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Extremal black holes in dynamical Chern–Simons gravity

McNees, Robert and Stein, Leo C. and Yunes, Nicolás (2016) Extremal black holes in dynamical Chern–Simons gravity. Classical and Quantum Gravity, 33 (23). Art. No. 235013. ISSN 0264-9381.

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Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern–Simons (dCS) gravity, where the Einstein–Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.

Item Type:Article
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URLURL TypeDescription Paper
Stein, Leo C.0000-0001-7559-9597
Yunes, Nicolás0000-0001-6147-1736
Additional Information:© 2016 IOP Publishing Ltd. Received 31 August 2016; Accepted for publication 4 October 2016; Published 8 November 2016. We would like to thank the Kavli Institute for Theoretical Physics for their hospitality during the completion of this work. We would also like to thank Kent Yagi, Frans Pretorius, and Albion Lawrence for useful discussions. RM acknowledges support from a Loyola University Chicago Summer Research Stipend. LCS acknowledges that support for this work was provided by NASA through Einstein Postdoctoral Fellowship Award Number PF2-130101 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the NASA under contract NAS8-03060, and further acknowledges support from the NSF grant PHY-1404569. NY acknowledges support from NSF CAREER Award PHY-1250636. The research of RM and NY was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. Some calculations used the computer algebra-system MAPLE, in combination with the GRTENSORII package. Other calculations used the computer algebra-system MATHEMATICA, in combination with the XTENSOR package [48–50]. Finally, RM (@mcnees) and LCS (@duetosymmetry) would like to thank Twitter for facilitating discussion during the early stages of this collaboration.
Group:TAPIR, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Loyola University ChicagoUNSPECIFIED
NASA Eistein Postdoctoral FellowshipPF2-130101
Issue or Number:23
Record Number:CaltechAUTHORS:20161108-092700195
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Official Citation:Robert McNees et al 2016 Class. Quantum Grav. 33 235013
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71801
Deposited By: Tony Diaz
Deposited On:08 Nov 2016 17:33
Last Modified:09 Mar 2020 13:19

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