Evaporation phenomena in f(T) gravity

Abstract

We formulate evaporation phenomena in a generic model of generalized teleparallel gravity in Weitzenbock space–time with a diagonal and nondiagonal tetrad basis. We also perform perturbation analysis around the constant torsion scalar solution called the Nariai space–time, which is an exact solution of the field equations as the limiting case of the Schwarzschild – de Sitter space–time and in the limit where two black holes and their cosmological horizons coincide. By a carefully analysis of the horizon perturbation equation, we show that (anti)evaporation cannot happen if we use a diagonal tetrad basis. This result implies that a typical black hole in any generic form of generalized teleparallel gravity is frozen in its initial state if we use diagonal tetrads, but in the case of nondiagonal tetrads the analysis is completely different. With a suitable nontrivial nondiagonal tetrad basis we investigate the linear stability of the model under simultaneous perturbations of the metric and torsion. We observe that in spite of the diagonal case, both evaporation and antievaporation can happen. These phenomena depend on the initial phase of the horizon perturbation. In the first mode, when we restrict ourselves to the first lower modes (anti)evaporation takes place. So, in the nondiagonal case, the physical phenomena are reasonable. This is an important advantage of using nondiagonal tetrads instead of diagonal ones. We also see that this is a universal feature, completely independent from the form of the model.