Olivera Miskovic

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter gravity action in four dimensions recovers the standard regularization given by the holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows one to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as T{sub j}{sup i}={+-}(l{sup 2}/8{pi}G)C{sub j}{sup i}, which has been observed in recent literature in solitonic solutions and hydrodynamic models. A general procedure to generate the counterterm series for anti-de Sitter gravity in any even dimension from the corresponding Euler term is also briefly discussed.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in

Thermodynamics of Einstein-Born-Infeld black holes with negative cosmological constant

D

Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension

Renormalized AdS action and Critical Gravity

D

Conformal mass in AdS gravity

and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to

Holography in 3D AdS gravity with torsion

Dg4

Nonlinear electrodynamics in 3D gravity with torsion

the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.

Black hole solutions in Chern-Simons AdS supergravity

We study the thermodynamics associated to topological black hole solutions of AdS gravity coupled to nonlinear electrodynamics (Born-Infeld) in any dimension, using a background-independent regularization prescription for the Euclidean action given by boundary terms, which explicitly depend on the extrinsic curvature (Kounterterms series). A finite action principle leads to the correct definition of thermodynamic variables as Noether charges, which satisfy a Smarr-like relation. In particular, for the odd-dimensional case, a consistent thermodynamic description is achieved if the internal energy of the system includes the vacuum energy for AdS spacetime.

Free energy of a Lovelock holographic superconductor

We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of a Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics. These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, we derive a quantum statistical relation directly from the Euclidean action and not from the integration of the first law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists, in addition to the bulk action, of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian.