Actually, extrinsic curvature turns out to be pretty important in the Hamiltonian/ADM formulation of GR. The general idea is that we can foliate spacetime with spacelike hypersurfaces and specify initial data on one of them in the form of a spatial metric h. Einstein's equations then determine...
The graviton isn't the metric itself; its the deviation of the metric from the background Minkowski metric in linearized gravity, i.e. g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}.
We can always choose a gauge in which h_{\mu\nu} is traceless, the so-called transverse traceless gauge.
Cheers,
Matt
I think what they want is this:
\frac{dT}{d\tau}=\frac{dT}{dx^\alpha}\frac{dx^\alpha}{d\tau}=\frac{dT}{dx^\alpha}u^\alpha=\partial_{\boldsymbol{u}}T=\langle \boldsymbol{d}T,\boldsymbol{u}\rangle
The reason I love MTW is that you can never tell if a problem is infuriatingly easy or...
Hi,
Does anyone know if there's a closed formula for the n-point function in a CFT? Up to anharmonic ratios, of course. Most books just have it up until n=4.
Thanks,
Matt
I don't think you're misusing words, it's just that the word topology is used for lots of different things. It seemed to me that the OP was asking about the point-set topology of the manifold. This means that we need to determine which subsets can be considered open. Since a manifold is locally...
The Riemannian (or semi-Riemannian) metric doesn't directly induce a topology on the manifold itself, because it's an inner product on each of the tangent spaces, i.e. a norm TpM cross TpM -> R. Having said that, there is a natural topology inherited from the metric geodesics on a Riemannian...
We have F(a,b)+F(b,a)=F(a+b,a+b) by linearity, which equals (a+b) dot F(a+b) by definition. Since F(v) is orthogonal to v for all v because the acceleration is orthogonal to the velocity, this equals zero. So F(a,b)=-F(b,a).
-Matt
Hi,
Another way of stating t^a\nabla_a t=1 is that the Lie derivative of t along t^a equals 1. So Wald is just saying that the vector field t^a is properly normalized so that the function t changes at a constant rate of 1 along its integral curves. This normalization would be impossible to...
The problem is 2.1.b in Becker, Becker, and Schwarz. I can't figure out what I'm doing wrong... any help would be appreciated, I'm probably missing something dumb.
Homework Statement
For X^0=B\tau, X^1=B\cos \tau\cos\sigma, X^2=B\sin\tau\cos\sigma, X^i=0 for i>2, compute the energy and...