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

I'm having problems solving this problem I got in class.

I want to learn the concept and how to approach the solution.

Here it is:

Consider the metric

ds=dx^2+dy^2-dudv+2H(x,y,u)du^2

What form must the function H have for this metric to represent a plane gravitational wave propagating in vacuum?

This is how I'm approaching the problem:

first I let the metric be g_{σβ}=[1,0,0,0;0,1,0,0;0,0,2H,-1;0,0,-1,0]

and I know that in vacuum the Einstein equation in far outside the source's field leads to

T^{σβ} = 0

and I know that a metric representing a plane gravitational wave propagating in vacuum is

g_{σβ=[1,0,0,0;0,1,0,0;0,0,0,-1;0,0,-1,0]

coming from the metric ds^2=-dudv+dx^2+dy^2

Then I don't know how to put the pieces together. I was thinking relating the Einstein equation in terms of the ricci tensor and solving for the Christoffel symbols.

Not sure. I need to understand better the problem and how to approach this problem.

Thanks.

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

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

# Homework Help: Solving a metric in vacuum

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