The aim of this paper is to study the extra phase shift that general relativity (GR) predicts for a radial light ray propagating in the vicinity of a static spherical symmetric body. It appears that the gravitational phase shift test yields a better sensitivity than the gravitational frequency shift or the excess time delay of the photons. An experiment is proposed for this new test of GR pertaining exclusively to the wave aspect of light.
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach, shows that for gravitational waves interacting with irrotational dust, the equations are linearization unstable. The gravitational wave equations based on the Weyl curvature tensor must be solved by non-perturbative methods. The significance of this result for gravitational wave calculations and experiments is discussed.
Applying the Vaidya metrics in the model of Expansive Nondecelerative Universe (ENU) leads to compatibility of the ENU model both with the classic Newton gravitational theory and the general theory of relativity in weak fields
The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the expanding universe, predicts something different for the propagation of gravity waves on cosmological distance scales. This analysis indicates that gravitational radiation may not propagate as an unattenuated wave where effects of the Hubble expansion are felt. In such cases the energy does not travel over such large length scales but is evanescent and dissipat…
The gravitation field of the flat plate was investigated. It have been shown that there exist the internal solution of Einstein equations sewed together with external one, which described a ''homogeneous'' gravitational field.
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…
The prime candidate of LIGO/VIRGO sources of gravitational waves is the spiral in of black holes and neutron stars in compact binaries. While the early stages of the evolution of compact binaries is computable from post-Newtonian calculations, prediction of their late stages requires large scale numerical simulation. A fully covariant and strictly hyperbolic formulation for numerical relativity is described, and illustrated in a one-dimensional computation of a Gowdy-wave on the three-torus. This formulation allows foliations in full generality, in particular it poses no restriction on the lap…
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal, the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.
We derive two new retarded solutions in the teleparallel theory equivalent to general relativity (TEGR). One of these solutions gives a divergent energy. Therefore, we used the regularized expression of the gravitational energy-momentum tensor, which is a coordinate dependent. A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.
We present a simplified expression for the gravitational angular momentum in the framework of the teleparallel equivalent of general relativity (TEGR). The expression arises from the constraints equations of the Hamiltonian formulation of the TEGR. We apply this expression to the calculation of the angular momentum of plane-fronted gravitational waves in an arbitrary three-dimensional volume $V$ of space and compare the results with those obtained for linearised gravitational waves.
A corollary of general relativity that the average velocity of light between two points in a gravitational field is anisotropic has been overlooked. It is shown that this anisotropy can be probed by an experiment which constitutes another test of general relativity.
We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the evolution of time-symmetric, axisymmetric {\it and} non-axisymmetric Brill waves, including waves so strong that they collapse to form black holes under their own self-gravity. The critical amplitude for black hole formation is determined. The gravitational waves emitted in the black hole formation process are compared to those emitted in the head-on collisio…
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
We show the first simple, systematic and direct approach to decoupling gravitational sources in general relativity. As a direct application, a robust and simple way to generate anisotropic solutions for self-gravitating systems from perfect fluid solutions is presented.
Gravitational collapse of a class of spherically symmetric stars are investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with gravitational collapse.
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational gauge symmetry. The gravitational gauge group is studied in the paper. Then gravitational gauge interactions of pure gravitational gauge field is studied. It is found that the field equation of gravitational gauge field is just the Einstein's field equation. After that, the gravitational interactions of scalar field, Dirac field and vector fields are studied, …
The foundations of Einstein's first (1907) principle of equivalence are explored and their consequences are stated in terms of invariance under generalized Lorentz transformations, first explored by Hessenberg.
Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave signals from likely sources are crucial for the success of this endeavor. Modeling binary black hole sources of gravitational radiation requires solving the Eintein equations of General Relativity using powerful computer hardware and sophisticated numerical algorithms. This proceeding presents where we are in understanding ground-based gravitational …
We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass. Particular attention is paid to the construction of the underlying reference frame. Conceptual differences between the clock compass and the standard gravitational compass, which is based on the measurement of the mutual accelerations between the constituents of a swarm of test bodies, are highlighted. Our results are of direct operational relevance for the setup…
The gravitational radiation degrees of freedom of freedom are described in the framework of the 3+1 decomposition of spacetime. The relationship with eigenfields of the Kidder-Scheel-Teukolsky (KST) equations is established. This relationship is used to fix a parameter in the KST equations which is related to the ordering ambiguity of space derivatives in the Ricci tensor, which is inherent to first order evolution systems, like the ones currently used in Numerical Relativity applications.
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like those of black holes are discussed. Their properties are investigated by studying the geodesic structure of the corresponding space-times, as representing the motion of point-like test particles. The interaction between gravitational, electro-magnetic and scalar fields is also considered.
We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.
The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behaviors of more general solutions. Newtonian gravity contains only one dimensional constant, the gravitational constant, while the general relativity contains another dimensional constant, the speed of light,…
How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for…
The next generation of gravitational-wave detectors, conceived to begin operations in the 2030s, will probe fundamental physics with exquisite sensitivity. These observations will measure the equation of state of dense nuclear matter in the most extreme environments in the universe, reveal with exquisite fidelity the nonlinear dynamics of warped spacetime, put general relativity to the strictest test, and perhaps use black holes as cosmic particle detectors. Achieving each of these goals will require a new generation of numerical relativity simulations that will run at scale on the supercomput…
Gravitational-wave data analysis requires a detailed understanding of the highly relativistic, late stages of inspiral of neutron-star and black-hole binaries. A promising method to compute the late inspiral and its emitted waves is numerical relativity in co-rotating coordinates. The coordinates must be kept co-rotating via an appropriate choice of numerical relativity's lapse and shift functions. This article proposes a model problem for testing the ability of various lapse and shift prescriptions to keep the coordinates co-rotating.
We propose an approximation to general relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be implemented in existing multidimensional Newtonian gravitational hydrodynamics codes employing a Poisson solver. As a test of the formalism's utility, we display results for rapidly rotating (and therefore highly deformed) neutron stars.
We show how to decoupling two spherically symmetric and static gravitational sources through the most general possible extension of the so-called Minimal Geometric Deformation-decoupling. As a test, we decouple the Einstein-Maxwell system and reproduce the Reissner-Nordstrom black hole solution. We show the potential of this method to study i) the consequences of modified gravity on general relativity, ii) to investigate the conjectured dark matter, and iii) to study hairy black holes.
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.
It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field. The TEGR amounts to an alternative formulation of Einstein's general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of space-times with distinct topologies, and the outcome of these analises agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the s…
We show how the model of pseudo-complex general relativity can be tested using gravitational wave signals from coalescing compact objects. The model, which agrees with Einstein gravity in the weak-field limit, diverges dramatically in the near-horizon regime, with certain parameter ranges excluding the existence of black holes. We show that simple limits can be placed on the model in both the inspiral and ringdown phase of coalescing compact objects. We discuss further how these bounds relate to current observational limits. In particular, for minimal scenarios previously considered in the lit…
Any modification on gravity would affect not only gravitational wave (GW) generation but also GW propagation. Therefore, tests of general relativity (GR) with only GW generation or GW propagation will lead to an overestimate for deviations. Here we try to use one set of parameters to parameterize the modifications on both GW generation and GW propagation and then test GR with GW150914. In our simplest case, we find that graviton mass $μ<6.3\times10^{-23}{\rm eV/c^2}$ at $90\%$ C.L. and there are no deviations from GR at $90\%$ C.L..
A dynamical, non-Euclidean spacetime geometry in general relativity theory implies the possibility of gravitational radiation. Here we explore novel methods of detecting such radiation from astrophysical sources by means of matter-wave interferometers (MIGOs), using atomic beams emanating from supersonic atomic sources that are further cooled and collimated by means of optical molasses. While the sensitivities of such MIGOs compare favorably with LIGO and LISA, the sizes of MIGOs can be orders of magnitude smaller, and their bandwidths wider. Using a pedagogical approach, we place this problem…
In an extended, new form of general relativity, which is a teleparallel theory of gravity, we examine the energy-momentum and angular momentum carried by gravitational wave radiated from Newtonian point masses in a weak-field approximation. The resulting wave form is identical to the corresponding wave form in general relativity, which is consistent with previous results in teleparallel theory. The expression for the dynamical energy-momentum density is identical to that for the canonical energy-momentum density in general relativity up to leading order terms on the boundary of a large sphere …
For slowly spinning matter the rate of energy loss via radiation of gravitational waves is estimated in General Relativity (GR) within a generally covariant superenergy approach. This estimation differs from Einstein's Quadrupole Formula (EQF) by a suppression factor ($Π\ll1$). For a symmetric two-body-like distribution of scalar matter $Π$ is estimated to be $\ll(v/c)^2(r/R)^2$, where $v$ is orbital velocity of the bodies, $c$ - velocity of light, $r$ - radius of each body, and $R$ -- the inter-body distance. This contradiction with EQF is briefly discussed.
Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant $π$. Allowing $π$ to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of $π=3.115^{+0.048}_{-0.088}$, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable $π$ test robust against simulated beyond-GR effects.
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium …
Models of gravitational waveforms from coalescing black-hole binaries play a crucial role in the efforts to detect and interpret the signatures of those binaries in the data of large-scale interferometers. Here we summarize recent models that combine information both from analytical approximations and numerical relativity. We briefly lay out and compare the strategies employed to build such complete models and we recapitulate the errors associated with various aspects of the modelling process.
We discuss the potential of the advanced ground-based gravitational-wave detectors such as LIGO, Virgo, and KAGRA to detect generic deviations of gravitational waveforms from the predictions of general relativity. We use the parameterized post-Einsteinian formalism to characterize the deviations, and assess what magnitude of deviations are detectable by using an approximate decision scheme based on Bayesian statistics. We find that there exist detectable regions of the parameterized post-Einsteinian parameters for different binary masses from the observation of a single gravitational wave even…
Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this essay we show that, if advanced projects on the detection of Gravitational Waves (GWs) will improve their sensitivity, allowing to perform a GWs astronomy, accurate angular and frequency dependent response functions of interferometers for GWs arising from various Theories of Gravity, i.e. General Relativity and Extended Theories of Gravity, will be the definitive …
Quasi-normal modes (QNMs) uniquely characterize the final black-hole. Till now, only the QNM frequency and damping time are used to test General relativity. In this work, we show explicitly that another property of the QNMs --- their polarization --- can be a reliable tool for probing gravity. We provide a consistent test for General relativity by considering Chern-Simons gravity. Distinguishing Chern-Simons gravity from General relativity using only template matching is highly challenging. Thus a parameter that can differentiate between Chern-Simons gravity and GR will be a suitable candidate…
We provide a covariant derivation of plasma physics coupled to gravitation by utilizing the 3+1 formulation of general relativity, including a discussion of the Lorentz force law. We then reduce the system to the spherically symmetric case and show that all regions of the spacetime can be represented in a single coordinate system, thus revoking the need for junction conditions. We further show that the region exterior to the collapsing region is naturally described by the charged Vaidya spacetime in non-null coordinates.
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurat…
Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this proceeding paper it is shown that, if advanced projects on the detection of Gravitational Waves (GWs) will improve their sensitivity, allowing to perform a GWs astronomy, accurate angular and frequency dependent response functions of interferometers for GWs arising from various Theories of Gravity, i.e. General Relativity and Extended Theories of Gravity, will be …
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…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-i…
The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, using the so called adiabatically-amplified zero-point fluctuations process it has been shown how the standard inflationary scenario for the early universe can in principle provide a distinctive spectrum of relic gravitational waves. In this paper, it is shown that a weak modification of General Relativity produces a third massive polarization of gravitational waves and the primordial production of this polarization is analysed adapting the adiabatically-amplified zer…
We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ~0.01mHz - 1Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from bi…
We consider the so-called semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized, for the simplest composite quantum body - a hydrogen atom. We create a stationary electron quantum state in the atom in the absence of gravitational field and study its time evolution in the presence of the field, using the local Lorentz invariance property of spacetime. It is shown that this state with a definite energy in the absence of gravitational field is not anymore a stationary state in the field. Therefore, quantum measurements of passive gravitati…
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible …
This paper examines the historical controversy over whether gravitationally bound systems, such as binary stars, experienced orbital damping due to the emission of gravitational radiation, focusing especially on the period of the 1950s, but also discussing the work of Einstein and Rosen in the 1930s on cylindrical gravitational waves and the later quadrupole formula controversy.
In this article we elaborate on a recently proposed interpretation of DSR as an effective measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations. We provide several heuristic arguments to explain how such a new theory can emerge and discuss the possible observational consequences of this framework.
This document proposes data formats to exchange numerical relativity results, in particular gravitational waveforms. The primary goal is to further the interaction between gravitational-wave source modeling groups and the gravitational-wave data-analysis community. We present a simple and extendable format which is applicable to various kinds of gravitational wave sources including binaries of compact objects and systems undergoing gravitational collapse, but is nevertheless sufficiently general to be useful for other purposes.
The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the PITT code within the Einstein Toolkit. Using the new strain formula, we show that artificial non-linear drifts inherent in time integrated waveforms can be reduced for the case of a binary black hole merger configuration. For the test case of a rapidly spinning stellar core collapse model, however, we find that the drift must have different roots.
In the Tetrad Representation of General Relativity, the energy-momentum expression, found by Moller in 1961, is a tensor wrt coordinate transformations but is not a tensor wrt local Lorentz frame rotations. This local Lorentz freedom is shown to be the same as the six parameter normalized spinor degrees of freedom in the Quadratic Spinor Representation of General Relativity. From the viewpoint of a gravitational field theory in flat space-time, these extra spinor degrees of freedom allow us to obtain a local energy-momentum density which is a true tensor over both coordinate and local Lorentz …
