# Category Archives: Differential Geometry

## The Curvature, the Einstein Equations, and the Black hole II: The Curvature

In this lecture, we study different notions of curvatures of a Riemannian or a pseudo-Riemannian $n$-manifold $M$ with metric tensor $g_{ij}$. We will discuss only local expressions of curvatures as those are the ones we actually use for doing physics … Continue reading

## The Curvature, the Einstein Equations, and the Black Hole I: Riemannian and Pseudo-Riemannian Manifolds

This is the first part of the lecture note that is an extended version of the series of lectures I have given in the physics seminar at the University of Southern Mississippi. The majority of the audience were graduate students … Continue reading