Dempsey, D. and Dolan, S.R. orcid.org/0000-0002-4672-6523 (2016) Waves and null congruences in a draining bathtub. International Journal of Modern Physics D, 25 (9). 1641004. ISSN 0218-2718
Abstract
We study wave propagation in a draining bathtub: a black hole analogue in fluid mechanics whose perturbations are governed by a Klein–Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose here that a ‘pulse’ disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation numerically in the time domain using the method of lines. Starting with Gaussian initial data, we demonstrate that a pulse will propagate along a null congruence and thus trace out the light-cone of the effective geometry. Our new results reveal features, such as wavefront intersections, frame-dragging, winding and interference effects, that are closely associated with the presence of null circular orbits and the ergosphere.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 World Scientific Publishing. This is an author produced version of a paper subsequently published in International Journal of Modern Physics D. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Feb 2017 17:04 |
Last Modified: | 23 Apr 2017 23:57 |
Published Version: | https://doi.org/10.1142/S0218271816410042 |
Status: | Published |
Publisher: | World Scientific Publishing |
Refereed: | Yes |
Identification Number: | 10.1142/S0218271816410042 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:107653 |