I haven't yet had the pleasure of participating in a PF thread on this topic , although I have made at least one post that refers to it in passing. But I know there have been some in the past, such as this, so I wanted to post a quick treatment of the topic since it didn't seem like that previous thread ended in a clear answer.

My goal is to derive a simple equation for the proper acceleration of an observer traveling on a circular path around a Schwarzschild black hole at some...

Using formulas from previous posts, I now want to consider the question: what is the maximum amount of work that can be extracted by slowly lowering an object into a static, spherically symmetric gravitational field? This is a concrete, physical way of defining the concept of "potential energy".

We start with some comments and definitions. By "slowly lowering" we mean that the radial motion of the object is at some very slow, constant speed, so that we can ignore...

In two previous posts, we looked at various ways of interpreting the question "does gravity gravitate?" We left off at the end of the last post with an open question: what do the various "mass integrals" look like in a spacetime where GWs are being emitted? Let's look at that question now.

The key difference between GWs and other types of radiation is that GWs have zero stress-energy. They are oscillations in the curvature of spacetime. This fact makes it tempting...

In my previous post on this topic, I talked about two ways to answer the title question, one leading to the answer "no" and the other leading to the answer "yes". However, this will leave a lot of people who ask our title question unsatisfied, because the usual motivations for asking the question have little, if anything, to do with the general points I discussed. So let's look at some particular cases to hopefully shed some more light on the subject.

Consider...

This has come up in enough threads now that I feel the need to give my take on it in a convenient central location, so I can just link to it instead of having to restate it again and again.

Short answer: mu. (The terms of the question are not well-defined, so it doesn't have a well-defined answer.)

Somewhat less short answer: Yes and no. (It depends on how you define the terms "gravity" and "gravitate". There are possible definitions that...