Slowly evolving horizons in Einstein gravity and beyond

We study event horizon candidates for slowly evolving dynamical black holes in General Relativity and Einstein-Gauss-Bonnet (EGB) gravity. Such a type of horizon candidate has been termed as slowly evolving null surface (SENS). It signifies a near-equilibrium state of a dynamic black hole. We demonstrate the time evolution of such surfaces for three different metrics. First, we locate such a surface for a charged Vaidya metric and show that the parameter space of the black hole gets constrained to allow a physically admissible slowly evolving null surface. We then consider a supertranslated Vaidya solution that contains a non-spherical horizon and study the properties of the SENS. This spacetime generates a non-vanishing shear at the SENS due to the presence of the supertranslation field. The SENS for a spherically symmetric Vaidya-like solution in EGB gravity yields a bound on the accretion rate that depends on the size of the horizon. We also show that the first and second laws of black hole mechanics can be established for these slowly evolving surfaces.