Black holes, horizons and singularities

最近LIGO-Virgo合作的发现证实了黑洞的存在，这是广义相对论最有趣的预测之一。描述旋转黑洞的Einstein方程真空解的一个显著性质是，除了显对称性外，它们还具有隐对称性，这些对称性被广泛用于研究黑洞附近的物理效应。最近的研究表明，类似的隐藏对称性是任意数量时空维中黑洞解的共同属性。高维黑洞的研究是现代理论物理学的兴趣焦点，即弦理论和不同的膜世界模型。在我的建议的第一部分，我计划攻击四维和更高维黑洞的几个未解决的问题与他们的隐藏的对称性，这可能会在天体物理学应用和黑洞理论的影响。尽管广义相对论在天体物理学和宇宙学中取得了成功，但在小尺度上，这个理论是内部不一致的：经典地，它预测了黑洞和宇宙学中的奇点，当量子化时，它是不可重整化的。人们期望，对这一理论进行适当的修改，可以治愈这些疾病。我将研究引力理论的一类特殊的非定域修正，它（至少在树的层次上）不会引入新的非物理自由度（鬼）。这样的修改是否消除了奇点，使黑洞内部的时空变得规则？这个问题可能看起来很“学术”，但它对于理解小质量黑洞的蒸发变得很重要。这样的黑洞可能是在早期宇宙的演化过程中作为原始黑洞产生的。人们广泛讨论了在现代对撞机中产生微型黑洞的可能性。1974年，霍金预言这样的黑洞应该通过发射量子热辐射而衰变。如果黑洞完全消失，它内部积累的信息可能会丢失。这是一个著名的信息丢失悖论，现在被广泛讨论。我们的目标是回答以下问题：非定域性是否有助于解决信息丢失悖论？它能否改变霍金辐射，特别是在黑洞蒸发的最终状态。在最初的霍金推导中，黑洞产生的真实的量子形式上起源于任意大频率的真空零点涨落。这是黑洞物理学的另一个长期存在的问题，被称为transplanckian问题。非定域性能“涂抹”视界并解决transplanckian问题吗？霍金辐射的参数是如何被非定域性效应所修正的？非定域性是否改变了被发射的霍金量子和它们在黑洞内部传播的伙伴之间的纠缠？这些是我想回答的其他问题。

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.