Abstract
We study the capture cross-section of massless (photon) and massive test particles by the Schwarzschild–Tangherlini black hole, which is a solution of pure general relativity in higher dimensional spacetime with R×SD−2 topology. It is shown that an extra dimension weakens the gravitational attraction of a black hole, and consequently, radii of all the characteristic circular orbits, such as the radius of a photonsphere decrease in the higher dimensions. Furthermore, it is shown that in higher dimensions, there are no stable and bounded circular orbits. The critical impact parameters and capture cross-sections of photons and massive particles are calculated for several higher dimensions and it is shown that they also decrease with increasing dimension. Moreover, we calculate the capture cross-section of relativistic and non-relativistic test particles in the higher dimensions.
Highlights
The direct discovery of gravitational waves from the coalescence of black holes in close binary systems by LIGO-VIRGO collaboration [1,2,3,4,5], detection of the first image of a supermassive black hole in the center of the elliptic galaxy Messier 87 (M87) by the Event Horizon Telescope (EHT) [6], measurement of general relativistic effects through observation of S2 star [7,8] and hot spots [9] orbiting Sagittarius A* in the center of our galaxy by GRAVITY consortium make the study of black holes in various theories of gravity a hot topic in relativistic astrophysics
We have studied the characteristic circular orbits of the massive and massless particles around a Schwrazschild–Tangherlini black hole that is a solution of pure general relativity in higher dimensional spacetime with a R × S D−2 topology
By studying the circular orbits of test particles, we have determined the extra dimension of the spacetime weakens the gravitational attraction of the black hole and, radii of all the characteristic circular orbits, such as radii of the photonsphere, innermost stable and marginally bound circular orbits, decrease in the higher dimensions
Summary
The direct discovery of gravitational waves from the coalescence of black holes in close binary systems by LIGO-VIRGO collaboration [1,2,3,4,5], detection of the first image of a supermassive black hole in the center of the elliptic galaxy Messier 87 (M87) by the Event Horizon Telescope (EHT) [6], measurement of general relativistic effects through observation of S2 star [7,8] and hot spots [9] orbiting Sagittarius A* in the center of our galaxy by GRAVITY consortium make the study of black holes in various theories of gravity a hot topic in relativistic astrophysics. There is great interest in the alternate theories of gravity including higher dimensional gravitational field theories One of these is pure general relativity in higher dimensional spacetime with R × S D−2 topology which allows exact black hole solutions, e.g., spherical symmetric vacuum Schwarzschild–Tangherlini black hole solution [10]. We aim to study the capture cross-section of massive and massless (photon) particles by the Schwarzschild–Tangherlini black hole. The capture cross-section of a massive test particle by the Schwarzschild–Tangherlini black hole has not been studied in the literature.
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