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The tidal acceleration experienced by an object at the event horizon of ablack hole decreases as one over the square of the black hole's mass. As suchthere is a maximum mass at which a black hole can tidally disrupt an objectoutside of its event horizon and potentially produce observable emission. Thismaximum mass is known as the ``Hills mass'', and in full general relativity isa function of both the black hole's spin $a_\bullet$ and the inclination angleof the incoming object's orbit with respect to the black hole's spin axis$\psi$. In this paper we demonstrate that the Hills mass can be represented bya simple analytical function of $a_\bullet$ and $\psi$, the first generalsolution of this problem. This general solution is found by utilising thesymmetries of a class of critical Kerr metric orbits known as the innermostbound spherical orbits. Interestingly, at fixed black hole spin the maximumHills mass can lie at incoming orbital inclinations outside of the black hole'sequatorial plane $\psi \neq \pi/2$. When compared to previous results in theliterature this effect can lead to an increase in the maximum Hills mass (atfixed spin) by as much as a factor of $\sqrt{11/5} \simeq 1.48$ for a maximallyrotating black hole. We then demonstrate how Bayesian inference, coupled withan estimate of the mass of a black hole in a tidal disruption event, can beused to place conservative constraints on that black hole's spin. We provide apublicly available code tidalspin which computes these spin distributions.

The maximum mass of a black hole which can tidally disrupt a star: measuring black hole spins with tidal disruption events