# Varying Energy in a Schwartzschild Metric

1. Jun 6, 2012

### Meselwulf

This short work will help to calculate the varying energy for a non-rotating spherical distribution of mass.

The Energy changing in a Schwartzschild Metric

It is not obvious how to integrate an energy in the Schwartzschild metric unless you derive it correctly. The way this following metric will be presented will be:

$$\int_{t}^{t'} c^2 d\tau^2 dt = \int_{t}^{t'} (1 - 2\frac{Gm}{\Delta E} \frac{M}{r_s} c^2 dt^{2}) - \frac{dt}{(1-2\frac{Gm}{\Delta E} \frac{M}{r_s})} - r^2 d \phi dt$$

This will be interpeted as

$$\int_{t}^{t'} c^2 d\tau^2 dt = \int_{t}^{t'} (1 - 2\frac{Gm}{E - E'} \frac{M}{r_s} c^2 dt^{2}) - \frac{dt}{(1-2\frac{Gm}{E - E'} \frac{M}{r_s})} - r^2 d \phi dt$$

And this metric is dimensionally-consistent to calculate the energy changes within a metric. Usually, in the spacetime metric, we treat it as a energy efficient fabric. This can be a way to treat a metric with a type of energy variation consistent perhaps with a radiating body.

Last edited: Jun 6, 2012
2. Jun 6, 2012

### Meselwulf

I was inspired to find a more simple example of a varying energy from Loyd Motz' paper

A Gravity Generation of Electromagntic Radiation and the Luminosity of Quasars