The Evaluation of the M{\o}ller Energy Complex in Difference Coordinate Representations

TL;DR

This paper evaluates the Møller energy complex for Schwarzschild black holes across different coordinate systems, demonstrating its invariance under spatial transformations and time shifts, thus confirming its coordinate independence.

Contribution

It provides a detailed analysis showing the Møller energy complex's invariance under spatial and time coordinate transformations for Schwarzschild black holes.

Findings

Møller energy complex is invariant under spatial transformations.

Møller energy complex remains unchanged under time coordinate shifts.

The results support the coordinate independence of the Møller energy complex.

Abstract

The M{\o}ller energy complex of Schwarzschild black hole solution in several coodinates are evaluated. Our results show that the M{\o}ller energy complex is independent of not only the purely spatial transformation, but also the shift of time coordinate. So, we could conclude that a shift of time coordinates will not change the energy which is obtained by using the definition of M{\o}ller energy complex.