Black holes, horizons and singularities

LIGO-Virgo合作的最新发现证实了黑洞的存在，这是广义相对论最有趣的预言之一。描述旋转黑洞的爱因斯坦方程的真空解的一个显著性质是，除了显式对称性外，它们还具有隐式对称性，这种隐式对称性被广泛用于研究黑洞附近的物理效应。最近，类似的隐藏对称性被证明是任何时空维度黑洞解的共同特性。高维黑洞的研究是现代理论物理学，即弦理论和各种膜世界模型的研究热点。在我的提案的第一部分，我计划攻击几个未解决的问题，四维和高维黑洞与其隐藏的对称性相关，这些问题可能对天体物理应用和黑洞理论都有影响。尽管广义相对论在天体物理学和宇宙学上取得了成功，但在小尺度上，这一理论在内部是不一致的：经典地说，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局部修正，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？这个主题可能看起来很“学术”，但它对理解小质量黑洞的蒸发很重要。这样的黑洞可能是在早期宇宙的演化过程中产生的。关于在现代对撞机中产生迷你黑洞的可能性进行了广泛的讨论。1974年，霍金预言这样的黑洞会通过发射量子热辐射而衰变。如果黑洞完全消失，它内部积累的信息就会丢失。这是一个著名的信息丢失悖论，目前被广泛讨论。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？它能改变霍金辐射吗，尤其是在黑洞蒸发的最终状态。在最初的霍金推导中，黑洞产生的实量子在形式上起源于任意大频率的真空零点涨落。这是黑洞物理学中另一个长期存在的问题，被称为移植问题。非定域性能“涂抹”地平线并解决移植问题吗？非定域性效应如何改变霍金辐射的参数？非定域性是否会改变发射的霍金量子和它们在黑洞内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.