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.

我计划广泛研究改进的引力理论（MTG），并将我对量子引力的长期研究扩展到MTG。这项研究揭示了一些研究较少的主题，如黑洞在MTG，并提供令人信服的证据全息，弱引力猜想和天体全息在MTG。MTG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，在Einstein-Hilbert作用量中，Ricci标量被一个广义函数f（R）代替;第二个MTG是用曲率自由联系代替广义相对论中通常的无挠Levi-Civita联系。最简单的可能性（广义相对论的远程平行等价物（Telepalent Equivalent of General Relativity，TEGR））是使用挠率标量T，而不是广义相对论中的里奇标量。我们可以考虑一个更一般的理论，其中作用量是挠率标量f（T）的函数，这就产生了一类新的MTG。第三类MTG是用非度量性代替曲率或挠率来描述引力。最简单的可能性（广义相对论的对称远程平行等价物（英语：Symmetric Teleparallel Equivalent of General Relativity，STEGR））是使用非度规标量Q，而不是广义相对论中的Ricci或Torsion标量。很有趣的是，TEGR和STEGR等同于广义相对论。然而，考虑到一个更一般的理论，其中的作用量是一个函数的非度规标量f（Q），导致一类新的MTG。尽管在爱因斯坦引力下的全息术取得了很好的进展，但在MTG中的黑洞全息术并没有重大的突破。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。我也将研究黑洞的热力学，它们的稳定性，并找到它们的近视界几何。第二和第三个短期目标是扩展我在弱引力猜想和MTG中的楔形代数方面的研究。弱引力猜想是指在量子引力的自洽理论中，引力的强度从上到下受到其他规范力的强度的限制。最近人们发现，四维规范理论和爱因斯坦引力理论一样，包含了无限多的对称性，编码在广义二维流中。电流构成一个Kac-Moody代数，它是一个楔形代数同胚。我计划在MTG中构造这样一个代数。此外，在MTG和更远的地方建立这样一个楔形对称的黑洞是一个悬而未决的问题。特别是Wess-Zumino-Novikov-Witten模型测量的结果--黑洞。该计划中的研究项目的成果增强了我们在全球量子引力方面的知识，并为更多突破性发现打开了大门。