So far in my explanation of General Relativity, I’ve discussed the metric $$g_{ab}$$, from which one can calculate the curvature tensor $$R^{a}_{bcd}$$ by way of the connection $$\Gamma^{a}_{bc}$$. In practical astrophysical contexts: The metric is related to the gravitational potential … Continue reading
BioLogos has kindly published the first part of a 2-part series about thermodynamics and black holes. The links are here: One Way Streets: Black Holes and Irreversible Processes, Part 1 One Way Streets: Black Holes and Irreversible Processes, Part 2 … Continue reading
Suppose we have a field $$\Phi$$ in a curved spacetime, and we want to know how fast it is changing as you move in some direction in space or time. Because there is more than one possible direction to move … Continue reading
One of the things I’ve been trying to do on this blog is to explain Einstein’s theories of relativity. Here are my previous posts on this subject: Time as the Fourth Dimension? The Ten Symmetries of Spacetime Fields Geometry is … Continue reading
I’ve told you so far that the gravitational field is encoded in a $$4 \times 4$$ matrix known as the metric. Here it is, displayed as a nice table: $$! g_{ab} = \left( \begin{array}{cccc} g_{00} & g_{01} & g_{02} & … Continue reading