Gravitational radiation reaction affects the dynamics of gravitationally bound binary systems. Here we focus on the leading "tail" term which modifies binary dynamics at fourth post-Newtonian order, as first computed by Blanchet and Damour. We re-produce this result using effective field theory techniques in the framework of the Lagrangian formalism suitably extended to include dissipation effects. We recover the known logarithmic tail term, consistently with the recent interpretation of the logarithmic tail term in the mass parameter as a renormalization group effect of the Bondi mass of the system.
We argue that the well-known problem of the instabilities associated with the self-forces (radiation reaction forces) in classical electrodynamics are possibly stabilized by the introduction of gravitational forces via general relativity.
Gravitational radiation is locally defined where the wavefronts are roughly spherical. A local energy tensor is defined for the gravitational radiation. Including this energy tensor as a source in the truncated Einstein equations describes gravitational radiation reaction, such as back-reaction on a roughly spherical black hole. The energy-momentum in a canonical frame is covariantly conserved. The strain to be measured by a distant detector is simply defined.
The gravitational radiation-reaction force acting on perfect fluids at 3.5 post-Newtonian order is cast into a form which is directly applicable to numerical simulations. Extensive use is made of metric-coefficient changes induced by functional coordinate transformations, of the continuity equation, as well as of the equations of motion. We also present an expression appropriate for numerical simulations of the radiation field causing the worked out reaction force.
We derive the gravitational radiation-reaction force modifying the Effective One Body (EOB) description of the conservative dynamics of binary systems. Our result is applicable to general orbits (elliptic or hyperbolic) and keeps terms of fractional second post-Newtonian order (but does not include tail effects). Our derivation of radiation-reaction is based on a new way of requiring energy and angular momentum balance. We give several applications of our results, notably the value of the (minimal) "Schott" contribution to the energy, the radial component of the radiation-reaction force, and t…
In this Comment we compute the contributions of the radiation reaction force in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact binaries in circular orbits. (i) We point out and correct an inconsistency in the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all contributions from radiation reaction in the 2.5PN waveform are actually negligible since they can be absorbed into a modification of the orbital phase at the 5PN order.
Geodesic motion of a point particle in Kerr geometry has three constants of motion, energy $E$, azimuthal angular momentum $L$, and Carter constant $Q$. Under the adiabatic approximation, radiation reaction effect is characterized by the time evolution of these constants. In this letter we show that the scheme to evaluate them can be dramatically simplified.
We overview the recently proposed mode-sum regularization prescription (MSRP) for the calculation of the local radiation-reaction forces, which are crucial for the orbital evolution of binaries. We then describe some new results which were obtained using MSRP, and discuss their importance for gravitational-wave astronomy.
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.
It is demonstrated that, in the adiabatic approximation, non-Equatorial circular orbits of particles in the Kerr metric (i.e. orbits of constant Boyer-Lindquist radius) remain circular under the influence of gravitational radiation reaction. A brief discussion is given of conditions for breakdown of adiabaticity and of whether slightly non-circular orbits are stable against the growth of eccentricity.
Here we present the results of applying the generalized Riemann zeta-function regularization method to the gravitational radiation reaction problem. We analyze in detail the headon collision of two nonspinning black holes with extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.
Gravitational radiation reaction forces and balance equations for energy and momenta are investigated to 3/2 post-Newtonian (1.5PN) order beyond the quadrupole approximation, corresponding to the 4PN order in the equations of motion of an isolated system. By matching a post-Newtonian solution for the gravitational field inside the system to a post-Minkowskian solution (obtained in a previous work) for the gravitational field exterior to the system, we determine the 1PN relativistic corrections to the ``Newtonian" radiation reaction potential of Burke and Thorne. The 1PN reaction potential invo…
We compute the variation of the Fokker-Wheeler-Feynman total linear and angular momentum of a gravitationally interacting binary system under the second post-Minkowskian retarded dynamics. The resulting $O(G^2)$ equations-of-motion-based, total change in the system's angular momentum is found to agree with existing computations that assumed balance with angular momentum fluxes in the radiation zone.
Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation-reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5PN order, we determine the spin…
We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge cond…
Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-or…
We study gravitational radiation reaction in the equations of motion for binary systems with spin-orbit coupling, at order (v/c)^7 beyond Newtonian gravity, or O(v/c)^2 beyond the leading radiation reaction effects for non-spinning bodies. We use expressions for the energy and angular momentum flux at infinity that include spin-orbit corrections, together with an assumption of energy and angular momentum balance, to derive equations of motion that are valid for general orbits and for a class of coordinate gauges. We show that the equations of motion are compatible with those derived earlier by…
We discuss the leading order correction to the equation of motion of a particle with spin on an arbitrary spacetime. A particle traveling in a curved spacetime is known to trace a geodesic of the background spacetime if the mass of the particle is negligibly small. For a spinning particle, it is known that there appears a term due to the coupling of the spin and the Riemann tensor of the background spacetime. Recently we have found the equation of motion of a non-spinning particle which includes the effect of gravitational radiation reaction. This paper is devoted to discussion of a consistent…
The effect of gravitational radiation reaction on circular orbits around a spinning (Kerr) black hole is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in the strength of gravity $M/r$ (where $M$ is the mass of the black hole, $r$ is the orbital radius, and $G=c=1$). The radiation reaction makes the orbit shrink but leaves it circular, and drives the orbital plane very slowly toward antialignment with the spin of the hole: $\tan (ι/2) = \tan (ι_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$, where $ι$ is the angle between the normal to the orbital plane an…
The effect of gravitational radiation reaction on orbits around a spinning black hole is analyzed. Such orbits possess three constants of motion: $ι$, $e$, and $a$, which correspond, in the Newtonian limit of the orbit being an ellipse, to the inclination angle of the orbital plane to the hole's equatorial plane, the eccentricity, and the semi-major axis length, respectively. First, it is argued that circular orbits ($e=0$) remain circular under gravitational radiation reaction. Second, for elliptical orbits (removing the restriction of $e=0$), the evolution of $ι$, $e$, and $a$ is computed to…
We give a short personally-biased review on the recent progress in our understanding of gravitational radiation reaction acting on a point particle orbiting a black hole. The main motivation of this study is to obtain sufficiently precise gravitational waveforms from inspiraling binary compact stars with a large mass ratio. For this purpose, various new concepts and techniques have been developed to compute the orbital evolution taking into account the gravitational self-force. Combining these ideas with a few supplementary new ideas, we try to outline a path to our goal here.
The radiation reaction fields are calculated for an accelerated changing dipole in scalar and electromagnetic radiation fields. The acceleration reaction is shown to alter the damping of a time varying dipole in the EM case, but not the scalar case. In the EM case, the dipole radiation reaction field can exert a force on an accelerated monopole charge associated with the accelerated dipole. The radiation reaction of an accelerated charge does not exert a torque on an accelerated magnetic dipole, but an accelerated dipole does exert a force on the charge. The technique used is that originally d…
Starting from the recently obtained 2PN accurate forms of the energy and angular momentum fluxes from inspiralling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation - 4.5PN terms in the equation of motion - using the refined balance method proposed by Iyer and Will. We explore critically the features of their construction and illustrate them by contrast to other possible variants. The equations of motion are valid for general binary orbits and for a class of coordinate gauges. The limiting cases of circular orbits and radial infal…
The emission of radiation from an accelerated charge is analyzed. It is found that at zero velocity, the radiation emitted from the charge imparts no counter momentum to the emitting charge, and no radiation reaction force is created by the radiation. A reaction force is created by the stress force that exists in the curved electric field of the charge, and the work done in overcoming this force is the source of the energy carried by the radiation.
We discuss the radiation reaction problem for an electric charge moving in flat space-time of arbitrary dimensions. It is shown that four is the unique dimension where a local differential equation exists accounting for the radiation reaction and admitting a consistent mass-renormalization (the Dirac-Lorentz equation). In odd dimensions the Huygens principle does not hold; as a result, the radiation reaction force depends on the whole past history of a charge (radiative tail). We show that the divergence in the tail integral can be removed by the mass renormalization only in the 2+1 theory. In…
The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger's type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states…
We use effective field theory tools to study non-conservative effects in systems of gravitating objects in general spacetime dimension. Using the classical version of the Closed Time Path formalism, we treat both the radiative gravitational field and its dynamical sources within a single action principle. New results include the radiation-reaction effective action in arbitrary dimensions to leading and +1PN orders, as well as the generalized Quadrupole formula to order +1PN.
Recently, Angheben et.al. [hep-th/0503081] have presented a refined method for calculating the (tree-level) black hole temperature by way of the tunneling paradigm. In the current letter, we demonstrate how their formalism can be suitably adapted to accommodate the (higher-order) effects of the gravitational back-reaction.
We analyze the change in position (the position shift) of the wave packet of a charged scalar particle due to radiation reaction in the $\hbar \to 0$ limit of quantum electrodynamics. In particular, we re-express the formula previously obtained for the position shift in terms of Green's functions for the electromagnetic field, thus clarifying the relation between the quantum and classical derivations of the radiation-reaction force.
In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable for this kind of calculation. The results are valid for arbitrary many objects. The energy loss is then computed and compared to well-known results for the energy flux as a check.
The problem of back reaction of the gravitational radiation of the two merging black holes on the metric of the spacetime is investigated. It is shown for some models that large energy density of the gravitational waves close to the merger can lead to the disappearance of the visible accretion disc of the merged pair of black holes.
Hawking radiation is studied for arbitrary scalars, fermions, and spin-1 bosons, using a tunneling approach, to every order in $\hbar$ but ignoring back-reaction effects. It is shown that the additional quantum terms yield no new contribution to the Hawking temperature. Indeed, it is found that the limit of small $\hbar$ in the standard quantum WKB approximation is replaced by the near-horizon limit in the gravitational WKB approach.
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
We compute the leading Post-Newtonian (PN) contributions at linear order in the spin to the radiation-reaction acceleration and spin evolution for binary systems, which enter at fourth PN order. The calculation is carried out, from first principles, using the effective field theory framework for spinning compact objects, in both the Newton-Wigner and covariant spin supplementary conditions. A non-trivial consistency check is performed on our results by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone, up to …
We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh "in-in" formalism and separating conservative and non-conservative terms according to the formulation in [1210.2745], which we show promotes Feynman's $i0$-prescription and cutting rules to a prominent role at the classical level. The resulting integrals, involving both Feynman and retarded propagators, can be bootstrapped to all orders in the velocity via differential equa…
We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-tim…
We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiati…
We present a new set of 3.5 Post-Newtonian equations in which Newtonian hydrodynamics is coupled to the nonconservative effects of gravitational radiation emission. Our formalism differs in two significant ways from a similar 3.5 Post-Newtonian approach proposed by Blanchet (1993, 1997). Firstly we concentrate only on the radiation-reaction effects produced by a time-varying mass-current quadrupole $S_{ij}$. Secondly, we adopt a gauge in which the radiation-reaction force densities depend on the fourth time derivative of $S_{ij}$, rather than on the fifth, as in Blanchet's approach. This diffe…
The aim of this paper is to highlight a recently proposed method for the treatment of classical radiative effects, in particular radiation reaction, via effective field theory methods. We emphasize important features of the method, and in particular the doubling of fields. We apply the method to two simple systems: for the mass-rope system in 1+1 dimensions we derive an effective action for the mass which describes a damped harmonic oscillator, while for the electromagnetic charge-field system, i.e. the system of an accelerating electric charge in 3+1 d, we derive the leading Abraham-Lorentz-D…
This thesis reports on work undertaken in comparing the effects of the phenomenon of radiation reaction in classical and quantum theories of electrodynamics. Specifically, it is concerned with the prediction of the change in position of a particle due to the inclusion of the self-force in the theory. We calculate this position shift for the classical theory, treating radiation reaction as a perturbation in line with the reduction of order procedure. We calculate the contributions to the position shift in the $\hbar\to 0$ limit of quantum field theory to order $e^2$ in the coupling, the order o…
This work continues the investigation of radiation phenomena from atom-field interactions, extending our earlier study of quantum radiation from a stationary atom's internal degree of freedom, modeled by a harmonic oscillator, to the emittance of classical radiation. By assuming that the atom interacts with a quantum scalar field initially in a coherent state, we show how a stochastic component of the internal dynamics of the atom arises from the vacuum fluctuations of the field, resulting in the emittance of quantum radiation, whose reaction induces quantum dissipation in the internal dynamic…
We address issues with extant formulations of dissipative effects in the effective field theory (EFT) which describes the post-Newtonian (PN) inspiral of two gravitating bodies by (re)formulating several parts of the theory. Novel ingredients include gauge invariant spherical fields in the radiation zone; a system zone which preserves time reversal such that its violation arises not from local odd propagation but rather from interaction with the radiation sector in a way which resembles the balayage method; 2-way multipoles to perform zone matching within the EFT action; and a double-field rad…
We compute the leading Post-Newtonian (PN) contributions at quadratic order in the spins to the radiation-reaction acceleration and spin evolution for binary systems, entering at four-and-a-half PN order. Our calculation includes the back-reaction from finite-size spin effects, which is presented for the first time. The computation is carried out, from first principles, using the effective field theory framework for spinning extended objects. At this order, nonconservative effects in the spin-spin sector are independent of the spin supplementary conditions. A non-trivial consistency check is p…
After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here we revise and explain some of the paradoxical issues that one faces when approaching the problem, mostly associated with regimes of uniform proper acceleration. The answers we provide can be found in the literature and are the synthesis of a large body of research. We just present them in a personal way that may help in their understanding. Besides, after the presentation of the standard answers we motivate and present a twist to tho…
We obtain the total impulse in the scattering of non-spinning binaries in general relativity at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$, including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multi-loop" integration techniques from collider physics. The complete results are i…
We investigate the semiclassical limit and quantum corrections to the metric in a unitary quantum gravity formulation of the CGHS 2d dilaton gravity model. A new method for calculating the back-reaction effects has been introduced, as an expansion of the effective metric in powers of the matter energy-momentum tensor. In the semiclassical limit the quantum corrections can be neglected, and we show that physical states exists which contain the Hawking radiation. The first order back-reaction effect is entirely due to the Hawking radiation. It causes the black-hole mass to monotonically decrease…
We consider an atom in interaction with a massless scalar quantum field. We discuss the structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom through the quantum vacuum. Our main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the spontaneous excitation of a uniformly accelerated atom in its ground state. This gives an understanding of the role of the different physical processes underlying the Unruh effect. The atom's evolution into equilibrium and the Einstein c…
In a generic spacetime a massless field propagates not just on the surface of the forward lightcone of a source, but in its interior. This inside-the-lightcone "tail radiation" is often described as having "scattered" off the spacetime curvature. In this work, we study the propagation of such tail radiation for a compact, static, spherically symmetric weak-field (i.e. low density) mass distribution that is well off the line-of-sight (LOS) between a source and an observer, and that is coupled to the radiation only gravitationally. For such perturbers, there are four distinct epochs in the obser…
We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial frame can be related in a simple manner to the fields of a uniformly accelerated charged particle in its rest frame. Since the latter field is static and easily obtainable, it is possible to derive the fields of an arbitrarily moving charged particle by a coordinate transformation. More importantly, this formalism allows us to calculate the self-force on a c…
Considering perturbations off the Reissner-Nordstrom metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we do a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to a rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstrom or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle take the classical form of mass times velocity plus an electromagnetic radiation reaction term while the Bondi mass loss eq…
This work deals with the motion of a radially falling star in Schwarzschild geometry and correctly identifies radiation reaction terms by the perturbative method. The results are: i) identification of all terms up to first order in perturbations, second in trajectory deviation, and mixed terms including lowest order radiation reaction terms; ii) renormalisation of all divergent terms by the $ζ$ Riemann and Hurwitz functions. The work implements a method previously identified by one of the authors and corrects some current misconceptions and results.
We deduce from energy conservation a lower bound on the mass of any system capable of imparting a constant acceleration to a charged body. We also point out a connection between this bound and the so called dominant energy condition of general relativity.
Radiation-reaction forces originating from the emission of gravitational waves (GW) bring binaries to close proximity and are thus responsible for virtually all the mergers that we can observe in GW interferometers. We show that there exists a supplementary radiation-reaction force between two binaries interacting gravitationally, changing in particular the decay rate of the semimajor axis under the emission of GW. This new binary-binary force is in some settings of the same order-of-magnitude than the usual 2.5PN force for an isolated binary and presents some striking features such as a depen…
Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, …
We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field having regard to the radiation back reaction. It is shown that unlike the massive case not all the divergences resulting from the self-action of the particle are Lagrangian, i.e. can be canceled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of homogeneo…
