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

我计划对修正引力理论（MTG）进行广泛的研究，并延伸我对量子引力的长期研究，重点是MTG，提出的研究将揭示一些研究较少的课题，如MTG中的黑洞，并为MTG中的全息，弱引力猜想和天体全息提供有力的证据，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，其中里奇标量被爱因斯坦-希尔伯特作用中的一般函数f(R)所取代。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列维-奇维塔连接。最简单的可能性（广义相对论的遥平行等效（TEGR））是在广义相对论的作用下使用扭转标量T，而不是里奇标量。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，这导致了一个新的MTG类别。第三个MTG是使用非度量性，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下使用非度量标量Q，而不是里奇标量或扭转标量。很有趣的是，TEGR和STEGR等价于广义相对论。然而，考虑到一个更一般的理论，其中作用是一个非度量标量f(Q)的函数，导致了一个新的MTG类。在任何MTG中都很少有已知的黑洞解。尽管爱因斯坦引力全息学取得了出色的进展，我的第一个短期目标是建立MTG中旋转黑洞的可能全息，并研究黑洞的热力学、稳定性和近视界几何。第二个和第三个短期目标是扩展我对弱引力猜想的研究，以及MTG中的楔形代数。弱引力猜想是指在自洽量子引力理论中，引力的强度从上面被其他规范力的强度所限制。最近发现，四维规范理论，以及爱因斯坦引力理论，包含了无限数量的对称性，编码在广义的二维电流中。这些电流构成了一个与楔形代数同胚的Kac-Moody代数。我打算在MTG中构造这样一个代数，而且，在MTG及更大范围内建立这样一个黑洞的楔形对称是一个悬而未决的问题。尤其是黑洞，这是测量Wess-Zumino-Novikov-Witten模型的结果。本提案中研究项目的成果增强了我们在全球范围内的量子引力知识，并为更多突破性发现打开了大门。

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.