arXiv subjects

O. B. Zaslavskii

Publications and source records attributed to O. B. Zaslavskii.

At least 127 records · Page 7Linked to original sources

arXiv2004

Classical model of elementary particle with Bertotti-Robinson core and extremal black holes

We discuss the question, whether the Reissner-Nordström RN) metric can be glued to another solutions of Einstein-Maxwell equations in such a way that (i) the singularity at r=0 typical of the RN metric is removed (ii), matching is smooth. Such a construction could be viewed as a classical model of an elementary particle balanced by its own forces without support by an external agent. One choice is the Minkowski interior that goes back to the old Vilenkin and Fomin's idea who claimed that in this case the bare delta-like stresses at the horizon vanish if the RN metric is extremal. However, the relevant entity here is the integral of these stresses over the proper distance which is infinite in the extremal case. As a result of the competition of these two factors, the Lanczos tensor does not vanish and the extremal RN cannot be glued to the Minkowski metric smoothly, so the elementary-particle model as a ball empty inside fails. We examine the alternative possibility for the extremal RN metric - gluing to the Bertotti-Robinson (BR) metric. For a surface placed outside the horizon there always exist bare stresses but their amplitude goes to zero as the radius of the shell approaches that of the horizon. This limit realizes the Wheeler idea of "mass without mass" and "charge without charge". We generalize the model to the extremal Kerr-Newman metric glued to the rotating analog of the BR metric.

gr-qc↗

arXiv2004

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

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.

gr-qc↗

arXiv2004

Near-extremal and extremal quantum-corrected two-dimensional charged black holes

We consider charged black holes within dilaton gravity with exponential-linear dependence of action coefficients on dilaton and minimal coupling to quantum scalar fields. This includes, in particular, CGHS and RST black holes in the uncharged limit. For non-extremal configuration quantum correction to the total mass, Hawking temperature, electric potential and metric are found explicitly and shown to obey the first generalized law. We also demonstrate that quantum-corrected extremal black holes in these theories do exist and correspond to the classically forbidden region of parameters in the sense that the total mass $M_{tot} Q$.

gr-qc↗

arXiv2003

Two-dimensional quantum-corrected black hole in a finite size cavity

We consider the gravitation-dilaton theory (not necessarily exactly solvable), whose potentials represent a generic linear combination of an exponential and linear functions of the dilaton. A black hole, arising in such theories, is supposed to be enclosed in a cavity, where it attains thermal equilibrium, whereas outside the cavity the field is in the Boulware state. We calculate quantum corrections to the Hawking temperature $T_{H}$, with the contribution from the boundary taken into account. Vacuum polarization outside the shell tend to cool the system. We find that, for the shell to be in the thermal equilibrium, it cannot be placed too close to the horizon. The quantum corrections to the mass due to vacuum polarization vanish in spite of non-zero quantum stresses. We discuss also the canonical boundary conditions and show that accounting for the finiteness of the system plays a crucial role in some theories (e.g., CGHS), where it enables to define the stable canonical ensemble, whereas consideration in an infinite space would predict instability.

hep-th↗

arXiv2003

Boulware state and semiclassical thermodynamics of black holes in a cavity

A black hole, surrounded by a reflecting shell, acts as an effective star-like object with respect to the outer region that leads to vacuum polarization outside, where the quantum fields are in the Boulware state. We find the quantum correction to the Hawking temperature, taking into account this circumstance. It is proportional to the integral of the trace of the total quantum stress-energy tensor over the whole space from the horizon to infinity. For the shell, sufficiently close to the horizon, the leading term comes from the boundary contribution of the Boulware state.

gr-qc↗

arXiv2003

Exactly solvable models of two-dimensional dilaton cosmology with quantum backreaction

We consider general approach to exactly solvable 2D dilaton cosmology with one-loop backreaction from conformal fields taken into account. It includes as particular cases previous models discussed in literature. We list different types of solutions and investigate their properties for simple models, typical for string theory. We find a rather rich class of everywhere regular solutions which exist practically in every type of analyzed solutions. They exhibit different kinds of asymptotic behavior in past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of field equations. For some kinds of solutions the weak energy condition is violated independent of a specific model. We find also the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a comoving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum backreaction in an infinite past.

hep-th↗

arXiv2002

Classification of static and homogeneous solutions in exactly solvable models of two-dimensional dilaton gravity

We give the full list of types of static (homogeneous)solutions within a wide family of exactly solvable 2D dilaton gravities with backreaction of conformal fields. It includes previously known solutions as particular cases. Several concrete examples are considered for illustration. They contain a black hole and cosmological horizon in thermal equilibrium, extremal and ultraextremal horizons, etc. In particular, we demonstrate that adS and dS geometries can be \QTR{it}{exact} solutions of semiclassical field equations for a \QTR{it}{nonconstant} dilaton field.

hep-th↗

arXiv2002

Exactly solvable models in 2D semiclassical dilaton gravity and extremal black holes

Previously known exactly solvable models of 2D semiclassical dilaton gravity admit, in the general case, only non-extreme black holes. It is shown that there exist exceptional degenerate cases, that can be obtained by some limiting transitions from the general exact solution, which include, in particular, extremal and ultraextremal black holes. We also analyze properties of extreme black holes without demanding exact solvability and show that for such solutions quantum backreaction forbids the existence of ultraextreme black holes. The conditions,under which divergencies of quantum stresses in a free falling frame can disappear, are found. We derive the closed equation with respect to the metric as a function of the dilaton field that enables one, choosing the form of the metric, to restore corresponding Lagrangian. It is demonstrated that exactly solvable models, found earlier, can be extended to include an electric charge only in two cases: either the dilaton-gravitation coupling is proportional to the potential term, or the latter vanishes. The second case leads to the effective potential with a negative amplitude and we analyze, how this fact affects the structure of spacetime. We also discuss the role of quantum backreaction in the relationship between extremal horizons and the branch of solutions with a constant dilaton.

hep-th↗

arXiv2002

Regular self-consistent geometries with infinite quantum backreaction in 2D dilaton gravity and black hole thermodynamics: unfamiliar features of familiar models

We analyze the rather unusual properties of some exact solutions in 2D dilaton gravity for which infinite quantum stresses on the Killing horizon can be compatible with regularity of the geometry. In particular, the Boulware state can support a regular horizon. We show that such solutions are contained in some well-known exactly solvable models (for example, RST). Formally, they appear to account for an additional coefficient $B$ in the solutions (for the same Lagrangian which contains also ''traditional'' solutions) that gives rise to the deviation of temperature $T$ from its Hawking value $T_{H}$. The Lorentzian geometry, which is a self-consistent solution of the semiclassical field equations, in such models, is smooth even at $B\neq 0$ and there is no need to put B=0 ($T=T_{H}$) to smooth it out$.$ We show how the presence of $B\neq 0$ affects the structure of spacetime. In contrast to ''usual'' black holes, full fledged thermodynamic interpretation, including definite value of entropy, can be ascribed (for a rather wide class of models) to extremal horizons, not to nonextreme ones. We find also new exact solutions for ''usual'' black holes (with $T=T_{H}$). The properties under discussion arise in the \QTR{it}{weak}-coupling regime of the effective constant of dilaton-gravity interaction. Extension of features, traced in 2D models, to 4D dilaton gravity leads, for some special models, to exceptional nonextreme black holes having no own thermal properties.

hep-th↗

arXiv2002

Entropy of semiclassical 2D dilaton black holes away from the Hawking temperature

Recently we showed that in semiclassical 2D dilaton gravity the regularity of a black hole horizon may be compatible with divergencies of Polyakov-Liouville stresses on it, the temperature deviating from its Hawking value. This makes the question about thermal properties of such solutions non-trivial. We demonstrate that, adding to gravitation-dilaton part of the action certain counterterms, which diverge on the horizon but are finite outside it, one may achieve finiteness of the effective gravitation-dilaton couplings on the horizon. This gives for the entropy S the Bekenstein - Hawking value in the nonextreme case and S=0 in the extreme one similarly to what happens to ''standard '' black holes.

hep-th↗

arXiv2002

Thermodynamics of black holes with an infinite effective area of a horizon

In some kinds of classical dilaton theory there exist black holes with (i) infinite horizon area $A$ or infinite $F$ (the coefficient at curvature in Lagrangian) and (ii) zero Hawking temperature $T_{H}$. For a generic static black hole, without an assumption about spherical symmetry, we show that infinite $A$ is compatible with a regularity of geometry in the case $T_{H}=0$ only. We also point out that infinite $T_{H}$ is incompatible with the regularity of a horizon of a generic static black hole, both for finite or infinite $A$. Direct application of the standard Euclidean approach in the case of an infinite ''effective'' area of the horizon $A_{eff}=AF$ leads to inconsistencies in the variational principle and gives for a black hole entropy $S$ an indefinite expression, formally proportional to $T_{H}A_{eff}$. We show that treating a horizon as an additional boundary (that is, adding to the action some terms calculated on the horizon) may restore self-consistency of the variational procedure, if $F$ near the horizon grows not too rapidly. We apply this approach to Brans-Dicke black holes and obtain the same answer S=0 as for ''usual'' (for example, Reissner-Nordström) extreme classical black holes. We also consider the exact solution for a conformal coupling, when $A$ is finite but $F$ diverges and find that in the latter case both the standard and modified approach give rise to an infinite action. Thus, this solution represents a rare exception of a black hole without nontrivial thermal properties.

gr-qc↗

arXiv2001

Quantum backreaction of massive fields and self-consistent semiclassical extreme black holes and acceleration horizons

We consider the effect of backreaction of quantized massive fields on the metric of extreme black holes (EBH). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum backreaction is consistent with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass M_{tot} and charge Q we show that for all cases of physical interest M_{tot}< Q. We also discuss different types of quantum-corrected Bertotti-Robinson spacetimes, find for them exact self-consistent solutions and consider situations in which tiny quantum corrections lead to the qualitative change of the classical geometry and topology. In all cases one should start not from a classical background with further adding quantum corrections but from the quantum-corrected self-consistent geometries from the very beginning.

gr-qc↗

arXiv2001

Quasi-exactly solvable quartic Bose Hamiltonians

We consider Hamiltonians, which are even polynomials of the forth order with the respect to Bose operators. We find subspaces, preserved by the action of Hamiltonian These subspaces, being finite-dimensional, include, nonetheless, states with an \QTR{it}{infinite} number of quasi-particles, corresponding to the original Bose operators. The basis functions look rather simple in the coherent state representation and are expressed in terms of the degenerate hypergeometric function with respect to the complex variable labeling the representation. In some particular degenerate cases they turn (up to the power factor) into the trigonometric or hyperbolic functions, Bessel functions or combinations of the exponent and Hermit polynomials. We find explicitly the relationship between coefficients at different powers of Bose operators that ensure quasi-exact solvability of Hamiltonian.

quant-ph↗

arXiv2001

General approach to potentials with two known levels

We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $ξ(x)$ and one parameter $ΔE=E_{2}$-$E_{1}$. We show how the quantum numbers of both levels depend on properties of the function $ξ(x)$. Our approach does not need resorting to the technique of supersymmetric (SUSY) quantum mechanics but automatically generates both the potential and superpotential.

quant-ph↗

arXiv2001

Entropy of massive fields near a black hole and vacuum polarization: thermodynamics without statistical mechanics

Starting from the Frolov-Zel'nikov stress-energy tensor of quantum massive fields in the Schwarzschild background, we recover the contribution $S_{q}$ of these field into the entropy of a black hole. For fermions with the spin $%s=1/2$ $S_{q}>0$, for scalar fields $S_{q}>0$ provided the coupling parameter is restricted to some interval, and $S_{q}<0$ for vector fields. The appearance of negative values of $S_{q}$ is attributed to the fact that in the situation under discussion there are no real quanta to contribute to the entropy, so $S_{q}$ is due to vacuum polarization entirely and has nothing to do with the statistical-mechanical entropy. We also consider the spacetime with an acceleration horizon - the Bertotti-Robison spacetime - and show that $S_{q}=0$ for massive fields similarly to what was proved earlier for massless fields.

gr-qc↗

arXiv2000

Quantum anharmonic oscillator and quasi-exactly solvable Bose systems

We extend the notion of quasi-exactly solvable (QES) models from potential ones and differential equations to Bose systems. We obtain conditions under which algebraization of the part of the spectrum occurs. In some particular cases simple exact expressions for several energy levels of an anharmonic Bose oscillator are obtained explicitly. The corresponding results do not exploit perturbation theory and include strong coupling regime. A generic Hamiltonian under discussion cannot, in contrast to QES potential models, be expressed as a polynomial in generators of $sl_{2}$ algebra. The suggested approach is extendable to many-particle Bose systems with interaction.

quant-ph↗

arXiv2000

Quantum extreme black holes at finite temperature and exactly solvable models of 2d dilaton gravity

It is argued that in certain 2d dilaton gravity theories there exist self-consistent solutions of field equations with quantum terms which describe extreme black holes at nonzero temperature. The curvature remains finite on the horizon due to cancelation of thermal divergencies in the stress-energy tensor against divergencies in the classical part of field equations. The extreme black hole solutions under discussion are due to quantum effects only and do not have classical counterparts.

hep-th↗

arXiv1999

Nonextreme black holes near the extreme state and acceleration horizons: thermodynamics and quantum-corrected geometry

We consider the class of metrics that can be obtained from those of nonextreme black holes by limiting transitions to the extreme state such that the near-horizon geometry expands into a whole manifold. These metrics include, in particular, the Rindler and Bertotti - Robinson spacetimes. The general formula for the entropy of massless radiation valid either for black-hole or for acceleration horizons is derived. It is argued that, as a black hole horizon in the limit under consideration turns into an acceleration one, the thermodynamic entropy $S_{q}$ of quantum radiation is due to the Unruh effect entirely and $S_{q}=0$ exactly. The contribution to the quasilocal energy from a given curved spacetime is equal to zero and the only nonvanishing term stems from a reference metric. In the variation procedure necessary for the derivation of the general first law, the metric on a horizon surface changes along with the boundary one, and the account for gravitational and matter stresses is an essential ingredient of the first law. This law confirms the property $S_{q}=0$. The quantum-corrected geometry of the Bertotti - Robinson spacetime is found and it is argued that backreaction of quantum fields mimics the effect of the cosmological constant $Λ_{eff\text{}}$ and can drastically change the character of spacetime depending on the sign of $Λ_{eff}$ --- for instance, turn $AdS_{2}\times S_{2}$ into $dS_{2}\times S_{2}$ or $Rindler_{2}\times S_{2}$. Two latter solutions can be thought of as the quantum versions of the cold and ultracold limits of the Reissner-Nordstrom-de Sitter metric.

gr-qc↗