Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws

Abstract

An idealized "test" object in general relativity moves along a geodesic. However, if the object has a finite mass, this will create additional curvature in the spacetime, causing it to deviate from geodesic motion. If the mass is nonetheless sufficiently small, such an effect is usually treated perturbatively and is known as the gravitational self-force due to the object. This issue is still an open problem in gravitational physics today, motivated not only by basic foundational interest, but also by the need for its direct application in gravitational-wave astronomy. In particular, the observation of extreme-mass-ratio inspirals by the future space-based detector LISA will rely crucially on an accurate modeling of the self-force driving the orbital evolution and gravitational wave emission of such systems. In this paper, we present a novel derivation, based on conservation laws, of the basic equations of motion for this problem. They are formulated with the use of a quasilocal (rather than matter) stress-energy-momentum tensor---in particular, the Brown-York tensor---so as to capture gravitational effects in the momentum flux of the object, including the self-force. Our formulation and resulting equations of motion are independent of the choice of the perturbative gauge. We show that, in addition to the usual gravitational self-force term, they also lead to an additional "self-pressure" force not found in previous analyses, and also that our results correctly recover known formulas under appropriate conditions. Our approach thus offers a fresh geometrical picture from which to understand the self-force fundamentally, and potentially useful new avenues for computing it practically.

arXiv commentv1: 41 pages, 12 figures. To be submitted for publication, comments welcome; v2: 42 pages. Comments and references added; v3: Matches published version

References in corpus (56)

• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Laser Interferometer Space Antenna
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• The motion of point particles in curved spacetime
• Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Self-force via a Green's function decomposition
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Relativistic Dynamics and Extreme Mass Ratio Inspirals
• A Rigorous Derivation of Gravitational Self-force
• The use of Generalised Functions and Distributions in General Relativity
• Second-order gravitational self-force
• A Rigorous Derivation of Electromagnetic Self-force
• The Gravitational Universe
• Mass, inertia and gravitation
• Motion in alternative theories of gravity
• The self-consistent gravitational self-force
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Equation of Motion of Small Bodies in Relativity
• Second Order Gravitational Self-Force
• Nonlinear gravitational self-force: second-order equation of motion
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Gravitational self-force from radiation-gauge metric perturbations
• Mechanics of extended masses in general relativity
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• X-MRIs: Extremely Large Mass-Ratio Inspirals
• Self force on static charges in Schwarzschild spacetime
• Gravitational wave sources in the era of multi-frequency gravitational wave astronomy
• An introduction to the Lorentz-Dirac equation
• Mass and Angular Momentum in General Relativity
• The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy
• Self-forces from generalized Killing fields
• Gauge and motion in perturbation theory
• Electromagnetic self-forces and generalized Killing fields
• Gauge and Averaging in Gravitational Self-force
• Non-equilibrium thermodynamics of gravitational screens
• Generalized deviation equation and determination of the curvature in General Relativity
• Lecture notes on black hole binary astrophysics
• Momentum in General Relativity: Local versus Quasilocal Conservation Laws
• Rigid motion revisited: rigid quasilocal frames
• Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
• Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations
• Quasilocal Conservation Laws: Why We Need Them
• A fully relativistic radial fall
• Geoids in General Relativity: Geoid Quasilocal Frames
• Post-Newtonian Conservation Laws in Rigid Quasilocal Frames
• Indirect (source-free) integration method. II. Self-force consistent radial fall
• Rigid Quasilocal Frames
• The classical point-electron in Colombeau's theory of nonlinear generalized functions
• On the Existence and Utility of Rigid Quasilocal Frames
• Geometry and Motion in General Relativity

Cited by in corpus (6)

• Energy exchange between relativistic fluids: the polytropic case
• Testing gravity with Extreme-Mass-Ratio Inspirals
• Quasilocal conservation laws in cosmology: a first look
• The problem of motion in gauge theories of gravity
• Energy of cosmological spacetimes and perturbations: a quasilocal approach
• Dynamics of a relativistic discrete body: rigidity conditions, and covariant equations of motion