Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem

Abstract

According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric deviations from the Kerr metric have been suggested to study observational signatures in both the electromagnetic and gravitational-wave spectra that differ from the expected Kerr signals. Due to the no-hair theorem, however, such spacetimes cannot be regular everywhere outside the event horizons, if they are solutions to the Einstein field equations; they are often characterized by naked singularities or closed time-like loops in the regions of the spacetime that are accessible to an external observer. For observational tests of the no-hair theorem that involve phenomena in the vicinity of the circular photon orbit or the innermost stable circular orbit around a black hole, these pathologies limit the applicability of the metrics only to compact objects that do not spin rapidly. In this paper, we construct a Kerr-like metric which depends on a set of free parameters in addition to its mass and spin and which is regular everywhere outside of the event horizon. We derive expressions for the energy and angular momentum of a particle on a circular equatorial orbit around the black hole and compute the locations of the innermost stable circular orbit and the circular photon orbit. We demonstrate that these orbits change significantly for even moderate deviations from the Kerr metric. The properties of our metric make it an ideally suited spacetime to carry out strong-field tests of the no-hair theorem in the electromagnetic spectrum using the properties of accretion flows around astrophysical black holes of arbitrary spin.

Rotating charged black hole with Weyl corrections

“…It indicates that for α = 0 the radius r ± depends on the polar angle coordinate θ, which is similar to those in the modified Kerr metrics by the deformation parameter ǫ [46] or the polymeric function P in loop quantum gravity [47]. Furthermore, the position and the shape of horizons are defined by the parameters M , a, α and q.…”

“…In order to eliminate the elements g ′ 01 and g ′ 13 , we must use a transformation [46,47] to the coordinates (u ′ , r ′ , θ ′ , φ ′ ) which is given by…”

Testing the space-time geometry around black hole candidates with the available radio and X-ray data

“…However, in order to reproduce the correct Newtonian limit, we have to impose 0 = 1 = 0, while 2 is strongly constrained by Solar System experiments (Johannsen & Psaltis 2011b). In what follows, I will examine only the simplest case in which 3 = 0, while all the other deformation parameters are set to zero.…”

“…If our metric does it, it is not very important if it is an exact solution of the vacuum Einstein's equations (in this case, we are actually considering the possibility the BH candidate is a compact object made of exotic matter) or not, in the sense that we eventually get the same qualitative constraints (Bambi 2011e, 2012aLi & Bambi 2012). In this review paper, I will focus the discussion on the metric proposed by Johannsen and Psaltis (JP) to describe the gravitational field around non-Kerr BHs in putative alternative theories of gravity (Johannsen & Psaltis 2011b). In Boyer-Lindquist coordinates, the JP metric is given by the line element…”

Circular orbits and accretion process in a class of Horndeski/Galileon black holes

“…The radiation efficiency of accretion disks, η, for Schwarzschild and Kerr black holes was obtained by Novikov and Thorne [32] which its value lies in the range of 0.057-0.43 depending on the black hole spin. The Kerr-like metric was constructed by Johannsen and Psaltis [19] and then Johannsen [18] has studied the accretion disks around such black holes. The study of the geodesic motion and the circular orbits of charged particles around weakly magnetized rotating black holes are carried out by Tursunov et al [40].…”