Revisiting the Gravitational Energy of the Schwarzschild Spacetime with a New Approach to the Calculations

Recently, a new method to simplify calculations in teleparallel theories has been put forward. In this article, this method is improved and used to analyze the gravitational energy-momentum tensor (density) of the Schwarzschild solution in a frame that is arbitrarily accelerated along the z-direction. It is shown that, for a special type of frame, one cannot make the gravitational energy density vanish along the observer's worldline, regardless of the observer's acceleration. The role played by the frame and its relation to the observers' worldlines are investigated. It is shown that, for the aforementioned special frames, the results for the gravitational energy and angular momenta are consistent with what we would expect.