Search

We analyse the stability issue of the vector and axial modes of the torsion and nonmetricity tensors around general backgrounds in the framework of cubic Metric-Affine Gravity. We show that the presence of cubic order invariants defined from the curvature, torsion and nonmetricity tensors allow the cancellation of the well-known instabilities arising in the vector and axial sectors of quadratic Metric-Affine Gravity. For the resulting theory, we also obtain Reissner-Nordstr\"om-like black hole solutions with dynamical torsion and nonmetricity, which in general include massive tensor modes for these quantities, thus avoiding further no-go theorems that potentially prevent a consistent interaction of massless higher spin fields in the quantum regime., Comment: 50 pages. arXiv admin note: text overlap with arXiv:2402.08937

We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the presence of the traceless nonmetricity tensor. This quantity switches on four of the eleven fundamental parts of the irreducible representation of the curvature tensor under the pseudo-orthogonal group, in such a way that three of them present similar algebraic types as the ones obtained in Weyl-Cartan geometry, whereas the remaining one includes thirty independent components and gives rise to a new algebraic classification. The latter is derived by means of its principal null directions and their levels of alignment, obtaining a total number of sixteen main algebraic types, which can be split into many subtypes. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity., Comment: 48 pages, 5 figures, minor changes, references added. It matches the version published in PRD

We analyse the stability of the vector and axial sectors of Poincar\'e gauge theory around general backgrounds in the presence of cubic order invariants defined from the curvature and torsion tensors, showing how the latter can in fact cancel out well-known instabilities arising from the quadratic curvature invariants of the theory and accordingly help in the construction of healthy models with both curvature and torsion. For this task, we introduce the most general parity preserving cubic Lagrangian with mixing terms of the curvature and torsion tensors, and find the relations of its coefficients to avoid a pathological behaviour from the vector and axial modes of torsion. As a result, on top of the gravitational constant of General Relativity and the mass parameters of torsion, our action contains 23 additional coupling constants controlling the dynamics of this field. As in the quadratic Poincar\'e gauge theory, we show that a further restriction on the cubic part of the action allows the existence of Reissner-Nordstr\"om-like black hole solutions with dynamical torsion., Comment: 16 pages, minor changes, references added. It matches the version published in PRD

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: Matches published version in PRD. 23+20 pages, 5 appendices

We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric space-times., Comment: 22 pages, minor changes, references added. It matches the version published in PRD Mathematica file as supplemental material available at https://community.wolfram.com/groups/-/m/t/2996064

In the framework of Metric-Affine Gravity, the existing correspondence between the Einstein tensor and the energy-momentum tensor of matter provided by General Relativity is extended towards a post-Riemannian description in terms of the torsion and nonmetricity fields, which are sourced by the spin, dilation and shear currents of matter. In this work, we focus on the dynamical role of the traceless part of the nonmetricity tensor and its intrinsic connection with shears, defining a model which encloses a new black hole solution endowed with shear charges. We show that the extension in the presence of dynamical torsion and Weyl vector leads to the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity so far., Comment: 21 pages, 0 figures, minor changes, references added. It matches the version published in JCAP

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 figure

We construct Pleba\'nski-Demia\'nski stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolsk\'y and Vr\'atn\'y, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characterised by the mass, orbital angular momentum, acceleration, NUT parameter, cosmological constant and electromagnetic charges of the Riemannian sector of the theory, as well as by the spin and dilation charges of the torsion and nonmetricity fields. The former is subject to a constraint representing a decoupling limit with the parameters responsible of axial symmetry, beyond which the geometry of the space-time is expected to be corrected., Comment: 18 pages, minor changes, references added. It matches the version published in JCAP

We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum. The corresponding Kerr-Newman-de Sitter solution is also compatible with a cosmological constant and additional electromagnetic fields., Comment: 13 pages, 0 figures, minor changes, references added. It matches the version published in JCAP

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 pages; Matches published version in EPJC

Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing independent connection components, the notion of symmetry concerns, not just the metric, but also the connection. As discovered recently, in teleparallel geometries, axial symmetry can be realised in two branches, while only one of these has a continuous spherically symmetric limit. In the current paper, we consider a very generic $f(T,B,\phi,X)$ family of teleparallel gravities, whose action depends on the torsion scalar $T$ and the boundary term $B$, as well as a scalar field $\phi$ with its kinetic term $X$. As the field equations can be decomposed into symmetric and antisymmetric (spin connection) parts, we thoroughly analyse the antisymmetric equations and look for solutions of axial spacetimes which could be used as ans\"atze to tackle the symmetric part of the field equations. In particular, we find solutions corresponding to a generalisation of the Taub-NUT metric, and the slowly rotating Kerr spacetime. Since this work also concerns a wider issue of how to determine the spin connection in teleparallel gravity, we also show that the method of "turning off gravity" proposed in the literature, does not always produce a solution to the antisymmetric equations., Comment: 26 pages, 1 figure. Matches published version in PRD

We propose a gravitational model which allows the independent dynamical behaviour of the torsion and nonmetricity fields to be displayed in the framework of Metric-Affine gauge theory of gravity. For this task, we derive a new exact black hole solution referred to this model which extends the role of torsion of the main well-known exact solutions based on Weyl-Cartan geometry and constitutes the first known isolated gravitational system characterized by a metric tensor with independent spin and dilation charges., Comment: 15 pages, 0 figures, minor changes, references added. It matches the version published in JCAP

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 added

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., Comment: A missing -1 factor in the pseudo-vectorial sector has been detected in Appendix D, conclusions partially changed in sections 3.3 and 4

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 added

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. D

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. C