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

Abstract The innermost stable circular orbit (ISCO) offers a fundamental test of spacetime structure. However, the influence of anisotropic energy--momentum tensors on its properties in higher-dimensional black hole spacetimes remains to be fully elucidated. 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. We assume that the energy--momentum tensor satisfies the weak energy condition, possesses a nonpositive trace, and obeys constraints on radial and tangential pressures, which are collectively equivalent to the dominant energy condition with additional constraints. 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. The results show that the allowed equations of state of matter at the ISCO depend explicitly on the spacetime dimension. In the large-$D$ limit, both the radial and tangential equations of state vanish, corresponding to a pressureless dust behavior. These findings advance our understanding of orbital stability in higher-dimensional gravitational systems and highlight the fundamental differences from four-dimensional black hole dynamics.