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

Marius Oltean, Richard J. Epp, Carlos F. Sopuerta, Alessandro D. A. M. Spallicci, and Robert B. Mann
Phys. Rev. D 101, 064060 – Published 26 March 2020

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.

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  • Received 21 November 2019
  • Accepted 13 February 2020

DOI:https://doi.org/10.1103/PhysRevD.101.064060

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Marius Oltean1,2,3,4,5,*, Richard J. Epp6, Carlos F. Sopuerta1,2, Alessandro D. A. M. Spallicci4,5,7, and Robert B. Mann6,8

  • 1Institute of Space Sciences (ICE, CSIC), Campus Universitat Autònoma de Barcelona, Carrer de Can Magrans s/n, 08193 Cerdanyola del Vallès (Barcelona), Spain
  • 2Institute of Space Studies of Catalonia (IEEC), Carrer del Gran Capità, 2-4, Edifici Nexus, despatx 201, 08034 Barcelona, Spain
  • 3Departament de Física, Facultat de Ciències, Universitat Autònoma de Barcelona, Edifici C, 08193 Cerdanyola del Vallès (Barcelona), Spain
  • 4Observatoire des Sciences de l’Univers en région Centre (OSUC), Université d’Orléans, 1A rue de la Férollerie, 45071 Orléans, France
  • 5Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E), Centre National de la Recherche Scientifique (CNRS), 3A Avenue de la Recherche Scientifique, 45071 Orléans, France
  • 6Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
  • 7Pôle de Physique, Collegium Sciences et Techniques (CoST), Université d’Orléans, Rue de Chartres, 45100 Orléans, France
  • 8Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

  • *oltean@ice.cat

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Issue

Vol. 101, Iss. 6 — 15 March 2020

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