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Mass in Schwarzschild's metric

  1. Aug 16, 2014 #1


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    Gold Member

    I think this will be a quick question...
    If the Schw's metric is a solution of the vacuum, then what does the mass [itex]M_0[/itex] in the metric correspond to? I thought it was the mass of the star.... but if that's true then why is it a vacuum solution?
    Or is it vacuum because it describes the regions outside the star of radius [itex]R_{0}[/itex]([itex]r>R_{0},~~ M_0 \equiv M(R_{0}) [/itex]) ?
    Last edited: Aug 16, 2014
  2. jcsd
  3. Aug 16, 2014 #2
    For the exterior Schwarzschild metric, the parameter M would technically signify the total mass-energy content of the entire space-time.

    Because it describes the exterior vacuum region of the mass-energy distribution, i.e. the region where the energy-momentum tensor vanishes everywhere.
  4. Aug 16, 2014 #3


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    So would it be wrong to try and describe the interior of the star with a function [itex]M(r)[/itex] instead of [itex]M_{0}[/itex] the total mass?
  5. Aug 16, 2014 #4


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    Staff: Mentor

    Not at all, but the metric won't be the Schwarzchild metric in the interior region. It will, however, have to join smoothly to the Schwarzchilld metric for ##M_0## at the surface.
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