Question

The M is Schwarzschild metric comes from Newtonian limit. But in the Newtonian limit the total energy also reduces to M. Is there any particular reason for using mass instead of total energy? Doesn't it feel unnatural that total energy is used in stress-energy tensor, but not in Schwarzschild metric? And yes, I understand that Schwarzschild is a Ricci-Flat solution.

Answer 1

In general relativity, the Schwarzschild metric represents the curvature of spacetime around a spherically symmetric mass. The mass is used instead of total energy because the mass is a fundamental property that remains constant regardless of the reference frame.

Step-by-step explanation:

In general relativity, the Schwarzschild metric describes the curvature of spacetime around a spherically symmetric mass. The parameter M in the Schwarzschild metric represents the mass of the object. The reason for using mass instead of total energy is because in the Newtonian limit, the total energy reduces to the mass. Additionally, the mass of an object is a fundamental property that remains constant regardless of the reference frame, whereas the total energy can vary depending on the frame of reference.