Black holes, horizons and singularities

黑洞、视界和奇点

• 批准号: RGPIN-2020-03889
• 负责人: Frolov, Valeri
• 金额: $ 2.99万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762461
• 关键词: Black; holes; horizons; singularities

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.

LIGO-Virgo 合作的最新发现证实了黑洞的存在，这是广义相对论中最有趣的预测之一。描述旋转黑洞的爱因斯坦方程的真空解的一个显着特性是，除了显式对称性之外，它们还具有隐藏的对称性，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的时空维度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。在我的提案的第一部分中，我计划解决四维和更高维黑洞的几个未解决的问题，这些问题与其隐藏的对称性有关，这可能会对天体物理学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，该理论在内部是不一致的：传统上它预测黑洞和宇宙学中的奇点，并且当量子化时它是不可重整化的。预计对该理论的适当修改可能会治愈这些疾病。我将研究引力理论的一类特殊的非局部修改，它（至少在树级别）不会引入新的非物理自由度（幽灵）。这样的修改是否可以消除奇点并使黑洞内部的时空变得规则？这个主题可能看起来相当“学术”，但它对于理解小质量黑洞的蒸发变得很重要。在早期宇宙的演化过程中，这样的黑洞可能是太初产生的。人们对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，霍金预测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，其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：非局部性能否帮助解决信息丢失悖论？它能否改变霍金辐射，特别是在黑洞蒸发的最终状态。在原始的霍金推导中，黑洞产生的真实量子在形式上源自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，称为跨普朗克问题。非定域性能否“涂抹”视界并解决跨普朗克问题？霍金辐射的参数如何通过非局域性的影响而改变？非定域性是否会改变发射的霍金量子与其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。