Aspects of Black Holes in Modified Theories of Gravity: Holography, Weak Gravity Conjecture and Wedge Algebra

修正引力理论中的黑洞方面：全息术、弱引力猜想和楔代数

基本信息

批准号：
RGPIN-2022-03636
负责人：
Ghezelbash, AmirMasoud
金额：
$ 1.75万
依托单位：
University of Saskatchewan
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=763192
关键词：
Aspects Black Holes Modified Theories

项目摘要

I plan to extensively study the modified theories of gravity (MTG), and extend my long-term research on quantum gravity, with focus on MTG. The proposed research sheds light on some less-studied subjects such as black holes in MTG, and provide compelling evidence on holography, weak gravity conjecture and celestial holography in MTG. MTG are necessary to explain the observed accelerating expansion of the universe, that general relativity can't explain. The first MTG is f(R) theory, in which the Ricci scalar is replaced by a general function f(R), in the Einstein-Hilbert action. The second MTG is to use the curvature-free connection, instead of the usual torsion-free Levi-Civita connection in general relativity. The simplest possibility (Teleparallel Equivalent of General Relativity (TEGR)) is to use the torsion scalar T, instead of Ricci scalar in the action of general relativity. We can consider a more general theory, where the action is a function of torsion scalar f(T), which leads to a new class of MTG. The third MTG is to use the non-metricity, instead of curvature or torsion to describe the gravity. The simplest possibility (Symmetric Teleparallel Equivalent of General Relativity (STEGR)) is to use the non-metricity scalar Q, instead of Ricci or Torsion scalars in the action of general relativity. It's quite interesting that TEGR and STEGR are equivalent to general relativity. However considering a more general theory, where the action is a function of non-metricity scalar f(Q), leads to a new class of MTG. There are very few known black hole solutions in any of MTG. Despite the excellent progress in holography in Einstein gravity, there is no significant breakthrough in black hole holography in MTG. The first short-term objective of the proposal is related to establishing the possible holography for the rotating black holes in MTG. As well I will study the thermodynamics of black holes, their stability, and finding their near horizon geometry. The second and third short-term objectives are extending my research on the weak gravity conjecture, and wedge algebra in MTG. The weak gravity conjecture refers to the fact that the strength of gravity is bounded from above by the strengths of the other gauge forces in a self-consistent theory of quantum gravity. It has been recently discovered that four-dimensional gauge theories, as well as Einstein gravitational theories, contain an infinite number of symmetries, encoded in the generalized two dimensional currents. The currents constitute a Kac-Moody algebra which is homeomorphic to a wedge algebra. I plan to construct such an algebra in MTG. Moreover, it is an open question to establish such a wedge symmetry for black holes in MTG and beyond. Especially the black holes, which are the result of gauging the Wess-Zumino-Novikov-Witten models. The outcome of research projects in this proposal enhances our knowledge in quantum gravity worldwide, and opens the door to more breakthrough discoveries.

我计划广泛研究修正的引力理论（MTG），并扩展我对量子引力的长期研究，重点是 MTG。拟议的研究揭示了一些研究较少的主题，例如 MTG 中的黑洞，并提供了一些建议。 MTG 中的全息论、弱引力猜想和天体全息论对于解释观测到的宇宙加速膨胀是必要的，而广义相对论无法解释第一个 MTG 是 f(R) 理论。其中，在爱因斯坦-希尔伯特作用中，里奇标量被通用函数 f(R) 取代。第二个 MTG 是使用无曲率连接，而不是广义相对论中通常的无扭转 Levi-Civita 连接。最简单的可能性（广义相对论的远平行等效（TEGR））是在广义相对论的作用中使用扭转标量 T，而不是 Ricci 标量。我们可以考虑一个更一般的理论，其中作用是扭转标量 f(T) 的函数，这导致了一种新的 MTG。第三种 MTG 是使用非度量，而不是曲率或扭转来计算最简单的可能性（广义相对论的对称远平行等效（STEGR））是使用非度量标量 Q，而不是 Ricci 或 Torsion。广义相对论作用中的标量非常有趣的是，TEGR 和 STEGR 相当于广义相对论，然而考虑到更一般的理论，其中作用是非度量标量 f(Q) 的函数，导致了一类新的。 MTG 中已知的黑洞解决方案很少，尽管在爱因斯坦引力全息术方面取得了巨大进展，但 MTG 中的黑洞全息术尚未取得重大突破。该提案的短期目标与建立 MTG 中旋转黑洞的可能全息术有关，我还将研究黑洞的热力学、它们的稳定性，并找到它们的第二个和第三个短期几何结构。目标是扩展我对弱引力猜想和 MTG 中的楔形代数的研究。弱引力猜想是指在自洽的量子理论中，引力的强度受到其他力规强度的限制。重力。最近发现，四维规范理论以及爱因斯坦引力理论包含无限数量的对称性，这些对称性被编码在广义二维电流中，这些电流构成了与楔形代数 I 同胚的 Kac-Moody 代数。计划在 MTG 中构造这样的代数此外，在 MTG 及其他黑洞中建立这样的楔形对称性是一个悬而未决的问题，特别是黑洞，这是的结果。测量 Wess-Zumino-Novikov-Witten 模型。本提案中的研究项目成果增强了我们对全球量子引力的了解，并为更多突破性发现打开了大门。