Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 26, Issue 21, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/26/21/213001
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Funding
- Science and Technology Facilities Council [PP/E001025/1] Funding Source: researchfish
- STFC [PP/E001025/1] Funding Source: UKRI
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This review is concerned with the gravitational self-force acting on a mass particle in orbit around a large black hole. Renewed interest in this old problem is driven by the prospects of detecting gravitational waves from strongly gravitating binaries with extreme mass ratios. We begin here with a summary of recent advances in the theory of gravitational self-interaction in curved spacetime, and proceed to survey some of the ideas and computational strategies devised for implementing this theory in the case of a particle orbiting a Kerr black hole. We review in detail two of these methods: (i) the standard mode-sum method, in which the metric perturbation is regularized mode-by-mode in amultipole decomposition, and (ii) m-mode regularization, whereby individual azimuthal modes of the metric perturbation are regularized in 2+ 1 dimensions. We discuss several practical issues that arise, including the choice of gauge, the numerical representation of the particle singularity, and how high-frequency contributions near the particle are dealt with in frequency-domain calculations. As an example of a full end-to-end implementation of the mode-sum method, we discuss the computation of the gravitational self-force for eccentric geodesic orbits in Schwarzschild, using a direct integration of the Lorenz-gauge perturbation equations in the time domain. With the computational framework now in place, researchers have recently turned to explore the physical consequences of the gravitational self-force; we will describe some preliminary results in this area. An appendix to this review presents, for the first time, a detailed derivation of the 'regularization parameters' necessary for implementing the mode-sum method in Kerr spacetime.
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