Recent content by snoopies622

hmm i thought the path of a static observer in Schwarzschild spacetime was a Killing vector, since the metric doesn't change as one simply advances in time. https://physics.stackexchange.com/questions/214434/killing-vectors-in-schwarzschild-metric?rq=1

Follow up: It looks like — just going by my geometric intuition here — that Killing fields must have zero divergence. Can one please give an example of a vector field with zero divergence that is not a Killing field?

Thanks Peter, i think i'm getting a feel for it now. Like the way a set of particles in a stone move when the stone is either translated or rotated.

It comes up at the top of this search, but strangely not finding the quote in the cited PF thread itself...

I found this quote on a different PF thread: For parallel transport, you move the vector in a direction that is always parallel to the curve. For Lie transport, you move the vector so that its direction is always perpendicular to the curve. Thoughts? It sounds like this restricts the...

I don't have an intuitive feel for Killing vectors. Wikipedia says, " . . . more simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object." That just sounds like...

Thank you both. Fascinating subject.

Doing a few calculations, i'm struck by this asymmetry: From the perspective of the inertial observer (A), the accelerating spaceship (B) has a speed which asymptotically approaches the speed of light, while from B's reference frame, A's speed asymptotically approaches zero. I haven't yet...

Thanks KDP, that helps a lot!

Question: the Wikipedia article says that, given a spacetime point defined by X,T in the inertial coordinate system, the time in the accelerated frame is t = \alpha ^{-1} arctanh(T/X) which of course is undefined at X=0. I can see why this would be the case when T>=0 since a beam of light...

Thanks, i think i get it now. For me this is another case where changing x to xi and the hyperbolas to circles is very intuitively helpful.

I'm not perfectly clear about how Rindler coordinates work. Here's what i do understand: Suppose I'm in an inertial reference frame and i define the location of the events around me with (x,t), (ignoring the y and z directions here) and a spaceship approaches me from afar and then flies away...

I did find it troubling that one could start with an approach that assumes a gravitational field to arrive at a relationship which doesn't involve gravity at all.

Thank you both. I've done a little more reading about this since i posted this question and realize it's not as simple a matter as i thought. I'm always interested in the underlying premises, the axioms as it were. Here's an interesting video where the function is apparently derived using the...

I'm trying to understand the Maxwell-Boltzmann gas molecule speed distribution. Suppose we have a container of gas such that all the molecules are identical. At first I was under the mistaken impression that one starts with the premise that the distribution of their translational kinetic...