Asymptotically flat, parametrized black hole metric preserving Kerr symmetries
Abstract
Recently the Event Horizon Telescope Collaboration, with verylong baseline interferometric observations, resolved structure at the scale of ∼5 Schwarzschild radii about the center of M 87^{*} , the supermassive black hole resident at the center of Messier 87. This important observation has paved the way for testing what is known as the "nohair" theorem, stating that isolated black holes are described by the Kerr metric, parametrized only by their mass and spin. Generic, parametrized spacetimes beyond Kerr allow one to arbitrarily test the nohair theorem for deviations from the Kerr result with no prior theoretical knowledge or motivation. In this paper, we present such a new general, stationary, axisymmetric and asymptotically flat black hole solution with separable geodesic equations (thus preserving symmetries of a Kerr black hole), extending the previous work of Johannsen. In this new metric, five free nonlinear functions parameterically deviate from the Kerr result, allowing one to effectively transform to many alternative black hole solutions present in the literature. We then derive analytic expressions for the Keplerian and epicyclic frequencies, the orbital energy and angular momentum, and the location of the innermost stable orbit of circular equatorial particle orbits. We also compute the image of the photon rings in the new spacetime, which correspond to the boundary of the black hole shadow image taken by the Event Horizon Telescope. We finally compare each quantity for the Kerr result against various parametrizations of the metric, finding that, especially for highly rotating black holes, the two solutions disagree significantly. Such a metric parametrization allows one to perform the nohair tests in a modelindependent way, and finally map constraints to specific alternative theories of gravity.
 Publication:

Physical Review D
 Pub Date:
 April 2020
 DOI:
 10.1103/PhysRevD.101.084030
 arXiv:
 arXiv:2002.01028
 Bibcode:
 2020PhRvD.101h4030C
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 17 pages, 13 figures