In General Relativity the covariant derivative of contravariant vectors $A^\mu$ is: \begin{equation} \nabla_\mu A^\nu=\partial_\mu A^\nu+\Gamma^\nu_{\mu\alpha}A^\alpha \end{equation} where $\Gamma^\nu_{\mu\alpha}$ are Christoffel symbols. My question: how do we prove it verifies the Leibniz pr...

I'm learning about centripetal force and I was shown a scenario where a man was spinning a rope attached to a ball over his head. There's a centripetal acceleration toward the center and therefore a force must be acting in the same direction as the centripetal acceleration — the centripetal force...

How does an air conditioner work? A thermodynamics textbook discusses this topic in a fairly abstract way (notes): A refrigerator or heat pump is a device which, with work input, moves thermal energy from cold regions to hot regions. Without the work input, this could not be achieved, as it ...

According to Wikipedia: Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. My question is about this sh...