Simulating Binary Neutron Stars with Hybrid Equation of States: Gravitational Waves, Electromagnetic Signatures, and Challenges for Numerical Relativity
The gravitational wave and electromagnetic signatures connected to the merger of two neutron stars allow us to test the nature of matter at supranuclear densities. Since the Equation of State governing the interior of neutron stars is only loosely constrained, there is even the possibility that strange quark matter exists inside the core of neutron stars. We investigate how strange quark matter cores affect the binary neutron star coalescence by performing numerical relativity simulations. Interestingly, the strong phase transition can cause a reduction of the convergence order of the numerical schemes to first order if the numerical resolution is not high enough. Therefore, an additional challenge is added in producing high-quality gravitational wave templates for Equation of States with a strong phase transition. Focusing on one particular configuration of an equal mass configuration consistent with GW170817, we compute and discuss the associated gravitational wave signal and some of the electromagnetic counterparts connected to the merger of the two stars. We find that existing waveform approximants employed for the analysis of GW170817 allow describing this kind of systems within the numerical uncertainties, which, however, are several times larger than for pure hadronic Equation of States, which means that even higher resolutions have been employed for an accurate gravitational wave model comparison. We also show that for the chosen Equation of State, quasi-universal relations describing the gravitational wave emission after the moment of merger seem to hold and that the electromagnetic signatures connected to our chosen setup would not be bright enough to explain the kilonova associated to GW170817.
We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\geq 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and th…
A new exact solution of the Einstein-Maxwell equations for the gravitational collapse of a shell of matter in an already formed black hole is given. Both the shell and the black hole are endowed with electromagnetic structure and are assumed spherically symmetric. Implications for current research are outlined.
An algorithm is presented that incorporates the tensor form of Maxwell's equations in a general relativistic electromagnetic particle-in-cell code. The code simplifies to Schwartzschild space-time for a non-spinning central mass. The particle advance routine uses a fourth-order Runge-Kutta algorithm to integrate the four-velocity form of Lorentz force. The current density is calculated using the curved space-time of the metric.
We extend the Non-Relativistic formulation of General Relativity (NRGR) given in Goldberger et al. (Phys Rev D 73:104029, 2006) to incorporate the effects of electromagnetic charge of the constituents of the binary. We incorporate the photon field in NRGR by giving the field decomposition and power counting rules. Using these, we develop the Feynman rules to describe photon and graviton interactions with point particle worldline. We then find the corrections to the Einstein-Infeld-Hoffmann Lagrangian (Einstein et al. in Ann Math 39:65-100, 1938) due to the presence of the photon field and elec…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spa…
Recently there have been suggestions that the Lorentz force law is inconsistent with special relativity. This is difficult to understand, since Einstein invented relativity in order to reconcile electrodynamics with mechanics. Here we investigate the momentum of an electric charge and a magnetic dipole in the frame in which both are at rest, and in an infinitesimally boosted frame in which both have a common velocity. We show that for a dipole composed of a magnetic monopole-antimonopole pair the torque is zero in both frames, while if the dipole is a point dipole, the torque is not zero, but …
"Electromagnetic mass" where gravitational mass and other physical quantities originate from the electromagnetic field alone has a century long distinguished history. In the introductory chapter we have divided this history into three broad categories -- classical, quantum mechanical and general relativistic. Each of the categories has been described at a length to get the detailed picture of the physical background. Recent developments on Repulsive Electromagnetic Mass Models are of special interest in this introductory part of the thesis. In this context we have also stated motivation of our…
In this Letter, we investigate the group delay of optical pulses through multilayer dielectric mirrors (MDM) combined with gravitational wave (GW). We find that the delay increases linearly with MDM length for the transmitted wave packet, whereas the Hartman effect disappears. Our study provides insight into the nature of both quantum tunnelling and GW.
Direct observations of compact objects, in the form of radiation spectra, gravitational waves from VIRGO/LIGO, and forthcoming direct imaging, are currently one of the primary source of information on the physics of plasmas in extreme astrophysical environments. The modeling of such physical phenomena requires numerical methods that allow for the simulation of microscopic plasma dynamics in presence of both strong gravity and electromagnetic fields. In Bacchini et al. (2018) we presented a detailed study on numerical techniques for the integration of free geodesic motion. Here we extend the st…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature metrics. Field equations imply that at least one of the surfaces must be of constant curvature leading to the symmetry of the metric (``spontaneous symmetry emergence''). We classify all global solutions in the case when the Lorentzian surface is of constant curvature. These solutions are invariant with respect to the Lorentz SO(1,2) or Poincare IO(1,1) groups…
General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part of this thesis, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in general relativity in terms of their masses and spins and which states that these compact objects are described by the Kerr metric. I invest…
We consider arbitrary stationary and axisymmetric black holes in general relativity in $(d +1)$ dimensions (with $d \geq 3$) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically deSitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes pr…
We build extended sources for the Reissner-Nordström metric. Our models describe a neutral perfect fluid core bounded by a charged thin shell, and feature everywhere positive rest mass density and everywhere non-negative active gravitational mass, as well as classical electron radius and electromagnetic total mass. We contrast our results with previously discussed models featuring similar properties at the expense of including anisotropic pressures within the fluid. Our charged thin shells are restricted by the 2D texture equation of state which causes the continuity of the active gravitationa…
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero. The principal difference between droplet-like solutions with spherical symmetry and those with cylindrical one has been established. In the first case there exists a possibility of…
The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime met…
In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here we show that general relativity lends the theoretical tools for designing devices made of such versatile materials. Given a desired device function, the theory describes the electromagnetic properties that turn this function into fact. We consider media that facilitate space-time transformations and include negative refraction. Our theory unifies the concepts operating behind the scenes of perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect a…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different features of the fields, such as the derivation of electromagnetic sources for the Maxwell field in the form of thin layers, construction of new solutions, and generation techniques.
Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar …
The problem of constructing a model of an extended charged particle within the context of general relativity has a long and distinguished history. The distinctive feature of these models is that, in some way or another, they require the presence of negative mass in order to maintain stability against Coulomb's repulsion. Typically, the particle contains a core of $negative$ mass surrounded by a positive-mass outer layer, which emerges from the Reissner-Nordström field. In this work we show how the Einstein-Maxwell field equations can be used to construct an extended model where the mass is pos…
In a static spherically symmetric Einstein-Maxwell spacetime the class of astrophysical solution found out by Ray and Das (2002) and Pant and Sah (1979) are revisited here in connection to the phenomenological relationship between the gravitational and electromagnetic fields. It is qualitatively shown that the charged relativistic stars of Tolman (1939) and Bayin (1978) type are of purely electromagnetic origin. The existence of this type of astrophysical solutions is a probable extension of Lorentz's conjecture that electron-like extended charged particle possesses only `electromagnetic mass'…
The \textit{axial} electromagnetic (EM) perturbations of the black hole (BH) solutions in general relativity coupled to nonlinear electrodynamics (NED) were studied for both electrically and magnetically charged BHs, assuming that the EM perturbations do not alter the spacetime geometry in our preceding paper [Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, the formalism for the \textit{polar} EM perturbations of the BHs in general relativity coupled to the NED is presented. We show that the quasinormal modes (QNMs) spectra of polar EM perturbations of the electrically a…
Following the general formalism presented by Rezzolla, Ahmedov and Miller (MNRAS, 322, 723 2001), we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gr…
We demonstrate the flexibility and utility of the Berger-Rigoutsos Adaptive Mesh Refinement (AMR) algorithm used in the open-source numerical relativity code GRChombo for generating gravitational waveforms from binary black-hole inspirals, and for studying other problems involving non-trivial matter configurations. We show that GRChombo can produce high quality binary black-hole waveforms through a code comparison with the established numerical relativity code Lean. We also discuss some of the technical challenges involved in making use of full AMR (as opposed to, e.g. moving box mesh refineme…
The simplest electromagnetic fields' (general- as well as special-relativistic) classification is formulated which is based on physically motivated ideas. According to this classification these fields can belong to three types (electric, magnetic and null), each of them being split in pure and impure subtypes. Only pure null type field propagates with the fundamental velocity $c$, all other fields have the propagation velocity less than that of light. The reference-frame-based methods of elimination of alternative three-fields (e.g., magnetic in the electric type case) are given for pure subty…
One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash between the spatial nonseparability of entangled states in QM, and the complete spatial separability of all physical systems in GR, i.e., between the nonlocality implied by the superposition principle, and the locality implied by the equivalence principle. Experimental consequences of this conceptual tension will be explored for macroscopically coherent quantum fluids, such as superconductors, superfluids, and atomic Bose-Einstein condensates (BECs), subjected to tidal and Lense-Thir…
In addition to the emission of gravitational waves (GWs) the coalescence and merger of two neutron stars will produce a variety of electromagnetic (EM) signals. In this work we combine a large set of numerical relativity simulations performed by different groups and we present fits for the mass, kinetic energy, and the velocities of the dynamical ejected material. Additionally, we comment on the geometry and composition of the ejecta and discuss the influence of the stars' individual rotation. The derived fits can be used to approximate the luminosity and lightcurve of the kilonovae (macronova…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein's equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spac…
We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura formalism is extended for arbitrary spacetime dimensions $D \ge 4$, and then, the so-called cartoon method, which was originally proposed as a robust method for simulating axisymmetric 4D spacetimes, is described for 5D spacetimes of several types of symmetries. Implementing 5D numerical relativity codes with the cartoon methods, we perform test simulations …
The equilibrium conditions for charges and currents, apparent in exact solutions of the field equations, lead one to regard the Hermitian theory of relativity as the theory of a field endowed with two sources: electromagnetic and colour four-currents.
General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can prob…
Electromagnetic observations have been used over the past decades to understand the nature of black holes and the material around them. Our ability to learn about the fundamental physics relies on our understanding of two key ingredients in the modeling of these electromagnetic observations: the gravity theory that describes the black hole, and the astrophysics that produces the observed radiation. In this work we study our current ability to constrain and detect deviations from General Relativity using the accretion disk spectrum of stellar-mass black holes in binary systems. Our analysis com…
The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in $(3+1)$-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We …
The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in General Relativity has remained obscure and no interpretation has achieved wide acceptance. In principle, they cannot represent {\em energy} and the term {\em superenergy} has be…
The third observing run of the LIGO-Virgo collaboration has resulted in about hundred gravitational-wave triggers including the binary neutron star merger GW190425. However, none of these events have been accompanied with an electromagnetic transient found during extensive follow-up searches. In this article, we perform new numerical-relativity simulations of binary neutron star and black hole - neutron star systems that have a chirp mass consistent with GW190425. Assuming that the GW190425's sky location was covered with sufficient accuracy during the electromagnetic follow-up searches, we in…
In general relativity without a cosmological constant, a classical theorem due to Hawking states that stationary black holes must be topologically spherical. This result is one of the several ingredients that collectively imply the uniqueness of the Kerr metric. If, however, general relativity describes gravity inexactly at high energies or over cosmological scales, Hawking's result may not apply, and black holes with non-trivial topology may be, at least mathematically, permissible. While tests involving electromagnetic and gravitational-wave data have been used to place tight constraints on …
On the basis of all commutation relations of the k-deformed phase space incorporating the k-Minkowski space-time, we have derived in this paper an extended first approximation of both Maxwell's equations and Lorentz force in doubly (or deformed) special relativity (DSR). For this purpose, we have used our approach of the special relativistic version of Feynman's proof by which we have established the explicit formulations of electric and magnetic fields. As in Fock's nonlinear relativity (FNLR), the laws of electrodynamics depend on the particle mass which therefore constitutes a common point …
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…
We present fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $λ\le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions…
An electromagnetic analog of the Kerr-Newman solution in general relativity is derived, based on Minkowski's formulation for electromagnetic fields in moving media. The equivalent system is a distribution of charges and currents largely localized within a spinning disk of radius a. This occurs in a rotating medium of inhomogeneous index of refraction and "frame dragging" at exactly half the angular velocity of the electrical charge.
Electromagnetic mass models are proved to exist in higher dimensional theory of general relativity corresponding to charged dust distribution. Along with the general proof a specific example is also sited as a supporting candidate.
The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another could provide an important observational signature to test this scenario. We develop and implement an algorithm for accurately computing the cosmological observables arising from bubble collisions directly from the Lagrangian of a single scalar field. We first simulate the collision spacetime by solving Einstein's equations, starting from nucleation and endin…
Relativity theory is useful for understanding the phenomenology of the magnetoelectric effect of the antiferromagnet chromium sesquioxide Cr_2 O_3 in two respects: (i) One gets a clear idea about the physical dimensions of the electromagnetic quantities involved, in particular about the dimensions of the magnetoelectric moduli that we suggest to tabulate in future as dimensionless relative quantities; (ii) one can recognize and extract a temperature dependent, 4-dimensional pseudoscalar from the data of magnetoelectric experiments with Cr_2 O_3. This pseudoscalar piece of Cr_2 O_3 is odd under…
We consider static, spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{μν} F^{μν}$. After a brief review on black hole (BH) and solitonic solutions, obtained so far with pure electric or magnetic fields, an attempt is made to obtain dyonic solutions, those with both electric and magnetic charges. A general scheme is suggested, leading to solutions in quadratures for an arbitrary Lagrangian function $L(f)$ (up to some monotonicity restrictions); such solutions are ex…
A method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly non-linear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field.
With the discovery of the black hole binary (BBH) coalescence GW150914 the era of gravitational-wave (GW) astronomy has started. It has recently been shown that BBH with masses comparable to or higher than GW150914 would be visible in the eLISA band a few years before they finally merge in the band of ground-based detectors. This would allow for pre-merger electromagnetic alerts, dramatically increasing the chances of a joint detection, if BBH are indeed luminous in the electromagnetic band. In this paper we explore a quite different aspect of multi-band GW astronomy, and verify if, and to wha…
We show that in the realm of general relativity a non minimal coupling between the electromagnetic and the gravitational fields may produce an era of accelerated expansion.
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a permanent displacement of test masses in a laser interferometer gravitational wave detector. Christodoulou derived a precise formula for this permanent displacement in the Einstein vacuum (EV) case. We prove in Theorem 6 that for the EM equations this permanent displacement exhibits a…
A particle in the vicinity of a Schwarzschild black hole is known to trace a geodesic of the Schwarzschild background, to a first approximation. If the interaction of the particle with its own field (scalar, electromagnetic or gravitational) is taken into account, the path is no longer a background geodesic and the self-force that the particle experiences needs to be taken into consideration. In this dissertation, a recently proposed method for the calculation of the self-force is implemented. According to this method the self-force comes from the interaction of the particle with the Regular-R…
While quantum field theory could more aptly be called the "quantum field framework" $-$ as it encompasses a vast variety of varying concepts and theories $-$ in comparison, relativity, both special and general, is more commonly portrayed as less of a "general framework". Viewed from this perspective, the paradigm of "analogue space-times" is to promote the specific theory of general relativity (Einstein gravity) to a framework which covers relativistic phenomena at large. Ultimately, this then also gives rise to new proposals for experiments in the laboratory, as it allows one to move general …
In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, to produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.
Effective-one-body (EOB) numerical-relativity (NR) waveform models for spin-aligned binary black holes (BBHs), known as the SEOBNR waveform models, are based on the EOB theoretical framework and NR simulations. SEOBNR models have played an important role in the LIGO scientific collaboration (LSC) gravitational wave (GW) data analysis for both signal search and parameter estimation. SEOBNR models for quasi-circular orbits have evolved through version 1 to version 4 by extending their validity domain and including more NR results. Along another direction, we recently extended SEOBNRv1 model to S…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general relativity. An incident photon in the presence of a very long wavelength gravitational wave will have a finite probability of being returned as a final photon with a frequency shift whose magnitude is equal to the gravitational wave frequency. The effect is due to the non-linear coupling between electromagnetic and gravitational waves. The frequency modulati…
We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the impact of black hole spin on the dynamical formation and evolution of minidisks. We find that during the late inspiral the sizes of minidisks are primarily determined by the interplay between the tidal field and the effective innermost stable orbit around each black hole. Our calculations support that a minidisk forms when the Hill sphere around each black hole is significantly larger than the black hole's effective innermost stable orbit. As the binary inspirals, t…
The energy--momentum tensor in general relativity contains only localized contributions to the total energy--momentum. Here, we consider a static, spherically symmetric object consisting of a charged perfect fluid. For this object, the total gravitational mass contains a non--localizable contribution of electric coupling (ordinarily associated with electromagnetic mass). We derive an explicit expression for the total mass which implies that the non--localizable contribution of electric coupling is not bound together by gravity, thus ruling out existence of the objects with pure Lorentz electro…
Superradiant scattering processes are studied in general relativistic systems which, unlike rotating and/or charged black holes, do not exhibit an event horizon. Inspired by Zel'dovich's seminal works on the amplification of waves by a rotating cylinder, we analyse, in the context of General Relativity, the possibility of superradiance for electromagnetic waves reflecting off a rotating star and for charged scalar perturbations impinging on a charged sphere. The role of energy dissipation in these systems is analysed and compared with the role of the event horizon in black hole superradiance.
The gravitational analog of the electromagnetic Poynting vector is constructed using the field equations of general relativity in the Hilbert gauge. It is found that when the gravitational Poynting vector is applied to the solution of the linear mass quadrupole oscillator, the correct gravitational quadrupole radiation flux is obtained. Further to this, the Maxwell-like gravitational Poynting vector gives rise to Einstein's quadrupole radiation formula. The gravitational energy-momentum (pseudo) tensor obtained is symmetric and traceless. The former property allows the definition of angular mo…
