Scalarized black holes in teleparallel gravity

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.

Black hole solutions in scalar-tensor symmetric teleparallel gravity

“…The metric (72a) has the same form as an extremal Reissner-Nordström black hole and it exhibits a horizon at r = M . In fact, the metric reproduces the well known BBMB black hole geometry in Riemannian conformal scalartensor theory [25][26][27], as well as the very recently found analogue in torsional scalar-tensor teleparallel gravity [63]. Several comparisons with these solutions can be made.…”

“…In this section we will provide a no-hair theorem for our theory that will constrain the functions A, B and V for which it will be possible to find asymptotically Minkowski black hole solutions. Similarly to the procedure done in [63] (or [32]) we will first find the trace of the vacuum field equations ( 15)…”

“…( 73), which may hint for a closer correspondence between these particular models. Also, while the nonmetricity scalar of the solution (72a), ( 73) is given by Q = −2M 2 /r 4 , in the respective torsional scalar-tensor model the torsion scalar behaves rather similarly, T = −2M 2 /r 4 + 8/r 2 [63].…”

“…In these lines the most general spherically symmetric and static connection compatible with vanishing curvature and vanishing nonmetricity, as written down in Refs. [58][59][60][61], has yielded nontrivial exact black hole solutions in torsion based f (T ) [62] and scalar-tensor gravities [63], as well as provided an appropriate starting point for perturbative weak field explorations [64][65][66][67][68][69][70][71][72]. Recently the authors of Ref.…”

“…VI. There are different ways to fully solve these equations, and by treating them case by case we are able to find different classes of exact solutions, such as the so-called Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) solution [25][26][27], which was first discovered in Riemannian conformal scalar-tensor theory and very recently also in torsional teleparallel scalar-tensor theory [63]. We also report several new black hole solutions which are characteristic of the present nonmetricity-scalar theory.…”