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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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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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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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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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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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