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Black hole stereotyping: induced gravito-static polarization

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Abstract

We discuss the black hole effective action and define its static subsector. We determine the induced gravito-static polarization constants (electric Love numbers) of static black holes (Schwarzschild) in an arbitrary dimension, namely the induced mass multipole as a result of an external gravitational field. We demonstrate that in 4d these constants vanish thereby settling a disagreement in the literature. Yet in higher dimensions these constants are non-vanishing, thereby disproving (at least in d > 4) speculations that black holes have no effective couplings beyond the point particle action. In particular, when l/(d−3) is half integral these constants demonstrate a (classical) renormalization flow consistent with the divergences of the effective field theory. In some other cases the constants are negative indicating a novel non-spherical instability. The theory of hypergeometric functions plays a central role.

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Authors and Affiliations

  1. Racah Institute of Physics, Hebrew University, Jerusalem, 91904, Israel

    Barak Kol

  2. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Michael Smolkin

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  1. Barak Kol
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  2. Michael Smolkin
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Correspondence to Michael Smolkin.

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ArXiv ePrint: 1110.3764

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Kol, B., Smolkin, M. Black hole stereotyping: induced gravito-static polarization. J. High Energ. Phys. 2012, 10 (2012). https://doi.org/10.1007/JHEP02(2012)010

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  • DOI: https://doi.org/10.1007/JHEP02(2012)010

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