Conserved Currents With Higher-order Derivative Term In Einstein Gravity And Their Generalizations And Applications

Within the framework of general relativity,Komar integral plays an important role in the definition of conserved charges for asymptotically flat spacetimes.However,the results will diverge or have no physical significance when it is used to calculate the mass of asymptotically Ad S spacetimes.As a consequence,the usual Komar integral must be corrected.As is known,the usual Komar current is the second derivative of Killing vector.When the Killing vector is regarded as 1-form field in differential form,we make use of differential operators keeping the differential form unchanged to introduce higher-order derivative terms to modify the usual Komar current.In terms of the Komar-like integral corrected by higher-order derivatives,we calculate the conserved charges of asymptotically Ad S black holes,such as the 4,5,D-dimensional kerr-Ad S black hole and the charged rotating black holes in five-dimensional minimal gauged supergravity.Besides,there exists a different factor between the Komar expressions used to define the mass and angular momentum for the asymptotically flat rotating black holes.In order to eliminate such a difference,by utilizing the method in which the conserved current is generated via the action of the degree-preserving differential operators on a 1-form vector field,we modify the conventional Komar potential by including a nonlinear third-order derivative term of Killing vector.Conserved charges based on the higher-order corrected Komar potential unify the expressions of mass and angular momentum for asymptotically-flat rotating spacetimes.On the other hand,Lovelock gravity is the most natural higher-derivative extension of general relativity to higher dimensions of spacetimes.In the context of this gravity theory,we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters.Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically Ad S spacetimes.Besides,inspired with the cases of Einstein gravity and Lovelock gravity,we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor.On basis of the newly-constructed tensor,we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.