Surface gravity from tidal acceleration

Surface gravity plays a pivotal role in the characterization of black holes and also in formulating the laws of black hole thermodynamics. Despite its significance, defining surface gravity in general spacetimes is a nontrivial task and thus has multiple definitions that lack equivalence in dynamical scenarios. This paper reviews different notions of dynamical surface gravity and then proposes a new definition based on tidal acceleration, which is an alternative way of characterizing spacetime curvature. By integrating tidal acceleration from the horizon to infinity, we could retrieve surface gravity in familiar situations of Schwarzschild and Kerr spacetimes. We outline a generic procedure for calculating surface gravity and substantiate our proposal by investigating the surface gravity of stationary spacetimes and reproducing the results from the literature. Furthermore, we examine surface gravity in nonstationary spacetimes, with a focus on Vaidya spacetime as a model of evaporating black holes.