Barrow-type structure and thermodynamics of black holes

Abstract

The thermodynamics of black holes is investigated in the case of fractal-like event horizon, initially introduced by Barrow. The nature of the horizon surface is controlled by a parameter 0≤Δ≤1 with 0 corresponding to continuous space and 1 to completely fractal one. It is found that the entropy, the Helmholtz free energy, the mass and the heat capacity of the black hole are altered in the presence of non-zero Δ. As the black hole produces Hawking radiation, the dependence of its mass on time becomes softer as Δ increases, resulting in longer evaporation times. This effect makes relatively small primordial black holes to survive long enough so as to be potential ingredients of cold dark matter. The concept of Barrow-type structure can be generalized to the entire space resulting in a modified space-time metric.