Falloff of radiated energy in black hole spacetimes
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...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/61677 https://orcid.org/0000-0001-6211-1388 |
| _version_ | 1811093775095693312 |
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| author | Burko, Lior M. Hughes, Scott A |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Burko, Lior M. Hughes, Scott A |
| author_sort | Burko, Lior M. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:50:27Z |
| format | Article |
| id | mit-1721.1/61677 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:50:27Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/616772022-10-02T04:27:06Z Falloff of radiated energy in black hole spacetimes Burko, Lior M. Hughes, Scott A Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Hughes, Scott A. Hughes, Scott A. 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. National Science Foundation (U.S.) (No. PHY-0757344) National Science Foundation (U.S.) (No. DUE-0941327) National Science Foundation (U.S.) (Grant No. PHY-0449884) United States. National Aeronautics and Space Administration (EPSCoR RID Grant) United States. National Aeronautics and Space Administration (Grant No. NNX08AL42G) Theodore Dunham, Jr. Grant of the F.A.R. 2011-03-11T19:30:09Z 2011-03-11T19:30:09Z 2010-11 2010-07 Article http://purl.org/eprint/type/JournalArticle 1550-7998 http://hdl.handle.net/1721.1/61677 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. https://orcid.org/0000-0001-6211-1388 en_US http://dx.doi.org/10.1103/PhysRevD.82.104029 Physical Review D Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Burko, Lior M. Hughes, Scott A Falloff of radiated energy in black hole spacetimes |
| title | Falloff of radiated energy in black hole spacetimes |
| title_full | Falloff of radiated energy in black hole spacetimes |
| title_fullStr | Falloff of radiated energy in black hole spacetimes |
| title_full_unstemmed | Falloff of radiated energy in black hole spacetimes |
| title_short | Falloff of radiated energy in black hole spacetimes |
| title_sort | falloff of radiated energy in black hole spacetimes |
| url | http://hdl.handle.net/1721.1/61677 https://orcid.org/0000-0001-6211-1388 |
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