New Superpotential in Conservation Laws in General Relativity

TL;DR

This paper introduces a new superpotential formula in general relativity's conservation laws, combining Moller-based and higher derivative terms, potentially improving the evaluation of conserved quantities within the Schwarzschild metric.

Contribution

It presents a novel superpotential formula that incorporates higher derivatives of the metric, expanding the tools for analyzing conservation laws in general relativity.

Findings

The new superpotential satisfies integral and differential conservation laws.

It is composed of a Moller-based term and an antisymmetric tensor density.

Potential for improved evaluation of conserved quantities in Schwarzschild spacetime.

Abstract

This work refers to the new formula for the superpotential Uikl in conservation laws in general relativity satisfying the integral and differential conservation laws within the Schwarzschild metric. The new superpotential is composed of two terms. The first term is based on Mollers concept and its a function of the metric gik and its first derivative only. The second term is the antisymmetric tensor density of weight plus one and it consists of higher derivatives of the metric gik. Although the new superpotential consists of higher derivatives of the metric gik it might bring a new evaluation of the conservative quantities in general relativity