Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.084021· OSTI ID:21413434

Barack, Leor; Sago, Norichika ^[1]

---

1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ (United Kingdom)

We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self-force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett. 102, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.

• OSTI ID: 21413434
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.084021; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ANGULAR MOMENTUM
ASYMPTOTIC SOLUTIONS
BLACK HOLES
COMPUTERIZED SIMULATION
DELTA FUNCTION
DISTURBANCES
EQUATIONS
GAUGE INVARIANCE
GRAVITATIONAL RADIATION
HARMONICS
LORENTZ INVARIANCE
METRICS
NUMERICAL SOLUTION
ORBITS
PARTICLES
PERTURBATION THEORY
SCHWARZSCHILD METRIC
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL SOLUTIONS
OSCILLATIONS
RADIATIONS
SIMULATION