parameterizing deviations from GR are non-zero, rather than all of them differing from zero at the same time. The framework is well-adapted to a scenario where most sources have low signal-to-noise ratio, and information from multiple source…
The weight of light: colliding pulses of radiation in General Relativity
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等理工学院物理系CENTRA）；Center of Gravity, Niels Bohr Institute（尼尔斯·玻尔研究所引力中心）
The last years have brought upon us a golden age of observational gravitational physics. The several observations by the LIGO/Virgo/KAGRA collaboration about gravitational waves and by the EHT collaboration about the shadow and lensing of light around the supermassive black hole in the centre of M87 will point the scientific community in the correct direction to find an answer to the Kerr hypothesis. In order to follow that direction, the systematic construction and analysis of the physical properties of solutions within General Relativity with additional fields or within modified theories of …
Activities in data analysis and numerical simulation of gravitational waves have to date largely proceeded independently. In this work we study how waveforms obtained from numerical simulations could be effectively used within the data analysis effort to search for gravitational waves from black hole binaries. We propose measures to quantify the accuracy of numerical waveforms for the purpose of data analysis and study how sensitive the analysis is to errors in the waveforms. We estimate that ~100 templates (and ~10 simulations with different mass ratios) are needed to detect waves from non-sp…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes theory towards a specific objective: understanding how the combination of extended black objects and ultra-spinning rotation dynamics give rise to black hole topologies that depart from sphericity. The discussion aims to offer a compromise between giving a reasonably wide picture of the area of higher dimensional black holes, while at the same time going into de…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)\approx 0.35$ while r…
We propose a new approach toward reconstructing the late-time near-horizon geometry of merging binary black holes, and toward computing gravitational-wave echoes from exotic compact objects. A binary black-hole merger spacetime can be divided by a time-like hypersurface into a Black-Hole Perturbation (BHP) region, in which the space-time geometry can be approximated by homogeneous linear perturbations of the final Kerr black hole, and a nonlinear region. At late times, the boundary between the two regions is an infalling shell. The BHP region contains late-time gravitational-waves emitted towa…
I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the pre-merger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compa…
Geometrical inequalities show how certain parameters of a physical system set restrictions on other parameters. For instance, a black hole of given mass can not rotate too fast, or an ordinary object of given size can not have too much electric charge. In this article we are interested in bounds on the angular momentum and electromagnetic charges, in terms of total mass and size. We are mainly concerned with inequalities for black holes and ordinary objects. The former are the most studied systems in this context in General Relativity, and where most results have been found. Ordinary objects, …
We present a Bayesian data analysis pipeline for testing GR using gravitational wave signals from coalescing compact binaries, and in particular binary neutron stars. In this study, we investigate its performance when sources with spins are taken into account.
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of the dynamical variables into i) a fixed conformal 3-geometry, ii) a conformal factor possessing nonlinear dynamics and iii) transverse-traceless perturbations of the conformal 3-geometry.
Using a lattice equation of state combined with the D-dimensional Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a $2+1$ dimensional spacetime, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a $3+1$ dimensional spacetime, self-gravity lead…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued tha…
In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$ gravitationally interacting isolated bodies. Equations of motions of such a system are derived. Definitions of momentum, angular momentum, center of mass, force and torque are made in a relativistic theory. Dynamical (gravitational) skeleton is defined and the multipole moments of the dynamical skeleton are found. Equations of motion for a test body moving in a gravitat…
We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner-Nordström field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges $q$ and $Q$, respectively, the conditions of attraction (when $qQ>0$) and repulsion (when $qQ<0$) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, s…
We review the current status of attempts to numerically model the merger of neutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binary systems, and we describe the understanding of such events that is emerging from these calculations. To accurately model the physics of NSNS and BHNS mergers is a difficult task. It requires solving Einstein's equations for dynamic spacetimes containing black holes. It also requires evolving the hot, supernuclear-density neutron star matter together with the magnetic and radiation fields that can influence the post-merger dynamics. Older studies …
