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

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

Scattering of Straight Cosmic Strings by Black Holes: Weak Field Approximation

The scattering of a straight, infinitely long string moving with velocity $v$ by a black hole is considered. We analyze the weak-field case, where the impact parameter ($b_{imp}$) is large, and obtain exact solutions to the equations of motion. As a result of scattering, the string is displaced in the direction perpendicular to the velocity by an amount $\Delta b\sim -2\pi GMv\gamma/c^3 -\pi (GM)^2/ (4c^3 v b_{imp})$, where $\gamma=(1-(v/c)^2)^{-1/2}$. The second term dominates at low velocities $v/c<(GM/b_{imp})^{1/2}$ . The late-time solution is represented by a kink and anti-kink, propagating in opposite directions at the speed of light, and leaving behind them the string in a new ``phase''. The solutions are applied to the problem of string capture, and are compared to numerical results.Comment: 19 pages, 5 figure