Conserved Charges Of Einstein Gravity In A Connection Independent Formulation

By introducing an arbitrary affine connection without any constrains into the gravitational action which describes Einstein Gravity,scholar Junpei Harada proposed a connection independent formulation of General Relativity in 2020.In this thesis,based on his research,we investigate the conserved charges of Einstein Gravity in the connection independent formulation.Specifically,we introduce the connection independent formulation of General Relativity in details at first.It is worth to mentioning that unlike the situation under traditional metric formulation of Einstein Gravity,in such a formulation,with proper boundary conditions,to obtain the Einstein field equation,there is no necessity for us to add the Gibbons-Hawking-York term to avoid the influence of the boundary term produced during the variation of gravitational action.Then,we investigate the properties of General Relativity’s connection independent Lagrangian under the connection and conformal transformations.During this period,we reveal that the connection independent Lagrangian can be reproduced by converting the Levi-Civita connection in the boundary term into an arbitrary one in terms of the Gamma squared expression for the Einstein-Hilbert Lagrangian.Then,after varying the Lagrangian with respect to the metric tensor and an arbitrary affine connection,we derive the conserved Noether currents and the corresponding Noether potentials for Einstein gravity through utilizing the well-known Noether theorem.Particularly,we obtain a superpotential that generalizes naturally the usual Katz-Bicak-Lynden-Bell(KBL)one by including the contribution from an arbitrary reference connection.The potentials can be adopted to define conserved charges of Einstein gravity.By contrast with the usual metric formulation described by the Einstein-Hilbert Lagrangian,our analysis reveals that the connection independent formulation conveniently reproduces the KBL superpotential and it can provide a unified description for conserved charges defined by virtue of the KBL method and the covariant phase space approach.Finally,by utilizing the definition of conserved charges defined by the generalized KBL superpotential that contains the affine connection relies on an arbitrary referencing background,we acquire the mass and angular momentum of four-dimensional Kerr-Newman black hole and its generalization in Ad S spacetime.And they completely coincide with the results acquired through other standard methods in literature.