We show that the notion of the maximum force conjecture $F leqslant 1/4$ in general relativity, when applied to asymptotically flat singly spinning Myer-Perry black holes in any dimension, reveals the underlying thermodynamic instability in a number
of ways. In particular, the Hookean force law $F_1=kx$, suitably defined, is bounded by the conjectured limit, but in $dgeqslant 6$ it is further bounded by a dimensional dependent value less than $1/4$, which remarkably corresponds to the Emparan-Myers fragmentation (splitting of a black hole into two becomes thermodynamically preferable). Furthermore, we define another force as the square of the angular momentum to entropy ratio ($F_2=J^2/S^2$). In dimensions $dgeqslant 6$, the positive Ruppeiner scalar curvature region in the thermodynamic phase space is marked by the upper boundary $F_2=frac{1}{12}left(frac{d-3}{d-5}right)$ and the lower boundary $F_2=frac{1}{4}left(frac{d-3}{d-5}right)$, the latter corresponds to a black hole that suffers from Gregory-Laflamme instability. Surprisingly, the upper and lower boundaries correspond to $F=1/4$ when $d=6$ and $dto infty$, respectively. We discuss how the maximum force may be relevant to the underlying black hole microstructure and its relationship to cosmic censorship.
It is commonly known in the literature that large black holes in anti-de Sitter spacetimes (with reflective boundary condition) are in thermal equilibrium with their Hawking radiation. Focusing on black holes with event horizon of toral topology, we
study a simple model to understand explicitly how this thermal equilibrium is reached under Hawking evaporation. It is shown that it is possible for a large toral black hole to evolve into a small (but stable) one.
