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

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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.