Jerzy Matyjasek

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garcí a and by Bronnikov. It is shown that a simple generalization of the Bronnikovs electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Extremal limit of the regular charged black holes in nonlinear electrodynamics

Solutions of the coupled equations of general relativity and nonlinear electrodynamics with topology

REGULAR BLACK HOLES IN AN ASYMPTOTICALLY DE SITTER UNIVERSE

{\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{2}

SOME REMARKS ON THE EINSTEIN AND MØLLER PSEUDOTENSORS FOR STATIC AND SPHERICALLY-SYMMETRIC CONFIGURATIONS

are constructed and studied both analytically and numerically. It is shown that the near horizon limit of the extreme nonlinear black hole corresponds to the solution expressible in terms of the Lambert special functions. It is explicitly demonstrated that for the formulation of the nonlinear theory considered in this paper the resulting solutions do not belong to the Bertotti-Robinson class unless electrodynamics is Maxwellian. The question of the boundary conditions is briefly discussed.

Stress energy tensor of neutral massive fields in the Reissner-Nordstrom space-time

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are AdS2×S2 for the cold black hole, dS2×S2 when the event and cosmological horizon coincide, and the Plebanski–Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyzed.

Inside the degenerate horizons of regular black holes

It is shown that for the spherically-symmetric and static systems the hypotheses posed by Yang and Radinschi and by Vagenas can be related to the particular distribution of the source. Simple proofs are given and a number of examples are discussed with the special emphasis put on the quantum corrected Schwarzschild black hole.

Higher dimensional black holes with a generalized gravitational action

The approximation of the renormalized stress-energy tensor of the quantized massive scalar, spinor, and vector field in the Reissner- Nordstrom spacetime is constructed. It is achieved by functional differentiation of the lowest order of the Schwinger-DeWitt effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient a_{3}, and restricting thus obtained general formulas to spacetimes with vanishing curvature scalar. For the massive scalar field with arbitrary curvature coupling our results reproduce those obtained previously by Anderson, Hiscock, and Samuel by means of 6-th order WKB approximation.

Extremal limit for charged and rotating 2+1-dimensional black holes and Bertotti-Robinson geometry

The regularized stress-energy tensor of the quantized massive scalar, spinor and vector fields inside the degenerate horizon of the regular charged black hole in the (anti-)de Sitter universe is constructed and examined. It is shown that although the components of the stress-energy tensor are small in the vicinity of the black hole degenerate horizon and near the regular center, they are quite big in the intermediate region. The oscillatory character of the stress-energy tensor can be ascribed to various responses of the higher curvature terms to the changes of the metric inside the (degenerate) event horizon, especially in the region adjacent to the region described by the nearly flat metric potentials. Special emphasis is put on the stress-energy tensor in the geometries being the product of the constant curvature two-dimensional subspaces.

Cosmic strings in Lyra geometry

We consider the most general higher-order corrections to the pure gravity action in

(ren) of the quantized fields in the Unruh state in the Schwarzschild space-time

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