Black holes, horizons and singularities

LIGO和处女座合作最近的发现证实了黑洞的存在，这是广义相对论最耐人寻味的预测之一。描述旋转黑洞的爱因斯坦方程的真空解的一个显着特点是，除了显式对称性外，它们还具有隐藏对称性，这些对称性被广泛用于研究黑洞附近的物理效应。最近，有研究表明，在任何数量的时空维度中，类似的隐藏对称性是黑洞解的共同属性。高维黑洞的研究是现代理论物理的研究热点，也就是弦理论和各种膜世界模型。在我的提议的第一部分，我计划解决四维及更高维黑洞的几个悬而未决的问题，这些问题与它们的隐藏对称性有关，这可能会对天体物理应用和黑洞理论产生影响。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，这一理论内部是不一致的：经典地，它预测了黑洞和宇宙学中的奇点，当它被量子化时，它是不可重整化的。预计对这一理论的适当修改可能会治愈这些死亡。我将研究引力理论的一类特殊的非局部修正，它(至少在树的水平上)不会引入新的非物理自由度(鬼魂)。这样的修改是否消除了奇点，并使黑洞内部的时空变得规则？这个主题可能看起来很“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演化过程中作为原始黑洞产生的。关于在现代对撞机中产生微型黑洞的可能性，人们进行了广泛的讨论。1974年，霍金预测，这样的黑洞应该会通过发出量子热辐射而衰变。如果黑洞完全消失，其内部积累的信息也可能丢失。这是一个现在被广泛讨论的著名的信息损失悖论。我们的目标是回答以下问题：非地方性是否有助于解决信息损失悖论？它能否改变霍金辐射，特别是在黑洞蒸发的末态。在最初的霍金推导中，黑洞产生的实量子形式上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问题，也就是所谓的转普朗克问题。异地能“抹黑”地平线，解决地平线问题吗？非定域效应是如何改变霍金辐射参数的？非局域性是否改变了发射的霍金量子及其在黑洞内传播的伙伴之间的纠缠？这些是我想要回答的其他问题。

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.