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Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity

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Abstract

Astrophysical tests of general relativity belong to two categories: 1) “internal”, i.e. consistency tests within the theory (for example, tests that astrophysical black holes are indeed described by the Kerr solution and its perturbations), or 2) “external”, i.e. tests of the many proposed extensions of the theory. I review some ways in which astrophysical black holes can be used as natural laboratories for both “internal” and “external” tests of general relativity. The examples provided here (ringdown tests of the black hole “no-hair” theorem, bosonic superradiant instabilities in rotating black holes and gravitational-wave tests of massive scalar-tensor theories) are shamelessly biased towards recent research by myself and my collaborators. Hopefully this colloquial introduction aimed mainly at astrophysicists will convince skeptics (if there are any) that space-based detectors will be crucial to study fundamental physics through gravitational-wave observations.

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Notes

  1. Throughout this paper I will use geometrical units \(G=c=1\).

  2. The astrophysical plausibility of spontaneous scalarization is supported by detailed studies of stellar structure [6, 7], numerical simulations of collapse [8–10] and stability analyses [11]. While the strength of spontaneous scalarization phenomena is already strongly constrained by observations of binary pulsars [12], semiclassical vacuum instabilities seem to offer a viable mechanism to “seed” nonzero scalar fields in stars [13, 14].

  3. Tensor multi-scalar theories of gravity have also been investigated in depth (see e.g. [29] and references therein), but we will not consider them here.

  4. The strength of these tests will depend on two key elements: (i) the signal-to-noise ratio (SNR) of individual observations [70], that also affects accuracy in binary parameter estimation, and (ii) the number N of observations that can be used to constrain GR. The reason is that, given a theory whose deviations from GR can be parametrized by one or more universal parameters (e.g. coupling constants), the bounds on these parameters will scale roughly with \(\sqrt {N}\). As a matter of fact, the bounds could improve faster than \(\sqrt {N}\) if some events are particularly loud: see e.g. [69, 71] for detailed analyses addressing specific modifications to GR in the Advanced LIGO/eLISA context, respectively.

  5. Superradiant amplification is not possible for fermionic fields: see e.g. [89, 90].

  6. While our numerical results for the axial modes are supported by an analytical formula, in the polar case we have used two different functions to fit the numerical data at second order in the BH spin.

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Acknowledgments

The research reviewed in this paper was supported by NSF CAREER Grant No. PHY-1055103. I thank my collaborators on various aspects of the work described in this paper: Justin Alsing, Vitor Cardoso, Sayan Chakrabarti, Jonathan Gair, Leonardo Gualtieri, Michael Horbatsch, Akihiro Ishibashi, Paolo Pani, Alberto Sesana, Ulrich Sperhake, Marta Volonteri, Clifford Will and Helmut Zaglauer. Special thanks go to Paolo Pani for comments on an early draft and to Alberto Sesana for preparing Fig. 1, as well as excellent mojitos.

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  1. Department of Physics and Astronomy, The University of Mississippi, University, MS, 38677, USA

    Emanuele Berti

  2. California Institute of Technology, Pasadena, CA, 91109, USA

    Emanuele Berti

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Berti, E. Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity. Braz J Phys 43, 341–350 (2013). https://doi.org/10.1007/s13538-013-0128-z

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