Maximum force for black holes and Buchdahl stars

Black holes and Buchdahl stars are identified respectively by $\mathrm{\ensuremath{\Phi}}(R)=1/2,4/9$, where ${g}_{tt}=1--2\mathrm{\ensuremath{\Phi}}(R)$ for a spherically-symmetric static metric. We investigate the maximum force for black holes and Buchdahl stars when one of the participating objects is charged and/or rotating while the other is neutral and nonrotating. 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.

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