Unbounded Radius of Innermost Stable Circular Orbit in Higher-Dimensional Black Holes

TL;DR

This paper shows that in higher-dimensional black holes with certain energy conditions, the innermost stable circular orbit (ISCO) can have an unbounded radius, especially in dimensions eight and above, indicating fundamental differences from four-dimensional cases.

Contribution

It demonstrates that the ISCO radius in higher-dimensional black holes can be unbounded, extending understanding of orbital stability beyond four dimensions under specific energy conditions.

Findings

No upper bound on ISCO radius in higher dimensions.

ISCO may not exist for dimensions ≥8.

Unbounded ISCO radius depends on energy-momentum tensor components.

Abstract

The innermost stable circular orbit (ISCO) offers a fundamental test of spacetime structure. However, its behavior in higher-dimensional black holes influenced by anisotropic energy-momentum tensors remains insufficiently explored. In this work, we investigate the upper bound of the ISCO in higher-dimensional, static, spherically symmetric, and asymptotically flat black hole spacetimes in the presence of an anisotropic energy-momentum tensor. The energy-momentum tensor is assumed to satisfy the weak energy condition, possess a non-positive trace, and obey constraints on radial and tangential pressures, collectively equivalent to the dominant energy condition with additional constraints. By analyzing the effective potential for timelike geodesics and imposing ISCO conditions, we demonstrate the general absence of an upper bound on the ISCO radius in higher-dimensional spacetimes. For dimensions greater than or equal to eight, an ISCO may not exist, depending on the radial and tangential components of the energy-momentum tensor. If an ISCO exists, its radius remains unbounded. These findings advance our understanding of orbital stability in higher-dimensional gravitational systems and highlight fundamental differences from four-dimensional black hole dynamics.