arXiv subjects
Publications and source records attributed to Jerzy Matyjasek.
Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.
The components of the renormalized quantum Energy-Momentum tensor for a massive vector field coupled to the gravitational field configuration of a static Black-String are analytically evaluated using the Schwinger-DeWitt approximation. The general results are employed to investigate the pointwise energy conditions for the quantized matter field, and it is shown that they are violated at some regions of the spacetime, in particular the horizon of the black hole.
The approximation of the renormalized stress-energy tensor of the quantized massive scalar field in Reissner-Nordström spacetime is constructed. It is achieved by functional differentiation of the first two nonvanishing terms of the Schwinger-DeWitt expansion involving the coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $[a_{3}]$ and $[a_{4}]$ with respect to the metric tensor. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tensor. The approximation to the field fluctuation, $\langle ϕ^{2} \rangle,$ is constructed and briefly discussed.
The second-order term of the approximate stress-energy tensor of the quantized massive scalar field in the Bertotti-Robinson and Reissner- Nordström spacetimes is constructed within the framework of the Schwinger-DeWitt method. It is shown that although the Bertotti- Robinson geometry is a self-consistent solution of the ($Λ=0$) semiclassical Einstein field equations with the source term given by the leading term of the renormalized stress-energy tensor, it does not remain so when the next-to-leading term is taken into account and requires the introduction of a cosmological term. The addition of the electric charge to the system does not change this behavior. The near horizon geometry of the extreme quantum-corrected Reissner-Nordström black hole is analyzed. It has the $AdS_{2} \times S^{2}$ topology and the sum of the curvature radii of the two dimensional submanifolds is proportional to the trace of the second order term. It suggests that the "minimal" approximation should be constructed from the first two terms of the Schwinger-DeWitt expansion.
The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed. It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $a_{3}$ and $a_{4}.$ The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed.
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 $AdS_{2}\times S^{2}$ for the cold black hole, $dS_{2}\times S^{2}$ when the event and cosmological horizon coincide, and the Plebański- Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyzed
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.
Employing the Noether charge technique and Visser's Euclidean approach the entropy of the nonlinear black hole described by the perturbative solution of the system of coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed. The solution is parametrized by the exact location of the event horizon and charge. Special emphasis in put on the extremal configuration. Consequences of the second choice of the boundary conditions, in which the solution is paramerized by the charge and the total mass as seen by a distant observer is briefly examined.
Building on general formulas obtained from the approximate renormalized effective action, the stress-energy tensor of the quantized massive spinor and vector fields in the spacetime of the regular black hole is constructed. Such a black hole is the solution to the coupled system of nonlinear electrodynamics and general relativity. A detailed analytical and numerical analysis of the stress-energy tensor in the exterior region is presented. It is shown that for small values of the charge as well as large distances from the black hole the leading behavior of the stress-energy tensor is similar to that in the Reissner-Nordström geometry. Important differences appear when the inner horizon becomes close to the event horizon. A special emphasis is put on the extremal configuration and it is shown that the stress-energy tensor is regular inside the event horizon of the extremal black hole.
The approximate renormalized one-loop effective action of the quantized massive scalar, spinor and vector field in a large mass limit, i.e., the lowest order of the DeWitt-Schwinger expansion involves the coincidence limit of the Hadamard-DeWitt coefficient a3. Building on this and using Wald's approach we shall construct the general expression describing entropy of the spherically-symmetric static black hole being the solution of the semi-classical field equations. For the concrete case of the quantum-corrected Reissner-Nordstrom black hole this result coincides, as expected, with the entropy obtained by integration of the first law of black hole thermodynamics with a suitable choice of the integration constant. The case of the extremal quantum corrected black hole is briefly considered.
We consider the most general higher order corrections to the pure gravity action in $D$ dimensions constructed from the basis of the curvature monomial invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively solving the resulting sixth-order equations we analyze the influence of the corrections upon a static and spherically symmetric back hole. Treating the total mass of the system as the boundary condition we calculate location of the event horizon, modifications to its temperature and the entropy. The entropy is calculated by integrating the local geometric term constructed from the derivative of the Lagrangian with respect to the Riemann tensor over a spacelike section of the event horizon. It is demonstrated that identical result can be obtained by integration of the first law of the black hole thermodynamics with a suitable choice of the integration constant. We show that reducing coefficients to the Lovelock combination, the approximate expression describing entropy becomes exact. Finally, we briefly discuss the problem of field redefinition and analyze consequences of a different choice of the boundary conditions in which the integration constant is related to the exact location of the event horizon and thus to the horizon defined mass.
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 Garc{\'ı}a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's 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.
We examine backreaction of quantum massive fields on multiply-degenerate (ultraextremal) horizons. It is shown that, under influence of the quantum backreaction, the horizon of such a kind moves to a new position, near which the metric does not change its asymptotics, so the ultraextremal black holes and cosmological spacetimes do exist as self-consistent solutions of the semiclassical field equations.
The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in a good agreement with the numerical calculations. The back reaction of the quantized field upon the spacetime metric is briefly discussed.
We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace the origin of the inconsistency between a charge and rotation, considering the BR-like spacetime as a result of the limiting transition of a non-extremal black hole to the extremal state. We also find that the quasilocal energy and angular momentum of such BR-like spacetimes calculated within the boundary $l=const$ ($l$ is the proper distance) are constants independent of the position of the boundary.
The near horizon limit of the extreme nonlinear black hole is investigated. It is shown that resulting geometry belongs to the AdS2xS2 class with different modules of curvatures of subspaces and could be described in terms of the Lambert functions. It is demonstrated that the considered class of Lagrangians does not admit solutions of the Bertotti-Robinson type.
Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. Obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit, the exact location of the (degenerate) event horizon is given by $\rp = |e|.$ Similarly to the classical Reissner-Nordström solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for the boundary conditions of second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed.
Employing the approximate effective action constructed from the coincidence limit of the Hadamard-Minakshisundaram-DeWitt (HaMiDeW) coefficient a_{3}, the renormalized stress-energy tensor of the quantized massive scalar field in the spacetime of a static and electrically charged dilatonic black hole is calculated. Special attention is paid to the minimally and conformally coupled fields propagating in geometries with a=1, and to the power expansion of the general stress-energy tensor for small values of charge. A compact expression for the trace of the stress-energy tensor is presented.