Capture of Massless and Massive Particles by Parameterized Black Holes

Bobir Toshmatov,Ozodbek Rahimov,Bobomurat Ahmedov,Abdumirhakim Ahmedov

doi:10.3390/galaxies9030065

Abstract

We study an influence of the leading coefficient of the parameterized line element of the spherically symmetric, static black hole on the capture of massless and massive particles. We have shown that negative (positive) values of ϵ decreases (increases) the radius of characteristic circular orbits and consequently, increases (decreases) the energy and decreases (increases) the angular momentum of the particle moving along these orbits. Moreover, we have calculated and compared the capture cross section of the massive particle in the relativistic and non-relativistic limits. It has been shown that in the case of small deviation from general relativity the capture cross section for the relativistic and nonrelativistic particle has an additional term being linear in the small dimensionless deviation parameter ϵ.

Highlights

General relativity is considered as the most satisfactory theory of gravitation due to its conceptual and structural elegance, as well as its reasonable agreement with experimental and astronomical observations [1]
We study the capture of massless and massive particles by the black hole whose line element is the parameterized by the Rezzolla–Zhidenko method presented in [10] in terms of the bumpy parameters and ai with i = 0, 1, 2, . . . that defines the deviation from the general relativity
We have studied the capture of massless and massive particles by the spherically symmetric black hole whose line element is described by the Rezzolla–Zhidenko parameterization [10] up to O(x3) terms that takes only the coefficient as nonvanishing, including the PPN constraints

Summary

Introduction

General relativity is considered as the most satisfactory theory of gravitation due to its conceptual and structural elegance, as well as its reasonable agreement with experimental and astronomical observations [1]. The best laboratory to test the theory in a strong gravitational field is a black hole (and a neutron star) close environment. Thanks to the development of new modern technologies in recent years, we have obtained several observational breakthrough events such as the detected gravitational waves from the coalescence of two massive black holes or neutron stars in close binaries by the LIGO and Virgo scientific collaborations (for example, see [2,3,4,5,6]) and the discovery of the first image of the supermassive black hole at the center of the elliptic galaxy M87 by the Event Horizon Telescope (EHT) collaboration [7] that gave us an initial possibility to check general relativity in the strong field regime.

Equations of Motion

Capture of Photons

Capture of Massive Particles

Conclusions