Alberto García

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.

New regular black hole solution from nonlinear electrodynamics

Abstract Using a nonlinear electrodynamics coupled to General Relativity a new regular exact black hole solution is found. The nonlinear theory reduces to the Maxwell one in the weak limit, and the solution corresponds to a charged black hole for |q|≤2s c m≈1.05 m , with metric, curvature invariants, and electric field regular everywhere.

The Bardeen model as a nonlinear magnetic monopole

Abstract The Bardeen model — the first regular black hole model in General Relativity — is reinterpreted as the gravitational field of a nonlinear magnetic monopole, i.e., as a magnetic solution to Einstein equations coupled to a nonlinear electrodynamics.

Non-Singular Charged Black Hole Solution for Non-Linear Source

A non-singular exact black hole solution inGeneral Relativity is presented. The source is anon-linear electrodynamic field, which reduces to theMaxwell theory for weak field. The solution corresponds to a charged black hole with |q| ≤2scm ≈ 0.6 m, having metric, curvatureinvariants, and electric field boundedeverywhere.

Higher order corrections to primordial spectra from cosmological inflation

Abstract We calculate power spectra of cosmological perturbations at high accuracy for two classes of inflation models. We classify the models according to the behaviour of the Hubble distance during inflation. Our approximation works if the Hubble distance can be approximated either to be a constant or to grow linearly with cosmic time. Many popular inflationary models can be described in this way, e.g., chaotic inflation with a monomial potential, power-law inflation and inflation at a maximum. Our scheme of approximation does not rely on a slow-roll expansion. Thus we can make accurate predictions for some of the models with large slow-roll parameters.

The Cotton tensor in Riemannian spacetimes

Recently, the study of three-dimensional spaces is becoming of great interest. In these dimensions the Cotton tensor is prominent as the substitute for the Weyl tensor. It is conformally invariant and its vanishing is equivalent to conformal flatness. However, the Cotton tensor arises in the context of the Bianchi identities and is present in any dimension n. We present a systematic derivation of the Cotton tensor. We perform its irreducible decomposition and determine its number of independent components as n(n2 − 4)/3 for the first time. Subsequently, we show its characteristic properties and perform a classification of the Cotton tensor in three dimensions. We investigate some solutions of Einsteins field equations in three dimensions and of the topologically massive gravity model of Deser, Jackiw and Templeton. For each class examples are given. Finally, we investigate the relation between the Cotton tensor and the energy–momentum in Einsteins theory and derive a conformally flat perfect fluid solution of Einsteins field equations in three dimensions.

Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments α and β, respectively. For α≥3, β≥4, and |q|≤2scm the corresponding solutions are regular charged black holes. For α = 3, they also satisfy the weak energy condition. For α = β = 0 we recover the Reissner–Nordström singular solution and for α = 3, β = 4 the family includes a previous regular black hole reported by the authors.

Exact vacuum solution of a(1+2)-dimensional Poincaré gauge theory: BTZ solution with torsion

In (1+2)-dimensional Poincare gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {em translational} and {em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {em Cartans} (3-dimensional) {em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque.

Symmetries of the stationary Einstein - Maxwell-dilaton system

The gravity-coupled three-dimensional -model describing the stationary Einstein - Maxwell-dilaton system with a general dilaton coupling constant is studied. The Killing equations for the corresponding five-dimensional target space are solved explicitly. It is shown that for the symmetry algebra is isomorphic to the maximal solvable subalgebra of the sl(3,R). For two critical values and , the Killing algebra is enlarged to the full sl(3,R) and the corresponding to the five-dimensional Kaluza - Klein and the four-dimensional Brans - Dicke - Maxwell theories, respectively. These two models are examined in terms of the same real variables. Non-trivial discrete maps between subspaces of the target space are found and used to generate new arbitrary- solutions to the dilaton gravity.

Regular (2+1)-dimensional black holes within nonlinear electrodynamics

(2+1)-regular static black hole solutions with a nonlinear electric field are derived. The source to the Einstein equations is an energy momentum tensor of nonlinear electrodynamics, which satisfies the weak energy conditions and in the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class of solutions is regular; the metric, curvature invariants and electric field are regular everywhere. The metric becomes, for a vanishing parameter, the (2+1)-static charged BTZ solution. A general procedure to derive solutions for the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the electric field is formulated; for relevant electric fields one requires the fulfillment of the weak energy conditions.