Probing the black hole metric: Black hole shadows and binary black-hole inspirals
In general relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to the lowest order in spin, as the metrics of stellar objects; (ii) they are independent of mass when expressed in geometric units; and (iii) they are described by the Kerr metric. In this paper, we quantify the upper bounds on potential black-hole metric deviations imposed by observations of black-hole shadows and of binary black-hole inspirals in order to explore the current experimental limits on possible violations of the last two predictions. We find that both types of experiments provide correlated constraints on deviation parameters that are primarily in the tt components of the spacetimes when expressed in areal coordinates. We conclude that, currently, there is no evidence for deviations from the Kerr metric across the 8 orders of magnitude in mass and 16 orders in curvature spanned by the two types of black holes. Moreover, because of the particular masses of black holes in the current sample of gravitational-wave sources, the correlations imposed by the two experiments are aligned and of similar magnitudes when expressed in terms of the far-field, post-Newtonian predictions of the metrics. If a future coalescing black-hole binary with two low-mass (e.g., ∼3 M_⊙) components is discovered, the degeneracy between the deviation parameters can be broken by combining the inspiral constraints with those from the black-hole shadow measurements.
© 2021 American Physical Society. (Received 3 December 2020; accepted 22 March 2021; published 18 May 2021) D. P. is grateful to F. Özel for many discussions and for comments on the manuscript and thanks P. Christian, L. Medeiros, D. Heumann, L. Stein, and E. Berti for their input. C. T. and E. P. thank K. Chatziioannou, M. Isi, N. Johnson-McDaniel, P. Lasky, E. Thrane, S. Vitale, and A. Weinstein for helpful comments and discussions. D. P. is supported in part by NSF PIRE Grant No. 1743747 and NSF Grant No. AST-1715061. D. P. and I. M. acknowledge the hospitality of the Aspen Center of Physics, where initial discussions that led to this work took place in the summer of 2016. E. P. and I. M. acknowledge support from the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), through Project No. CE170100004. I. M. is a recipient of the Australian Research Council Future Fellowship No. FT190100574. C. T. acknowledges support of the National Science Foundation and the LIGO Laboratory. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement No. PHY-1764464. This research has made use of data, software and/or web tools obtained from the Gravitational Wave Open Science Center [82–86], a service of LIGO Laboratory, the LIGO Scientific Collaboration, and the Virgo Collaboration. LIGO is funded by the U.S. National Science Foundation. Virgo is funded by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale della Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by Polish and Hungarian institutes.
Published - PhysRevD.103.104036.pdf
Submitted - 2012.02117.pdf