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 $\alpha=1$. 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.Comment: 10 pages, Extended version of the plenary talk given at a Joint Meeting: 13th International Conference on Gravitation, Astrophysics, and Cosmology 15th Italian-Korean Symposium on Relativistic Astrophysics, Seoul, July 03--07, 201

Why the Entropy of a Black Hole is A/4A/4?

A black hole considered as a part of a thermodynamical system possesses the Bekenstein-Hawking entropy S_H =A_H /(4l_{\mbox{\scriptsize{P}}}^2), where $A_H$ is the area of a black hole surface and l_{\,\mbox{\scriptsize{P}}} is the Planck length. Recent attempts to connect this entropy with dynamical degrees of freedom of a black hole generically did not provide the universal mechanism which allows one to obtain this exact value. We discuss the relation between the 'dynamical' contribution to the entropy and $S_H$, and show that the universality of $S_H$ is restored if one takes into account that the parameters of the internal dynamical degrees of freedom as well as their number depends on the black hole temperature.Comment: 11 pages, Alberta Univ. Preprint Alberta-Thy-22-9

"Hybrid" Black Holes

We discuss a solution of the Einstein equations, obtained by gluing the external Kerr metric and the internal Weyl metric, describing an axisymmetric static vacuum distorted black hole. These metrics are glued at the null surfaces representing their horizons. For this purpose we use the formalism of massive thin null shells. The corresponding solution is called a "hybrid" black hole. The massive null shell has an angular momentum which is the origin of the rotation of the external Kerr spacetime. At the same time, the shell distorts the geometry inside the horizon. The inner geometry of the "hybrid" black hole coincides with the geometry of the interior of a non-rotating Weyl-distorted black hole. Properties of the "hybrid" black holes are briefly discussed.Comment: 9 page

Information loss problem and a `black hole' model with a closed apparent horizon

In a classical description the spacetime curvature inside a black hole infinitely grows. In the domain where it reaches the Planckian value and exceeds it the Einstein equations should be modified. In the absence of reliable theory of quantum gravity it is instructive to consider simplified models. We assume that a spacetime curvature is limited by some value (of the order of the Planckian one). We use modified Vaidya metric, proposed by Hayward, to describe the black hole evaporation process. In such a spacetime the curvature near $r=0$ remains finite, it does not have an event horizon and its apparent horizon is closed. If the initial mass of such a `black hole' is much larger than the Planckian one its properties (as seen by an external observer) are practically the same as properties of the `standard' black hole with the event horizon. We study outgoing null rays in the vicinity of the outer apparent and introduce a notion of quasi-horizon. We demonstrate that particles, trapped inside a `black hole' during the evaporation process, finally may return to external space after the evaporation is completed. We also demonstrate that such quanta would have very large blue-shift. The absence of the event horizon makes it possible restoration of the unitarity in evaporating black holes.Comment: 18 pages, 6 figures. New references added with their brief discussion. Conformal Carter-Penrose diagram is added. Found misprints are correcte

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 $\exp(-(\Box/\mu^2)^N) \Box^{-1}$, where $\mu$ 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.Comment: 10 pages, 4 Figure

Charged particle in higher dimensional weakly charged rotating black hole spacetime

We study charged particle motion in weakly charged higher dimensional black holes. To describe the electromagnetic field we use a test field approximation and use the higher dimensional Kerr-NUT-(A)dS metric as a background geometry. It is shown that for a special configuration of the electromagnetic field the equations of motion of charged particles are completely integrable. The vector potential of such a field is proportional to one of the Killing vectors (called primary Killing vector) from the `Killing tower' of symmetry generating objects which exists in the background geometry. A free constant in the definition of the adopted electromagnetic potential is proportional to the electric charge of the higher dimensional black hole. The full set of independent conserved quantities in involution is found. It is demonstrated, that Hamilton-Jacobi equations are separable, as well as the corresponding Klein-Gordon equation and its symmetry operators.Comment: 9 pages, no figure