Compatibility with a metric, also referred to as metricity, means, I believe, that the covariant derivative of the metric is zero: $$g_{ij;k}=g_{ij,k}-\Gamma^m_{ik}g_{mj}-\Gamma^m_{jk}g_{im}=0$$ This is true identically for a symmetric metric and the associated Levi-Civita connection. If a torsio...

According to Einstein, mass, say in the form of matter, curves space. It is the curvature of space that gives rise to gravity. Now I have heard there is an energy associated with the curvature of space. If so, it will have a mass equivalent. Is this mass in addition to the mass causing the curvat...

What is the main motivation and advantages of the density matrix formalism compared to the wavefunction formalism? From what I understand, the density matrix is more commonly used when you want to include mixed states and to trace out contributions you don't want to focus on in your problem. But ...