Recent content by La Guinee

In Carrol's text, he shows that the covariant derivative of the Ricci scalar is zero along a Killing vector. He then goes on to say something about how this intuitively justifies our notion of geometry not changing along a Killing vector. This same informal reasoning would seem to imply that...

Thank you all for the replies!

Is there a way to reasonably define "proper velocity" inside the event horizon? What would be the relation between this coordinate system and the standard Schwarzschild coordinates?

I don't know the answer to this question. Here's what I do know. We on the outside never see it cross the event horizon. However, in the frame of the particle, it does in fact cross the event horizon with no problem. And of course, once it does, it's doomed. You can calculate the amount of...

I see. That makes sense. I suppose this is a little off topic, but does string theory provide an answer to how curvature arises from the graviton?

My whole point was that QED is completely different because the photon mediates the EM force between particles, but in the case of gravity, it seems like there's no need for a mediator because the geometry of spacetime is the force. I know this gets into quantum gravity, but I think there's a...

If I understand things correctly, GR says that gravity isn't really a force at all, gravity is just particles moving in the geometry of spacetime. Given this, I don't understand the role of the graviton. I thought that gauge bosons were force mediators, that they somehow communicated and...

I see, thanks.

Consider a particle that has fallen inside the event horizon of a black hole. You can show that it must have a minimum radial velocity that scales as \frac{1}{\sqrt{r}} for small r. Where, by radial velocity I mean \frac{dr}{d \tau} and tau is the proper time. Doesn't this mean that as...

I found a paper that gives the estimate Lambda ~ 10^-52. That is indeed pretty small.

I take back what I just said. The condition would be that Lambda R^2 would have to be much less than 1, where R is the maximum distance over which Newtonian gravity has been observed to hold. Is this consistent with current estimates of the cosmological constant? In particular, the current...

I don't see how that makes sense. No matter how small the cosmological constant is, I can find an r much much greater than the cosmological constant. Unless you're saying the cosmological constant is small even compared to the size of the universe.

Wouldn't we have experimentally detected a potential that grows as r^2?

Ok. But if a nonzero cosmological constant has an r^2 potential it can't be compatible with our universe either. How does one reconcile this with the fact that people think the cosmological constant isn't zero?

Consider the vacuum solution to Einstein's equations with non-zero cosmological constant. Following Carroll, we can find the equation for the radial geodesic with the aid of killing vectors. It takes the standard form: E = T + V. But, with non-zero cosmological constant V(r) now has a term...