A covariant and conformally invariant approach to the symplectic structure of gravitational fields is natural to introduce when considering spacetimes with a nonzero cosmological constant. It utilizes the Normal Conformal Cartan Connection as a fundamental element of construction. The resulting symplectic potential is explicitly conformally invariant. One consequence is the regular behavior of...
The membrane paradigm illustrates a profound link between gravity on a stretched horizon and hydrodynamics. While this connection has been explored semi-classically, it holds potential for illuminating fundamental aspects of quantum spacetime, such as degrees of freedom, symmetries, and dynamics. In this work, we revisit the membrane viewpoint and introduce the concept of stretched Carroll...
The enhancement of the symmetry group for asymptotically flat spacetimes from the Poincare group to the infinite-dimensional BMS group gives a rich structure to the theory. The existence of supertranslations in the BMS group plays a key role in a variety of asymptotic phenomenon. In particular, there is a well-known "supertranslation ambiguity" in defining the angular momentum of an isolated...
In recent years there has been a renewed interest in the mathematical structure and gravitational physics of the null asymptote, in both classical and quantum regimes. From Carrollian Geometries, BMS symmetry, and the radiative phase space to quantization of null data, asymptotic graviton states, and infrared sectors, there is a vast ocean of mathematics and physics that can be learned from...
A 4-dimensional generally covariant gauge theory with local degrees of freedom is presented. It leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the Hamiltonian. We describe its observables, quantization, and some generalizations.
The Kerr spacetime hypothesis can be tested by using two approaches namely the top-bottom approach and bottom-up approach. The first one involves introducing the deviations in the Kerr metric through a theoretical model. The second approach involves introducing the deviations in terms of parameters. The metric proposed by Johannsen and Psaltis is one such parametrically deformed Kerr...
We present a Chern-Simons theory for the (2+1)-dimensional analog self-dual gravity theory that is based on the gauge group $SL(2,\mathbb{C})_ \mathbb{R}\triangleright\!\!\!< \mathbb{R}^6$. This is formulated by mapping the $3d$ complex self-dual dynamical variable and connection to $6d$ real variables which combines into a $12d$ Cartan connection.
Quantization is given by the...
This presentation looks into the realm of black hole thermodynamics, emphasizing its connection with boundary conditions. We will explore how various boundary conditions impact the thermodynamic properties of black holes and examine the geometric interpretations of different thermodynamic potentials. By studying the first laws of thermodynamics, we aim to unravel the interesting connection...
