Falloff of radiated energy in black hole spacetimes
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Hughes.pdf
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Author(s)
Burko, Lior M.
Hughes, Scott A
Date Issued
November 2010
Journal
Physical Review D
Publisher
American Physical Society
Citation
Burko, Lior M., and Scott A. Hughes. “Falloff of radiated energy in black hole spacetimes.” Physical Review D 82.10 (2010): 104029. © 2010 The American Physical Society.
Version
Final published version
Abstract
The goal of much research in relativity is to understand gravitational waves generated by a strong-field dynamical spacetime. Quantities of particular interest for many calculations are the Weyl scalar psi4, which is simply related to the flux of gravitational waves far from the source, and the flux of energy carried to distant observers, E˙. Conservation laws guarantee that, in asympotically flat spacetimes, psi4∝1/r and E˙∝1/r2 as r-->[infinity symbol]. Most calculations extract these quantities at some finite extraction radius. An understanding of finite radius corrections to psi4 and E˙ allows us to more accurately infer their asymptotic values from a computation. In this paper, we show that, if the final state of the system is a black hole, then the leading correction to psi4 is O(1/r3), and that to the energy flux is O(1/r4)—not O(1/r2) and O(1/r3), as one might naively guess. Our argument only relies on the behavior of the curvature scalars for black hole spacetimes. Using black hole perturbation theory, we calculate the corrections to the leading falloff, showing that it is quite easy to correct for finite extraction radius effects.
MIT Department
Massachusetts Institute of Technology. Department of Physics
MIT Kavli Institute for Astrophysics and Space Research
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DOI of Published Version
https://doi.org/10.1103/PhysRevD.82.104029
