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

• 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

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，并为 MTG 中的全息术、弱重力猜想和天体全息术提供了令人信服的证据。 MTG 对于解释观察到的宇宙加速膨胀是必要的，而广义相对论无法解释这一点。第一个 MTG 是 f(R) 理论，其中在爱因斯坦-希尔伯特作用中，Ricci 标量被替换为通用函数 f(R)。 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挠率标量 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，这导致了一类新的 MTG。 第三种MTG是使用非度量，而不是曲率或扭转来描述重力。最简单的可能性（广义相对论的对称远平行等效（STEGR））是在广义相对论的作用中使用非度量标量 Q，而不是 Ricci 或 Torsion 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，其中动作是非度量标量 f(Q) 的函数，导致了一类新的 MTG。 在任何 MTG 中，已知的黑洞解决方案都非常少。尽管爱因斯坦引力全息术取得了出色的进展，但MTG中的黑洞全息术却没有重大突破。该提案的第一个短期目标是为 MTG 中的旋转黑洞建立可能的全息术。我还将研究黑洞的热力学、它们的稳定性，并找到它们的近地平线几何结构。第二个和第三个短期目标是扩展我对弱引力猜想和MTG中楔代数的研究。弱引力猜想是指在自洽的量子引力理论中，引力的强度从上方受到其他规范力的强度的限制。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。这些电流构成与楔形代数同胚的 Kac-Moody 代数。我计划在 MTG 中构建这样一个代数。此外，为 MTG 及其他黑洞建立这种楔形对称性是一个悬而未决的问题。尤其是黑洞，它是测量韦斯-祖米诺-诺维科夫-维滕模型的结果。 该提案中的研究项目的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。