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Black hole mass as function proper time

  1. Nov 10, 2012 #1
    Hi there.

    1. The problem statement
    I am asked to write the equations wich give us the mass of a black hole as function the proper time.

    2. Relevant equations

    The Schwarzschild metrics is given by
    $$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$


    3. The attempt at a solution
    The proper time [itex]\tau[/itex] is related to the metrics by the eq.[itex]ds^2=-d\tau ^2 [/itex] hence I need to calculate the following expression [itex]\Delta\tau= - \int \sqrt{ds^2} [/itex] in order to get the proper time, and finally i have to solve for M, (the mass)

    Am I right? , any idea?

    Thanks
     
  2. jcsd
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