arXiv subjects

Valeri P. Frolov

Publications and source records attributed to Valeri P. Frolov.

At least 55 records · Page 3Linked to original sources

arXiv2018

Quantum scattering on a delta potential in ghost-free theory

We discuss the quantum-mechanical scattering of a massless scalar field on a $δ$-potential in a ghost-free theory and obtain analytic solutions for the scattering coefficients. Due to the non-locality of the ghost-free theory the transmission coefficient tends to unity for frequencies much larger than the inverse scale of non-locality, even for infinitely strong potentials. At the same time there exists a critical strength of the $δ$-potential barrier below which there is always a frequency that is totally reflected. These scattering properties in ghost-free theories are quite generic and distinguish them from local field theories. Moreover, we study quasi-normal states that are present for the $δ$-potential well. In the limit of vanishing non-locality, we recover the standard results of local field theory.

hep-th↗

arXiv2018

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in a perfect agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

hep-th↗

arXiv2018

New Metrics Admitting the Principal Killing-Yano Tensor

It is believed that in any number of dimensions the off-shell Kerr-NUT-(A)dS metric represents a unique geometry admitting the principal (rank 2, non-degenerate, closed conformal Killing-Yano) tensor. The original proof relied on the Euclidean signature and therein natural assumption that the eigenvalues of the principal tensor have gradients of spacelike character. In this paper we evade this common wisdom and construct new classes of Lorentzian (and other signature) off-shell metrics admitting the principal tensor with null eigenvalues, uncovering so a much richer structure of spacetimes with principal tensor in four and higher dimensions. A few observations regarding the Kerr-Schild ansatz are also made.

gr-qc↗

arXiv2018

Remarks on black hole entropy

The notion of black-hole entropy was introduced by Jacob Bekenstein in 1972. During past 45 years this subject was in the center of interests of the modern theoretical physics. In this paper we briefly discuss "puzzles" of the black-hole physics, connected with their entropy. We also demonstrate that when the standard energy conditions are violated entropy associated with the event horizon can have quite unexpected behavior.

gr-qc↗

arXiv2018

Principal Killing strings in higher-dimensional Kerr-NUT-(A)dS spacetimes

We construct special solutions of the Nambu-Goto equations for stationary strings in a general Kerr-NUT-(A)dS spacetime in any number of dimensions. This construction is based on the existence of explicit and hidden symmetries generated by the principal tensor which exists for these metrics. The characteristic property of these string configurations, which we call "principal Killing strings," is that they are stretched out from "infinity" to the horizon of the Kerr-NUT-(A)dS black hole and remain regular at the latter. We also demonstrate that principal Killing strings extract angular momentum from higher-dimensional rotating black holes and interpret this as the action of an asymptotic torque.

gr-qc↗

arXiv2018

The gravitational field of static p-branes in linearized ghost-free gravity

We study the gravitational field of static p-branes in D-dimensional Minkowski space in the framework of linearized ghost-free (GF) gravity. The concrete models of GF gravity we consider are parametrized by the non-local form factors $\exp(-\Box/μ^2)$ and $\exp(\Box^2/μ^4)$, where $μ^{-1}$ is the scale of non-locality. We show that the singular behavior of the gravitational field of p-branes in General Relativity is cured by short-range modifications introduced by the non-localities, and we derive exact expressions of the regularized gravitational fields, whose geometry can be written as a warped metric. For large distances compared to the scale of non-locality, $μr\rightarrow\infty$, our solutions approach those found in linearized General Relativity.

gr-qc↗

arXiv2018

Separation of variables in Maxwell equations in Plebanski-Demianski spacetime

A new method for separating variables in Maxwell's equations in four- and higher-dimensional Kerr-(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing-Yano tensor. The key observation is that Lunin's ansatz for the vector potential can be formulated in a covariant form - in terms of the principal tensor. In particular, focusing on the four-dimensional case we demonstrate separability of Maxwell's equations in the Kerr-NUT-(A)dS and the Plebanski-Demianski family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman-Penrose formalism.

hep-th↗

arXiv2018

Stationary black holes with stringy hair

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without cosmological constant. This solution is a warped product of two metrics. One of them is a deformed two-sphere whose Gaussian curvature is determined by the energy-density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(A)dS generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

gr-qc↗

arXiv2017

On the Liouville 2D dilaton gravity models with sinh-Gordon matter

We study 1+1 dimensional dilaton gravity models which take into account backreaction of the sinh-Gordon matter field. We found a wide class of exact solutions which generalizes black hole solutions of the Jackiw-Teitelboim gravity model and its hyperbolic deformation.

hep-th↗

arXiv2017

Black holes, hidden symmetries, and complete integrability

The study of higher-dimensional black holes is a subject which has recently attracted a vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional black holes. We start with the overview of the Liouville theory of completely integrable systems and introduce Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a `seed object' which generates all these symmetries. It determines the form of the black hole geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

gr-qc↗

arXiv2017

Remarks on non-singular black holes

We briefly discuss non-singular black hole models, with the main focus on the properties of non-singular evaporating black holes. Such black holes possess an apparent horizon, however the event horizon may be absent. In such a case, the information from the black hole interior may reach the external observer after the complete evaporation of the black hole. This model might be used for the resolution of the information loss puzzle. However, as we demonstrate, in a general case the quantum radiation emitted from the black hole interior, calculated in the given black hole background, is very large. This outburst of the radiation is exponentially large for models with the redshift function $α=1$. We show that it can be suppressed by including a non-trivial redshift function. However, even this suppression is not enough to guarantee self-consistency of the model. This problem is a manifestation of a general problem, known as the "mass inflation". We briefly comment on possible ways to overcome this problem in the models of non-singular evaporating black holes.

gr-qc↗

arXiv2017

Weakly charged generalized Kerr-NUT-(A)dS spacetimes

We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor $h_{ab}$, which is present in such a spacetime, and a derivative of the primary Killing vector, associated with $h_{ab}$. For the vanishing cosmological constant the obtained solution reduces to the Wald's electromagnetic field generated from the primary Killing vector.

gr-qc↗

arXiv2017

Quantum radiation from an evaporating non-singular black hole

In this paper we study quantum radiation from an evaporating spherically symmetric non-singular black hole. We used a modified Hayward metric for a description of a non-singular black hole. We assume that the mass parameter of this metric depends on the advanced time, and choose this dependence so that it properly reproduces both black hole formation and its subsequent evaporation. We consider a quantum massless scalar field propagating in this geometry and use 2D approximation for the calculation of the quantum average of the stress-energy tensor. For the calculation of this quantity it is sufficient to find a map between the Killing times $u_+$ and $u_-$ at the future and past null infinities, established by the propagation of the radial null rays. In this formalism the quantum energy flux at the future null infinity can be expressed in terms of the function $u_+(u_-)$ and its derivatives. We developed a special formalism, which allows one to reduce the problem of the calculation of the quantum energy flux and other observables to a solution of a simple set of ordinary differential equations. We used this approach to study quantum effects in two cases: i) with the trivial, $α=1$ and ii) the non-trivial, $α\ne1$, redshift function. In both cases there exists an outburst of the quantum energy radiation from the inner domain of the black hole, close to the inner part of its apparent horizon. For $α=1$ this outburst is exponentially large. It is a direct consequence of the so-called mass inflation effect. We showed, that this severe problem can be solved by a proper choice of the redshift function. However, even in this case the emitted energy can be much larger than the initial mass of the evaporating black hole. This means that for a construction of a self-consistent model of a non-singular evaporating black hole the back-reaction effects are highly important.

hep-th↗

arXiv2017

Quantum radiation from a sandwich black hole

We discuss quantum radiation of a massless scalar field from a spherically symmetric nonsingular black hole with finite lifetime. Namely, we discuss a sandwich black-hole model, where a black hole is originally created by a collapse of a null shell of mass $M$, and later, after some time $ΔV$, it is disrupted by the collapse of the other shell with negative mass $-M$. We assume that between the shells the metric is static and either coincides with the Hayward metric or with a special generalization of it. We show that in both cases for sufficiently large parameter $ΔV$ the radiation after the formation of the black hole practically coincides with the Hawking result. We also calculated the radiation, emitted from the black hole interior. This radiation contains peak at the moment when the second shell intersects the inner horizon. In the standard sandwich metric (with the Hayward interior) this outburst of the energy is exponentially large. In the modified metric, which includes additional non-trivial redshift parameter, this exponent is suppressed. This is a result of significant decrease of the surface gravity of the inner horizon in the latter case. We discuss possible consequences of this result in context of the self-consistency requirement for nonsingular models with quantum radiation.

hep-th↗

arXiv2016

Notes on non-singular models of black holes

We discuss static spherically symmetric metrics which represent non-singular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild asymptotic behavior at large $r$. We assume that the metric besides mass $M$ contains an additional parameter $\ell$, which determines the scale where modification of the solution of the Einstein equations becomes significant. We require that the modified metric obeys the limiting curvature condition, that is its curvature is uniformly restricted by the value $\sim \ell^{-2}$. We also make a "more technical" assumption that the metric coefficients are rational functions of $r$. In particular, the invariant $(\nabla r)^2$ has the form $P_n(r)/\tilde{P}_n(r)$, where $P_n$ and $\tilde{P}_n$ are polynomials of the order of $n$. We discuss first the case of four dimensions. We show that when $n\le 2$ such a metric cannot describe a non-singular black hole. For $n=3$ we find a suitable metric, which besides $M$ and $\ell$ contains a dimensionless numerical parameter. When this parameter vanishes the obtained metric coincides with Hayward's one. The characteristic property of such spacetimes is $-ξ^2=(\nabla r)^2$, where $ξ^2$ is a time-like at infinity Killing vector. We describe a possible generalization of a non-singular black-hole metric to the case when this equality is violated. We also obtain a metric for a charged non-singular black hole obeying similar restrictions as the neutral one, and construct higher dimensional models of neutral and charged black holes.

gr-qc↗

arXiv2016

Head-on collision of ultrarelativistic particles in ghost-free theories of gravity

We study linearized equations of a ghost-free gravity in four- and higher-dimensional spacetimes. We consider versions of such a theory where the nonlocal modification of the $\Box$ operator has the form $\Box \exp[(-\Box/μ^2)^N]$, where $N=1$ or $N=2n$. We first obtain the Newtonian gravitational potential for a point mass for such models and demonstrate that it is finite and regular in any number of spatial dimensions $d\ge 3$. The second result of the paper is calculation of the gravitational field of an ultrarelativistic particle in such theories. And finally, we study a head-on collision of two ultrarelativistic particles. We formulated conditions of the apparent horizon formation and showed that there exists a mass gap for mini-black-hole production in the ghost-free theory of gravity. In the case when the center-of-mass energy is sufficient for the formation of the apparent horizon, the latter has two branches, the outer and the inner ones. When the energy increases the outer horizon tends to the Schwarzschild-Tangherlini limit, while the inner horizon becomes closer to $r=0$.

hep-th↗

arXiv2016

Radiation from an emitter in the ghost free scalar theory

We study radiation emitted by a time-dependent source of a scalar massless field in the framework of the ghost-free modifications of the theory. We consider a simple model of the emitter: namely,we assume that it is point-like and monochromatic. We focused on the most common versions of the ghost-free theory, where the propagator $\Box^{-1}$ is modified as follows $\exp(-(\Box/μ^2)^N) \Box^{-1}$, where $μ$ is the characteristic mass-scale of such $GF_N$-theory. We demonstrated that far from the source, in the wave-zone, the radiation asymptotically converges to its "classical" value for any $N\ge 1$. However, in the near-zone the behavior of the field is quite different from the "classical" case. The difference of field amplitude for the ghost-free field and for the classical one has an oscillatory behavior in this domain. A number of oscillations increases with $N$. The amplitude of these oscillations remain finite for even $N$, while it infinitely grows with frequency for odd $N$. This behavior indicates that even in the classical domain $GF_N$ theories might have pathological behavior.

hep-th↗

arXiv2015

Deformed and twisted black holes with NUTs

We construct a new class of vacuum black hole solutions whose geometry is deformed and twisted by the presence of NUT charges. The solutions are obtained by `unspinning' the general Kerr-NUT-(A)dS spacetimes, effectively switching off some of their rotation parameters. The resulting geometry has a structure of warped space with the Kerr-like Lorentzian part warped to a Euclidean metric of deformed and/or twisted sphere, with the deformation and twist characterized by the `Euclidean NUT' parameters. In the absence of NUTs, the solution reduces to a well known Kerr-(A)dS black hole with several rotations switched off. New geometries inherit the original symmetry of the Kerr-NUT-(A)dS family, namely, they possess the full Killing tower of hidden and explicit symmetries. As expected, for vanishing NUT, twist, and deformation parameters, the symmetry is further enlarged.

hep-th↗