Equations of General Relativity
Equations of General Relativity
I have thought seriously about this question,
and have come to the conclusion that
what I have to say cannot reasonably be conveyed
without a certain amount of mathematical notation
and the exploration of genuine mathematical concepts.
Roger Penrose The Road to Reality
Problem 1.
Most cosmological models are based on the assumption that the Universe is spatially homogeneous and isotropic. Give examples to show that the two properties do not automatically follow one from the other.
A system with constant magnetic field is homogeneous but not isotropic, because the direction along the field and perpendicular to it are not equivalent. On the contrary, a spherically symmetric distribution of electric charges is by construction isotropic, but not, in general, homogeneous.
