Examinando por Autor "Olea, R."
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Ítem Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions(American Physical Society, 2018-08) Deruelle, N.; Merino, N.; Olea, R.In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid manifold whose geometry we construct explicitly. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions D=2, 4, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-defined variational principle with Dirichlet boundary conditions. © 2018 American Physical Society.Ítem Conserved charges for even dimensional asymptotically AdS gravity theories(American Physical Society, 2000-08) Aros, R.; Contreras, M.; Olea, R.; Troncoso, R.; Zanelli, J.Mass and other conserved Noether charges are discussed for solutions of gravity theories with locally anti-de Sitter (AdS) asymptotics in 2n dimensions. The action is supplemented with a boundary term whose purpose is to guarantee that it reaches an extremum on the classical solutions, provided the space-time is locally AdS space-time at the boundary. It is also shown that if space-time is locally AdS at spatial infinity, the conserved charges are finite and properly normalized without requiring subtraction of a reference background. In this approach, Noether charges associated with Lorentz and diffeomorphism invariance vanish identically for constant curvature space-times. The case of a zero cosmological constant is obtained as a limit of AdS space-time, where Λ plays the role of a regulator. ©2000 The American Physical Society.Ítem Conserved Charges for Gravity with Locally Anti–de Sitter Asymptotics(American Physical Society, 2000-02) Aros, R; Contreras, M.; Olea, R.; Troncoso, R.; Zanelli, J.A new formula for the conserved charges in 3+1 gravity for spacetimes with local anti-de Sitter asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the Λ = 0 limit.Ítem Conserved quantities for a charged rotating black holes in 5D Einstein-Maxwell-Chern-Simons theory(Institute of Physics Publishing, 2018-06) Diaz-Martinez, F.; Olea, R.In this work, we compute the conserved quantities of a charged rotating black hole which appears as the solution of Einstein-Maxwell action in five dimensions coupled to a Chern-Simons term for U(1) field. The addition of the Chern-Simons term will modify the Maxwell equations and the definition of charge but not the Einstein field equations. Upon the addition of suitable boundary terms for the pure gravity sector of the theory, which depend on the extrinsic and intrinsic curvatures (Kounterterms), we obtain the correct conserved quantities of the solution. © Published under licence by IOP Publishing Ltd.Ítem Counterterms, Kounterterms, and the variational problem in AdS gravity(Springer, 2020-08) Anastasiou, G.; Miskovic, O.; Olea, R.; Papadimitriou, I.We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms. © 2020, The Author(s).Ítem Einstein-AdS action, renormalized volume/area and holographic Rényi entropies(Springer Verlag, 2018-08) Anastasiou, G.; Araya, I.J.; Arias, C.; Olea, R.We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered. © 2018, The Author(s).Ítem Energy in higher-derivative gravity via topological regularization(American Physical Society, 2018-08) Giribet, G.; Miskovic, O.; Olea, R.; Rivera-Betancour, D.We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein's equations. We focus on the theory in four dimensions, in the presence of a negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method is qualitatively different due to the fact that it is intrinsically nonlinear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions such as gravitational waves in AdS, for which we also find results that are in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory. © 2018 authors. Published by the American Physical Society.Ítem Holographic correlation functions in Critical Gravity(Springer Verlag, 2017) Anastasiou, G.; Olea, R.We compute the holographic stress tensor and the logarithmic energy-momentum tensor of Einstein-Weyl gravity at the critical point. This computation is carried out performing a holographic expansion in a bulk action supplemented by the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined by the addition of this topological term has the remarkable feature that all Einstein modes are identically cancelled both from the action and its variation. Thus, what remains comes from a nonvanishing Bach tensor, which accounts for non-Einstein modes associated to logarithmic terms which appear in the expansion of the metric. In particular, we compute the holographic 1-point functions for a generic boundary geometric source.Ítem Noether-Wald Charges in Critical Gravity(Institute of Physics Publishing, 2018-06) Rivera-Betancour, D.; Olea, R.Critical Gravity theory is defined by a particular combination of quadratic couplings in the curvature added on top of 4D Einstein-Hilbert action with negative cosmological constant. As the Lagrangian is given by a Weyl-squared term, the asymptotic form of the curvature is not modified. The coupling of the W eyl 2 term is such the massive scalar mode is eliminated and the massive spin-2 mode become massless, rendering the theory consistent around the critical point. In the present work, we construct the Noether-Wald charges for the action of Critical Gravity. Such construction makes manifest a defining property of this theory: both the energy and entropy for Einstein black holes vanish identically. © Published under licence by IOP Publishing Ltd.Ítem Noether–Wald energy in Critical Gravity(Elsevier B.V., 2019-01) Anastasiou, G.; Olea, R.; Rivera-Betancour, D.Criticality represents a specific point in the parameter space of a higher-derivative gravity theory, where the linearized field equations become degenerate. In 4D Critical Gravity, the Lagrangian contains a Weyl-squared term, which does not modify the asymptotic form of the curvature. The Weyl2 coupling is chosen such that it eliminates the massive scalar mode and it renders the massive spin-2 mode massless. In doing so, the theory turns consistent around the critical point. Here, we employ the Noether–Wald method to derive the conserved quantities for the action of Critical Gravity. It is manifest from this energy definition that, at the critical point, the mass is identically zero for Einstein spacetimes, what is a defining property of the theory. As the entropy is obtained from the Noether–Wald charges at the horizon, it is evident that it also vanishes for any Einstein black hole. © 2018 The Author(s)Ítem Pontryagin Term and Magnetic Mass in 4D AdS Gravity(Institute of Physics Publishing, 2018-06) Araneda, R.; Aros, R.; Miskovic, O.; Olea, R.In the context of the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, 4D AdS gravity is suitably renormalized by adding the Gauss Bonnet term to the Einstein-Hilbert action. The subsequent addition of the Pontryagin term, with a specific coupling, allows to write the on-shell action in terms of the Weyl tensor and its dual, such that the action becomes stationary for asymptotic (anti) self-dual solutions in the Weyl tensor. The addition to the action of both topological invariants mentioned above does not modify the bulk dynamics, but it does modify the expression of the Noether current and, therefore, the conserved quantities of the theory. Here, we show that the method of Iyer and Wald leads to a fully-covariant Noether charge, which contains both the electric and magnetic parts of the Weyl tensor. For configurations which are globally (anti) self-dual in the Weyl tensor, both the action and the Noether charge identically vanish. This means that, for such spacetimes, the magnetic mass is equal to the electric mass. © Published under licence by IOP Publishing Ltd.Ítem Shape dependence of renormalized holographic entanglement entropy(Springer Science and Business Media Deutschland GmbH, 2020-09) Anastasiou, G.; Moreno, J.; Olea, R.; Rivera-Betancour, D.We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even- dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS4/CFT3, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property. © 2020, The Author(s).Ítem Spiky ice and penitente tilting(Institute of Physics Publishing, 2018-06) Guilleminot, P.; Olea, R.Under certain conditions, at high altitude, the surface of snow develops spike-like structures known as penitentes. This is a rather counterintuitive phenomenon, which is a consequence of surface sublimation at a given point as a result of the incidence of light scattered by the surrounding region. Following the existing literature, we model the time evolution of the phenomenon described above as a 1D diffusion equation with a non-local source term, as it represents the light coming from all the line of sight defined for a point of the curve. For small initial perturbations in the surface, the system undergoes a thermodynamic instability which triggers the formation of spikes. For sunlight coming in at a given angle, numerical simulations account for a feature observed in the real system: penitentes get tilted in the direction of the sunlight. © Published under licence by IOP Publishing Ltd.Ítem Thermodynamics of black holes in Einstein-Gauss-Bonnet AdS gravity coupled to nonlinear electrodynamics(World Scientific Publishing, 2012) Mišković, O.; Olea, R.In an arbitrary dimension D, we study quadratic corrections to Einstein-Hilbert action described by the Gauss-Bonnet term. We consider charged black hole solutions with anti-de Sitter (AdS) asymptotics, of interest in the context of gravity/gauge theory dualities (AdS/CFT). The electric charge here is due to the addition of an arbitrary nonlinear electrodynamics (NED) Lagrangian. Due to the existence of a vacuum energy for global AdS spacetime in odd dimensions in the framework of AdS/CFT correspondence, we derive a Quantum Statistical Relation directly from the Euclidean action and not from the First Law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists in supplementing the bulk action with counterterms that depend both on the extrinsic and intrinsic curvatures of the boundary (also known as Kounterterms). This procedure results in a consistent inclusion of the vacuum energy in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless the explicit form of the NED Lagrangian.Ítem Vacuum degeneracy and Conformal Mass in Lovelock AdS gravity(Springer Verlag, 2017-11) Arenas-Henriquez, G.; Miskovic, O.; Olea, R.It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case.