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.

Observational Constraints in Metric-Affine Gravity

We derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.Comment: 16 page

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

Black hole solutions in scalar-tensor symmetric teleparallel gravity

Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include $f(Q)$ gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other ($g_{rr}=1/g_{tt}$), the $f(Q)$ gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.Comment: Matches published version in JCAP. 24 pages, 1 figur

Cosmological Perturbation Theory in Metric-Affine Gravity

We formulate cosmological perturbation theory around the spatially curved FLRW background in the context of metric-affine gauge theory of gravity which includes torsion and nonmetricity. Performing scalar-vector-tensor decomposition of the spatial perturbations, we find that the theory displays a rich perturbation spectrum with helicities 0, 1, 2 and 3, on top of the usual scalar, vector and tensor metric perturbations arising from Riemannian geometry. Accordingly, the theory provides a diverse phenomenology, e.g. the helicity-2 modes of the torsion and/or nonmetricity tensors source helicity-2 metric tensor perturbation at the linear level leading to the production of gravitational waves. As an immediate application, we study linear perturbation of the nonmetricity helicity-3 modes for a general parity-preserving action of metric-affine gravity which includes quadratic terms in curvature, torsion, and nonmetricity. We then find the conditions to avoid possible instabilities in the helicity-3 modes of the spin-3 field.Comment: 23+20 pages, 5 appendice

Singularities and n-dimensional black holes in torsion theories

In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole regions of arbitrary codimension defined inside a spacetime of arbitrary dimension. We discuss this prescription by increasing the complexity of the particular torsion theory under study. In this sense, we start with Teleparallel Gravity, then we analyse Einstein-Cartan theory, and finally dynamical torsion models