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Black hole scalar charge from a topological horizon integral in Einstein-dilaton-Gauss-Bonnet gravity

Prabhu, Kartik and Stein, Leo C. (2018) Black hole scalar charge from a topological horizon integral in Einstein-dilaton-Gauss-Bonnet gravity. Physical Review D, 98 (2). Art. No. 021503. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20180730-132704495

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Abstract

In theories of gravity that include a scalar field, a compact object’s scalar charge is a crucial quantity since it controls dipole radiation, which can be strongly constrained by pulsar timing and gravitational wave observations. However, in most such theories, computing the scalar charge requires simultaneously solving the coupled, nonlinear metric and scalar field equations of motion. In this article, we prove that in linearly coupled Einstein-dilaton-Gauss-Bonnet gravity, a black hole’s scalar charge is completely determined by the horizon surface gravity times the Euler characteristic of the bifurcation surface, without solving any equations of motion. Within this theory, black holes announce their horizon topology and surface gravity to the rest of the Universe through the dilaton field. In our proof, a four-dimensional topological density descends to a two-dimensional topological density on the bifurcation surface of a Killing horizon. We also comment on how our proof can be generalized to other topological densities on general G-bundles, and to theories where the dilaton is nonlinearly coupled to the Euler density.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.98.021503DOIArticle
http://arxiv.org/abs/1805.02668arXivDiscussion Paper
ORCID:
AuthorORCID
Stein, Leo C.0000-0001-7559-9597
Additional Information:© 2018 American Physical Society. (Received 8 May 2018; published 30 July 2018) We would like to thank Béatrice Bonga and Robert M. Wald for useful conversations. We also thank David Garfinkle for comments on an earlier draft of the paper. K. P. is supported in part by the National Science Foundation (NSF) Grants No. PHY–1404105 and No. PHY–1707800 to Cornell University. L. C. S. acknowledges the support of NSF Grant No. PHY–1404569 and the support of the Brinson Foundation. Some calculations used the computer algebra system Mathematica [36], in combination with the xAct/xTensor suite [37,38].
Group:TAPIR, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-1404105
NSFPHY-1707800
NSFPHY-1404569
Brinson FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20180730-132704495
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180730-132704495
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88359
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:30 Jul 2018 20:44
Last Modified:09 Mar 2020 13:19

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