Hello everybody,(adsbygoogle = window.adsbygoogle || []).push({});

I was studying the lecture notes about the schwarzschild solution for general relativity. In a particular example they calculate the equations of motion of a particle falling straight into a black hole. But there are some things about the calculation I really don't get.

First of all they say that because the schwarzschild metric is time independent, so dg/dt = 0 => u_0 = const. Then they show that by using the initial conditions r = R and tau = 0 and t = 0 coincide, that u_0 equals to sqrt( g_00(R) ) = sqrt(1 - 2M/R).

I've tried to prove the constancy of u_0 from the geodesic equation, but all I got were some nasty coupled differential equations.

Somehow it is true that constancy of metric in one component direction implies that the four-velocity in that component is constant. But I don't see why that is true. And how can you show from this, that this means that u_0 = sqrt(1-2M/r) ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geodesics in schwarzschild solution

**Physics Forums | Science Articles, Homework Help, Discussion**