Superentropic Black Hole Shadows in Arbitrary Dimensions

TL;DR

This paper explores the shapes and transitions of black hole shadows in arbitrary dimensions, revealing unique geometric behaviors and transitions that differ from four-dimensional cases using Hamilton-Jacobi equations.

Contribution

It provides a detailed analysis of superentropic black hole shadows in higher dimensions, highlighting the absence of certain transitional behaviors present in four dimensions.

Findings

Four-dimensional shadows show D-shape, cardioid, and naked singularity configurations.

Higher-dimensional shadows lack the transitional behaviors seen in four dimensions.

Shadow shapes depend critically on the black hole mass parameter and spacetime dimension.

Abstract

We investigate the shadow behaviors of the superentropic black holes in arbitrary dimensions. Using the Hamilton-Jacobi mechanism, we first obtain the associated null geodesic equations of motion. By help of a spheric stereographic projection, we discuss the shadows in terms of one-dimensional real curves. Fixing the mass parameter m, we obtain certain shapes being remarkably different than four dimensional geometric configurations. We then study theirs behaviors by varying the black hole mass parameter. We show that the shadows undergo certain geometric transitions depending on the spacetime dimension. In terms of a critical value mc, we find that the four dimensional shadows exhibit three configurations being the D-shape, the cardioid and the naked singularity associated with m > mc, m = mc and m < mc, respectively. We reveal that the D-shape passes to the naked singularity via a critical curve called cardioid. In higher dimensions, however, we show that such transitional behaviors are removed.