Evaporation phenomena in f(T) gravity

TL;DR

This paper investigates evaporation phenomena in generalized teleparallel gravity, showing that the choice of tetrad basis (diagonal vs. non-diagonal) crucially affects whether black holes can evaporate or remain stable.

Contribution

It demonstrates that non-diagonal tetrads allow evaporation and anti-evaporation phenomena in f(T) gravity, unlike diagonal tetrads which freeze black hole evolution.

Findings

Diagonal tetrads prevent evaporation, freezing black holes.

Non-diagonal tetrads enable both evaporation and anti-evaporation.

Phenomena depend on initial horizon perturbation phase.

Abstract

We formulate evaporation phenomena in a generic model of generalized teleparallel gravity in Weitzenbock spacetime with diagonal and non-diagonal tetrads basis. We also perform the perturbation analysis around the constant torsion scalar solution named Nariai spacetime which is an exact solution of field equations as the limiting case of the Schwarzschild-de Sitter and in the limit where two back hole and their cosmological horizons coincide. By a carefully analysis of the horizon perturbation equation, we show that (anti)evaporation can not 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 the diagonal tetrads. But in the case of non-diagonal tetrads the analysis is completely different. By a suitable non trivial non-diagonal tetrad basis we investigate the linear stability of the model under perturbations of the metric and torsion simultaneously. We observe that in spite of the diagonal case, both evaporation and anti evaporation can happen. The phenomena depend on the initial phase of the horizon perturbation. In the first mode when we restrict ourselves to the first lower modes the (anti)evaporation happens. So, in non-diagonal case the physical phenomena is reasonable. This is an important advantage of using non-diagonal tetrads instead of the diagonal ones. We also see that this is an universal feature, completely independent from the form of the model.