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

I don't fully understand what is the regular method to state and solve problems in GR when no handy hints like spherical symmetry or homogeneity of time are assumed. If I find myself in arbitrary reference frame with coordinates [itex]x^0[/itex], [itex]x^1[/itex], [itex]x^2[/itex], [itex]x^3[/itex] the meaning of which is unknown beforehand (or known only locally), how do I proceed with boundary conditions and stress-energy tensor?

Consider the following simple problem: two point masses [itex]m_1[/itex], [itex]m_2[/itex] are separated by distance [itex]a[/itex]. Obviously [itex]T_{\mu\nu}[/itex] is a sum of two delta functions. Suppose the first mass is at the origin but where then is the second mass? Should I write [itex]\delta(x^1 - a)[/itex] or [itex]\delta(\sqrt{(x^1)^2 + x^1 x^2} - a)[/itex] or ...? You may say - OK, choose the coordinates in such a way that [itex]\delta(x^1 - a)[/itex] would be valid. But there are only 4 possible coordinate transformations, what if I had thousands of point masses?

So it seems that in general a statement of a problem in GR is interconnected with its very solution, which is confusing: are all problems solvable? uniquely? what would a "real mccoy" equation look like?

**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!

# Regular method to solve GR equations

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