"No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction

Self-gravitating scalar fields with nonminimal coupling to gravity and having a quartic self-interaction are considered in the domain of outer communications of a static black hole. It is shown that there is no value of the nonminimal coupling parameter $\zeta$ for which nontrivial static black hole solutions exist. This result establishes the correctness of Bekenstein ``no-scalar-hair'' conjecture for quartic self-interactions.Comment: 8 pages, RevTeX

Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L(F)$, $F = F_mn F^mn$ having a correct weak field limit, leads to nontrivial static, spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and $L(F)$ tends to a finite limit as $F \to \infty$. Properties and examples of such solutions, which include magnetic black holes and soliton-like objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called $FP$ duality) is used as a tool for this comparison.Comment: 6 pages, Latex2e. One more theorem, some comments and two references have been added. Final journal versio

No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black Holes

The vanishing of the electromagnetic field, for purely electric configurations of spontaneously broken Abelian models, is established in the domain of outer communications of a static asymptotically flat black hole. The proof is gauge invariant, and is accomplished without any dependence on the model. In the particular case of the Abelian Higgs model, it is shown that the only solutions admitted for the scalar field become the vacuum expectation values of the self-interaction.Comment: 8 pages, 2 figures, RevTeX; some changes to match published versio

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

Non-Abelian Einstein-Born-Infeld Black Holes

We construct regular and black hole solutions in SU(2) Einstein-Born-Infeld theory. These solutions have many features in common with the corresponding SU(2) Einstein-Yang-Mills solutions. In particular, sequences of neutral non-abelian solutions tend to magnetically charged limiting solutions, related to embedded abelian solutions. Thermodynamic properties of the black hole solutions are addressed.Comment: LaTeX, 14 pages, 6 postscript figures; typos corrected in reference

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

Vacuum polarization of massive scalar fields in the spacetime of the electrically charged nonlinear black hole

The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient $a_{3}.$ The result is compared with the analogous result derived for the Reissner-Nordstr\"om black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the extremality limit. The structure of the nonlinear black hole is briefly studied by means of the Lambert functions.Comment: 22 pages, 10 figure

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

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