Smarr's formula for black holes with non-linear electrodynamics

It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.Comment: 10 pages, 3 figures.Contribution to the Festscrift of Prof. A. Garci

Exploring AdS Waves Via Nonminimal Coupling

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a non-perturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity.Comment: 26 pages, 1 figure. Minor change

Deeper discussion of Schr\"odinger invariant and Logarithmic sectors of higher-curvature gravity

The aim of this paper is to explore D-dimensional theories of pure gravity whose space of solutions contains certain class of AdS-waves, including in particular Schrodinger invariant spacetimes. This amounts to consider higher order theories, and the natural case to start with is to analyze generic square-curvature corrections to Einstein-Hilbert action. In this case, the Schrodinger invariant sector in the space of solutions arises for a special relation between the coupling constants appearing in the action. On the other hand, besides the Schrodinger invariant configurations, logarithmic branches similar to those of the so-called Log-gravity are also shown to emerge for another special choice of the coupling constants. These Log solutions can be interpreted as the superposition of the massless mode of General Relativity and two scalar modes that saturate the Breitenlohner-Freedman bound (BF) of the AdS space on which they propagate. These solutions are higher-dimensional analogues of those appearing in three-dimensional massive gravities with relaxed AdS_3 asymptotic. Other sectors of the space of solutions of higher-curvature theories correspond to oscillatory configurations, which happen to be below the BF bound. Also, there is a fully degenerated sector, for which any wave profile is admitted. We comment on the relation between this degeneracy and the non-renormalization of the dynamical exponent of the Schrodinger spaces. Our analysis also includes more general gravitational actions with non-polynomial corrections consisting of arbitrary functions of the square-curvature invariants. The same sectors of solutions are shown to exist for this more general family of theories. We finally consider the Chern-Simons modified gravity in four dimensions, for which we derive both the Schrodinger invariant as well as the logarithmic sectors.Comment: This paper is dedicated to the memory of Laurent Houar

Black hole solutions in Euler-Heisenberg theory

We construct static and spherically symmetric black hole solutions in the Einstein-Euler-Heisenberg (EEH) system which is considered as an effective action of a superstring theory. We considered electrically charged, magnetically charged and dyon solutions. We can solve analytically for the magnetically charged case. We find that they have some remarkable properties about causality and black hole thermodynamics depending on the coupling constant of the EH theory $a$ and $b$, though they have central singularity as in the Schwarzschild black hole.Comment: 8 pages, 13 figures, figures corrected and some comments adde

The family of regular interiors for non-rotating black holes with T00=T11T^0_0 = T^1_1

We find the general solution for the spacetimes describing the interior of static black holes with an equation of state of the type $T^0_0 = T^1_1$ ($T$ being the stress-energy tensor). This form is the one expected from taking into account different quantum effects associated with strong gravitational fields. We recover all the particular examples found in the literature. We remark that all the solutions found follow the natural scheme of an interior core linked smoothly with the exterior solution by a transient region. We also discuss their local energy properties and give the main ideas involved in a possible generalization of the scheme, in order to include other realistic types of sources.Comment: 31 pages, 1 figure, version to appear in Physical Review

How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein's gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity. A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell's equations expressed in terms of the excitation H=(D,H) and the field strength F=(E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H= functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al. (eds.). Springer, Berlin (2000) to be published (Revised version uses Springer Latex macros; Sec. 6 substantially rewritten; appendices removed; the list of references updated

Dyonic BIon black hole in string inspired model

We construct static and spherically symmetric particle-like and black hole solutions with magnetic and/or electric charge in the Einstein-Born-Infeld-dilaton-axion system, which is a generalization of the Einstein-Maxwell-dilaton-axion (EMDA) system and of the Einstein-Born-Infeld (EBI) system. They have remarkable properties which are not seen for the corresponding solutions in the EMDA and the EBI system.Comment: 13 pages, 15 figures, Final version in PR

Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

The first regular exact black hole solution in General Relativity is presented. The source is a nonlinear electrodynamic field satisfying the weak energy condition, which in the limit of weak field becomes the Maxwell field. The solution corresponds to a charged black hole with |q| \leq 2 s_c m \approx 0.6 m, having the metric, the curvature invariants, and the electric field regular everywhere.Comment: 5 pages, RevTex, 6 figure

A physical application of Kerr-Schild groups

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminar study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ans\"atze to finding useful solutions to Einstein's equations.Comment: 18 page

Chiral Topologically Massive Gravity and Extremal B-F Scalars

At a critical ``chiral'' coupling, topologically massive gravity with a negative cosmological constant exhibits several unusual features, including the emergence of a new logarithmic branch of solutions and a linearization instability for certain boundary conditions. I show that at this coupling, the linearized theory may be parametrized by a free scalar field at the Breitenlohner-Freedman bound, and use this description to investigate these features.Comment: 16 pages; v2: added references, typos correcte