New torsion black hole solutions in Poincar\'e gauge theory

We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincar\'e gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordstr\"om type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordstr\"om-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled to gravity.Comment: 14 pages, 0 figures, minor changes, references adde

Einstein-Yang-Mills-Lorentz black holes

Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows one to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories.Comment: 10 pages, 0 figures, minor changes, references added. It matches the version published in Eur. Phys. J.

Extended Reissner-Nordstr\"om solutions sourced by dynamical torsion

We find a new exact vacuum solution in the framework of the Poincar\'e Gauge field theory with massive torsion. In this model, torsion operates as an independent field and introduces corrections to the vacuum structure present in General Relativity. The new static and spherically symmetric configuration shows a Reissner-Nordstr\"om-like geometry characterized by a spin charge. It extends the known massless torsion solution to the massive case. The corresponding Reissner-Nordstr\"om-de Sitter solution is also compatible with a cosmological constant and additional U(1) gauge fields.Comment: 12 pages, 0 figures, minor changes, references adde

Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models

In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular correspondence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. The applicability of the method is divided into two approaches: one associated with the Lorentz group SO(1,n-1) of the space-time rotations and another one with its subgroup SO(n-2). Solutions for both cases are presented by the explicit use of this correspondence and, interestingly, for the last one by imposing on our ansatz the same kind of rotation and reflection symmetry properties as for a nonvanishing space-time torsion. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them and it may be used in future research to find other exact solutions within this theory.Comment: 10 pages, 0 figures, minor changes, references added. It matches the version published in Phys. Rev.

Stability in quadratic torsion theories

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from the most general Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when torsion vanishes and investigating the behaviour of the vector and pseudovector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier