Maximum Force for Black Holes and Buchdahl Stars

TL;DR

This paper explores the maximum force between black holes and Buchdahl stars, revealing a universal maximum force in general relativity and its connection to pure Lovelock gravity and specific spacetime dimensions.

Contribution

It demonstrates the universality of maximum force in GR and extends the analysis to pure Lovelock gravity, identifying unique dimensional spectra.

Findings

Maximum force between Schwarzschild objects is universal.

The maximum force relates to fundamental constants in GR.

Pure Lovelock gravity and specific dimensions are singled out by this maximum force.

Abstract

Black hole and Buchdahl star are identified respectively by $\Phi(R)=1/2, 4/9$ where $g_{tt}=1-2\Phi(R)$ for a spherically symmetric static metric. We investigate the maximum force for black hole and Buchdahl star when one of the participating objects is charged and/or rotating while the other is neutral and non-rotating. It turns out that the maximum force between two Schwarzschild objects is universal, given in terms of the fundamental constant velocity of light and the gravitational constant in general relativity (GR) in the usual four dimensional spacetime. In general this feature uniquely picks out the pure Lovelock gravity (having only one $N$th order term in action which includes GR in the linear order $N=1$) and the dimensional spectrum, $D=3N+1$, where $N$ is degree of the Lovelock polynomial action.