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Beltran Jimenez, J., de Andres, D., & Delhom, A. (2020). Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity. Class. Quantum Gravity, 37(22), 225013–25pp.
Abstract: Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energy-momentum tensor, it respects isotropy. In this work we discuss this condition and, in particular, we show how the deformation matrix can be anisotropic even in the presence of isotropic sources due to the non-linear nature of the equations. Remarkably, we find that Eddington-inspired-Born-Infeld (EiBI) theories do not admit anisotropic deformations, but more general theories do. However, we find that the anisotropic branches of solutions are generally prone to a pathological physical behaviour.
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Navarro-Salas, J. (2024). Black holes, conformal symmetry, and fundamental fields. Class. Quantum Gravity, 41(8), 085003–14pp.
Abstract: Cosmic censorship protects the outside world from black hole singularities and paves the way for assigning entropy to gravity at the event horizons. We point out a tension between cosmic censorship and the quantum backreacted geometry of Schwarzschild black holes, induced by vacuum polarization and driven by the conformal anomaly. A similar tension appears for the Weyl curvature hypothesis at the Big Bang singularity. We argue that the requirement of exact conformal symmetry resolves both conflicts and has major implications for constraining the set of fundamental constituents of the Standard Model.
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Borja, E. F., Diaz-Polo, J., Garay, I., & Livine, E. R. (2010). Dynamics for a 2-vertex quantum gravity model. Class. Quantum Gravity, 27(23), 235010–34pp.
Abstract: We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.
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Borja, E. F., Freidel, L., Garay, I., & Livine, E. R. (2011). U(N) tools for loop quantum gravity: the return of the spinor. Class. Quantum Gravity, 28(5), 055005–28pp.
Abstract: We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity and describe the corresponding phase space in terms of spinors with the appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wavefunctions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.
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Lledo, M. A., & Sommovigo, L. (2010). Torsion formulation of gravity. Class. Quantum Gravity, 27(6), 065014–16pp.
Abstract: We explain precisely what it means to have a connection with torsion as a solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.
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Borja, E. F., Garay, I., & Strobel, E. (2012). Revisiting the quantum scalar field in spherically symmetric quantum gravity. Class. Quantum Gravity, 29(14), 145012–19pp.
Abstract: We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As a starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini et al (2009 Class. Quantum Grav. 26 215011 (arXiv: 0906.1774v1)) and a comparison between their result and the one given in this work is made.
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Babichev, E., & Fabbri, A. (2013). Instability of black holes in massive gravity. Class. Quantum Gravity, 30(15), 152001–7pp.
Abstract: We show that linear perturbations around the simplest black hole solution of massive bi-gravity theories, the bi-Schwarzschild solution, exhibit an unstable mode featuring the Gregory-Laflamme instability of higher dimensional black strings. The result is obtained for the massive gravity theory which is free from the Boulware-Deser ghost, as well as for its extension with two dynamical metrics. These results may indicate that static black holes in massive gravity do not exist. For the graviton mass of the order of the Hubble scale, however, the instability timescale is of order of the Hubble time.
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Clement, G., & Fabbri, A. (2015). A scenario for critical scalar field collapse in AdS(3). Class. Quantum Gravity, 32(9), 095009–16pp.
Abstract: We present a family of exact solutions, depending on two parameters alpha and b (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant Lambda. For b not equal 0 these solutions reduce to the static Banados-Teitelboim-Zanelli (BTZ) family of vacuum solutions, with mass M = -alpha. For b not equal 0, the solutions become dynamical and develop a strong spacelike central singularity. The alpha < 0 solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with alpha > 0 agrees qualitatively with that observed in numerical simulations of sub-critical collapse, including the independence of the near-critical regime on the angle deficit of the spacetime. We analyze in the Lambda = 0 approximation the linear perturbations of the self-similar threshold solution, alpha = 0, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.
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Bazeia, D., Losano, L., Menezes, R., Olmo, G. J., & Rubiera-Garcia, D. (2015). Robustness of braneworld scenarios against tensorial perturbations. Class. Quantum Gravity, 32(21), 215011–10pp.
Abstract: Inspired by the peculiarities of the effective geometry of crystalline structures, we reconsider thick brane scenarios from a metric-affine perspective. We show that for a rather general family of theories of gravity, whose Lagrangian is an arbitrary function of the metric and the Ricci tensor, the background and scalar field equations can be written in first-order form, and tensorial perturbations have a non negative definite spectrum, which makes them stable under linear perturbations regardless of the form of the gravity Lagrangian. We find, in particular, that the tensorial zero modes are exactly the same as predicted by Einstein's theory regardless of the scalar field and gravitational Lagrangians.
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Olmo, G. J., Rubiera-Garcia, D., & Sanchez-Puente, A. (2016). Impact of curvature divergences on physical observers in a wormhole space-time with horizons. Class. Quantum Gravity, 33(11), 115007–12pp.
Abstract: The impact of curvature divergences on physical observers in a black hole space-time, which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of general relativity coupled to Maxwell's electrodynamics and, roughly speaking, consists of two Reissner-Nordstrom (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not be as pathological as traditionally thought.
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