Radiation reaction and energy-momentum conservation
Dmitri Gal'tsov
备注：
Lecture given at the C.N.R.S. School "Mass and Motion in General Relativity", Orleans, France, 2008
发表信息：
"Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and B. Whiting, Springer Series: Fundamental Theories of Physics, Vol. 162, pp. 367-393, 2011
We discuss subtle points of the momentum balance for radiating particles in flat and curved space-time. An instantaneous balance is obscured by the presence of the Schott term which is a finite part of the bound field momentum. To establish the balance one has to take into account the initial and final conditions for acceleration, or to apply averaging. In curved space-time an additional contribution arises from the tidal deformation of the bound field. This force is shown to be the finite remnant from the mass renormalization and it is different both form the radiation recoil force and the Schott force. For radiation of non-gravitational nature from point particles in curved space-time the reaction force can be computed substituting the retarded field directly to the equations of motion. Similar procedure is applicable to gravitational radiation in vacuum space-time, but fails in the non-vacuum case. The existence of the gravitational quasilocal reaction force in this general case seems implausible, though it still exists in the non-relativistic approximation. We also explain the putative antidamping effect for gravitational radiation under non-geodesic motion and derive the non-relativistic gravitational quadrupole Schott term. Radiation reaction in curved space of dimension other than four is also discussed
The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving after fixing the Lorenz gauge, and have nontrivial charge. These "Multipole charges" receive contributions both from the charged matter and electromagnetic fields. The former is nothing but the electric multipole moment of the source. In a stationary configuration, there is a novel equipartition relation between the two contributions. The multipole charge, …
In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox". Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the non-thermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measur…
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…
We consider Hawking radiation as due to a tunneling process in a black hole were quantum corrections, derived from Quantum Einstein Gravity, are taken into account. The consequent derivation, satisfying conservation laws, leads to a deviation from an exact thermal spectrum. The non-thermal radiation is shown to carry information out of the black hole. Under the appropriate approximation, a quantum corrected temperature is assigned to the black hole. The evolution of the quantum black hole as it evaporates is then described by taking into account the full implications of energy conservation as …
Recent work, which treats the Hawking radiation as a semi-classical tunneling process at the horizon of the Schwarzschild and Reissner-Nordstrom spacetimes, indicates that the exact radiant spectrum is no longer pure thermal after considering the black hole background as dynamical and the conservation of energy. In this paper, we extend the method to investigate Hawking radiation as massless particles tunneling across the event horizon of the Kerr black hole and that of charged particles from the Kerr-Newman black hole by taking into account the energy conservation, the angular momentum conser…
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…
The classical first law of thermodynamic for Kerr-Newmann black hole (KNBH) is generalized to that in quantum form on event horizon. Then four quantum conservation laws on the KNBH equilibrium radiation process are derived, and Bekenstein-Hawking's relation S=A/4 is recovered. It can be argued that the classical entropy of black hole arise from the quantum entropy of field quanta or quasi-particles inside the hole.
An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conserva…
In this paper, by introducing a Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power $(E/E_{QG})^2$, we have investigated the effect of LIV on the Hawking radiation of the charged Dirac particle via tunneling from a Reissner-Nordström(RN) black hole. We first find the effect of LIV speeds up the black hole evaporation, leaving the induced Hawking temperature very sensitive to the changes in the energy of the radiation particle, but at the same energy level, insensitive to the changes in the charge of the radiation particle. This provides a phenom…
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.
We present a general parametrization for the leading order terms in a momentum power expansion of a non-universal Lorentz-violating, but rotational invariant, kinematics and its implications for two-body decay thresholds. The considered framework includes not only modified dispersion relations for particles, but also modified energy-momentum conservation laws, something which goes beyond effective field theory. As a particular and relevant example, bounds on the departures from special relativistic kinematics from the non-observation of vacuum Cherenkov radiation are discussed and compared wit…
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.
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.
Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.
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…
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…
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.
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.
It has been shown recently that information is lost in the Hawking radiation of the linear dilaton black holes in various theories when applying the tunneling formulism without considering quantum gravity effects. In this Letter, we recalculate the emission probability by taking into account of the log-area correction to the Bekenstein-Hawking entropy and the statistical correlation between quanta emitted. The crucial role of the black hole remnant on the entropy conservation is highlighted. We model the remnant as a higher dimensional linear dilaton vacuum in order to show that such a remnant…
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 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.
For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution $j_a$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the difference between the final and initial electromagnetic self-energy of the charge distribution, (ii) the net electromagnetic energy radiated to infinity (and/or into a black hole/white hole), and (iii) the total work done by the electromagnetic field on the charge distribution via the Lorentz force. A similar conservation theorem can be proven for linearize…
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…
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…
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…
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…
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…
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.
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…
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…
The back reactions of Hawking radiation allow nontrivial correlations between consecutive Hawking quanta, which gives a possible way of resolving the paradox of black hole information loss known as the hidden messenger method. In a recent work of Ma {\it et al} [arXiv:1711.10704], this method is enhanced by a general derivation using small deviations of the states of Hawking quanta off canonical typicality. In this paper, we use this typicality argument to study the effects of generic back reactions on the quantum geometries described by spin network states, and discuss the viability of entrop…
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…
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 …
We consider radiation transport theory applied to non-dispersive but refractive media. This setting is used to discuss Minkowski's and Abraham's electromagnetic momentum, and to derive conservation equations independent of the choice of momentum definition. Using general relativistic kinetic theory, we derive and discuss a radiation gas energy-momentum conservation equation valid in arbitrary curved spacetime with diffractive media.
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.
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…
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…
