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Varying Energy in a Schwartzschild Metric

  1. Jun 6, 2012 #1
    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:

    [tex]\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[/tex]

    This will be interpeted as

    [tex]\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[/tex]

    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. jcsd
  3. Jun 6, 2012 #2
    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

    I can't link
  4. Jun 6, 2012 #3
    Sorry.. was in a rush when I wrote this, I forgot my dummy variables, inserted now.
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