- #1
pstq
- 10
- 0
Hi there.
1. The problem statement
I am asked to write the equations which give us the mass of a black hole as function the proper time.
The Schwarzschild metrics is given by
$$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$
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
1. The problem statement
I am asked to write the equations which give us the mass of a black hole as function the proper time.
Homework Equations
The Schwarzschild metrics is given by
$$ ds^2=-(1- \frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+ r^2(d\theta^2+ \sin^2(\theta) d\phi^2) $$
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