Numerical study of hypershadows in higher-dimensional black holes

TL;DR

This paper introduces a numerical framework for computing and visualizing hypershadows in higher-dimensional black holes, enabling detailed analysis of their shapes and symmetries in five-dimensional spacetimes.

Contribution

The authors develop a flexible numerical method for hypershadow visualization, applicable to various higher-dimensional black hole metrics, and analyze their geometric properties systematically.

Findings

Validated spherical symmetry of Schwarzschild-Tangherlini hypershadow

Demonstrated dependence of hypershadow shape on observer position and black hole spin

Provided quantitative measures for hypershadow size and displacement trends

Abstract

We develop a fully numerical framework to compute and visualize the \emph{hypershadow}\cite{Novo:2024wyn}, the three-dimensional generalization of the black hole shadow in five-dimensional spacetimes. Our method is based on backward ray tracing and allows flexible control over observer position, enabling the reconstruction of the full shadow volume. For visualization, we combine discrete sampling with surface contouring and introduce reflection difference maps on central slices to quantify mirror symmetries. Applying this method to the Schwarzschild-Tangherlini and Myers-Perry geometries, we validate the former's spherical symmetry and systematically discuss the hypershadow's dependence on observer position and black hole spin parameters. We also provide compact quantitative measures for size reduction and global displacement, revealing clear monotonic trends. The framework is readily extendible to other metrics and opens the way to numerical studies of more exotic objects, such as black rings and their prospective toroidal hypershadows.