Black holes, horizons and singularities

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Recent discoveries by LIGO-Virgo collaboration have confirmed the existence of black holes, one of the most intriguing predictions of the general relativity. A remarkable property of vacuum solutions of the Einstein equations describing rotating black holes is that besides explicit symmetries they possess hidden symmetries which are widely used for study physical effects in the vicinity of black holes. More recently it was demonstrated that similar hidden symmetries are a common property of black hole solutions in any number of spacetime dimensions. Study of higher dimensional black holes is in the focus of interests of modern theoretical physics, namely of the string theory and different brane-world models. In the first part of my proposal I plan to attack several unsolved problems of four and higher dimensional black holes connected with their hidden symmetries which might have impact both in the astrophysical applications and the black hole theory. In spite of the success of the general relativity in astrophysics and cosmology, at small scales this theory is internally inconsistent: Classically it predicts singularities in black holes and in cosmology and when quantized it is non-renormalizable. It is expected that a proper modification of this theory may cure these deceases. I shall study a special class of non-local modifications of the gravitational theory which (at least at the tree level) does not introduce new unphysical degrees of freedom (ghosts). Does such modification remove the singularity and make the spacetime inside the black hole regular? This subject might look quite `academic', but it becomes important for understanding of evaporation of small mass black holes. Such black holes might be produced as primordial, during the evolution of the early universe. There was a wide discussion of the possibility of mini black hole production in the modern colliders. In 1974 Hawking predicted that such a black hole should decay by emitting the quantum thermal radiation. If the black hole completely disappears the information accumulated inside it can be lost. This is a famous information loss paradox which is widely discussed now. Our goal is to answer the following question: Can the non-locality help to solve the information loss paradox? Can it change the Hawking radiation, especially at the final state of the black hole evaporation. In the original Hawking derivation real quanta produced by a black hole are formally originated from vacuum zero-point fluctuations of an arbitrary large frequency. This is another longstanding problem of black hole physics, known as a transplanckian problem. Can the non-locality `smear' the horizon and solve the transplanckian problem? How the parameters of the Hawking radiation are modified by the effects of non-locality? Does the non-locality change entanglement between the emitted Hawking quanta and their partners propagating inside the black hole? These are other questions which I would like to answer.