Recent content by joshyxc1979

No its not a homework question, I read it in an article by J. of Math Phys 29 (2) feb 1988. Static uniform density stars must be spherical in GR

Using the metric $$ds^2=-V^2 dt^2 +g_{ab} dx^a dx^b$$, where $$g_{ij}$$ is the Riemannian metric of the constant t-surfaces, and V is the gravitational potential, show that Einstein's equation $$G_{ij}=8\pi T_{ij}$$ for perfect fluids reduces to the system $$D^a D_a V= 4 \pi V( \rho +3p)\\...

when you tried induction, did you try the binomial theorem?

iii is applying the triangle inequality for real numbers, which is a metric. here is a proof of that: http://math.ucsd.edu/~wgarner/math4c/derivations/other/triangleinequal.htm