Scalarized Black Holes in Teleparallel Gravity

TL;DR

This paper investigates the existence of scalarized black holes within teleparallel gravity, providing exact solutions for some models and establishing no-hair theorems for others, thus expanding understanding of black hole properties in alternative gravity theories.

Contribution

It presents new exact solutions for scalarized black holes in scalar-torsion theories and proves no-hair theorems for specific cases, advancing the study of black holes in teleparallel gravity.

Findings

Existence of scalarized black hole solutions in certain scalar-torsion models.

Proof of no-hair theorems for other scalar-torsion models.

Demonstration of scalar hair in teleparallel gravity theories.

Abstract

Black holes play a crucial role in the understanding of the gravitational interaction. Through the direct observation of the shadow of a black hole by the event horizon telescope and the detection of gravitational waves of merging black holes we now start to have direct access to their properties and behaviour, which means the properties and behaviour of gravity. This further raised the demand for models to compare with those observations. In this respect, an important question regarding black holes properties is to know if they can support "hairs". While this is famously forbidden in general relativity, in particular for scalar fields, by the so-called no-hair theorems, hairy black holes have been shown to exist in several class of scalar-tensor theories of gravity. In this article we investigate the existence of scalarized black holes in scalar-torsion theories of gravity. On one hand, we find exact solutions for certain choices of couplings between a scalar field and the torsion tensor of a teleparallel connection and certain scalar field potentials, and thus proof the existence of scalarized black holes in these theories. On the other hand, we show that it is possible to establish no-scalar-hair theorems similar to what is known in general relativity for other choices of these functions.