Shadow of Schwarzschild-Tangherlini black holes

TL;DR

This paper analytically examines how extra spatial dimensions influence the shadow of Schwarzschild-Tangherlini black holes, revealing that higher dimensions produce smaller, concentric circular shadows and affecting photon regions and energy emission rates.

Contribution

It provides an analytical study of black hole shadows in higher dimensions, extending the understanding of gravitational lensing beyond four-dimensional spacetime.

Findings

Shadows in higher dimensions are smaller than in 4D Schwarzschild black holes.

The shadow radius decreases as the number of dimensions increases.

Results reduce to the known Schwarzschild case when D=4.

Abstract

We study the shadow cast by the H$D$ Schwarzschild-Tangherlini black hole, and analytically calculate the influence of extra dimensions on the shadow of a black hole. A black hole casts a shadow as an optical appearance because of its strong gravitational field which is known to be a dark zone covered by a circle for a Schwarzschild black hole. We demonstrate that the null geodesic equation can be integrated by Hamilton-Jacobi approach, which enables us to investigate the shadow cast by the H$D$ Schwarzschild-Tangherlini black holes. Interestingly, it turns out that, for fixed values of the mass parameter, the shadow in H$D$ spacetimes are smaller when compared with 4$D$ Schwarzschild black hole. Further, the shadows of H$D$ Schwarzschild-Tangherlini black holes are concentric circles with a radius of the circle decreases with increase in $D$. We visualize the photon regions and the shadows in various dimensions for different values of the parameters, and the energy emission rates are is also investigated. Our results, in the limit $D=4$, reduced exactly to \emph{vis-$\grave{a}$-vis} Schwarzschild black hole case.