Probing the regular nature of the spacetime by direct measurement of black hole properties (2015)
In the following years Very Long Baseline Interferometry (VLBI) facilities will be able to directly image the accretion flow around the supermassive black hole candidate at the center of the Milky Way, Sgr A*. They will also be able to observe its shadow: an optical property which appears as a consequence of the strong gravitational field around it and which thus depends only on the physical parameters of the black hole. While there is no definitive evidence of the nature of the spacetime geometry around Sgr A*, it has been usually modeled by a Kerr black hole, by virtue of the no-hair theorem, which asserts that all uncharged black holes in 4-dimensional general relativity are described by this metric and thus completely specified by two parameters, the mass M and the spin parameter a. As a consequence, testing the no-hair theorem in nature with future observations allows us to not only verify that black holes in our universe are Kerr black holes, but to test the strong field predictions of general relativity In this work I investigate if the shadow, image and spectrum of a non-Kerr regular black hole inspired by noncommutative geometry may provide a measurement of the parameters characterizing Kerr and non-Kerr regular black holes to distinguish one from the other. Specifically, the non-Kerr solution studied here is the rotating black hole found by Smailagic and Spallucci in 2010 and known as the “Kerrr” black hole, where the third “r” stands for regular, in the sense of a pathology-free rotating black hole. The general strategy to derive this generalized solution consists of prescribing an improved form of the energy-momentum tensor, which accounts, at least phenomenologically, for the noncommutative fluctuations of the manifold at the origin and which vanishes for large distances with respect to the noncommutative geometry scale, l_{0}. Abstract The image and spectrum of Sgr A*, as the case of study, was modeled using the relativistic ray-tracing code GYOTO, assuming an optically thin, constant angular momentum torus in hydrodynamic equilibrium around the Kerr and "Kerrr" geometries. The model used includes a toroidal magnetic field and radiative cooling by bremsstrahlung, synchrotron, and inverse Compton processes. The assumptions provided here, for drawing the shadow and to model the accretion disk, do not provide a realistic scenario, but an easily accessible yet powerful analytical analogy. Then comparisons with the Kerr geometry are calculated by using the observables defined by Hioki and Maeda and the distortion parameter introduced by Tsukamoto, Li and Bambi. This work confirms that it is definitely challenging to test this kind of regular metric solely from observations of the shadow or accretion structures in the near future.