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Caustic echoes from a Schwarzschild black hole

Zenginoğlu, Anıl and Galley, Chad R. (2012) Caustic echoes from a Schwarzschild black hole. Physical Review D, 86 (6). Art. No. 064030. ISSN 2470-0010. doi:10.1103/PhysRevD.86.064030.

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We present the first numerical approximation of the scalar Schwarzschild Green function in the time domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront passes through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large l limit of quasinormal modes. We show that the fourfold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A twofold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.

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Additional Information:© 2012 American Physical Society. Received 27 June 2012; published 18 September 2012. We thank Marc Casals, Sam Dolan, Haixing Miao, Mark Scheel, Béla Szilágyi, Nicholas Taylor, Dave Tsang, and Huan Yang for discussions. A. Z. is supported by the NSF Grant No. PHY-1068881, and by a Sherman Fairchild Foundation Grant to Caltech. CRG is supported by an appointment to the NASA Postdoctoral Program (administered by Oak Ridge Associated Universities through a contract with NASA) at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA where part of this research was carried out.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NASA Postdoctoral ProgramUNSPECIFIED
Issue or Number:6
Classification Code:PACS: 04.70.Bw, 04.25.D-
Record Number:CaltechAUTHORS:20121019-105657502
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Official Citation:Zenginoğlu, A. and C. R. Galley (2012). "Caustic echoes from a Schwarzschild black hole." Physical Review D 86(6): 064030.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34988
Deposited By: Aucoeur Ngo
Deposited On:22 Oct 2012 15:12
Last Modified:09 Nov 2021 23:11

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