Recent content by latentcorpse

Hi, I have a 3d space with metric ds^2= -r^a dt^2 + r^bdr^2 +r^2 dy^2 and I need to construct an orthonormal frame. The first of these three basis vectors is fixed, let's say as e_0=A \partial_t + B \partial_r + C \partial_y To find the other two I set v_1=\partial_t, v_2=\partial_r and...

what was wrong with saying the length was bigger than twice the real part?

so (a-1)^2+(b-0)^2-1 \geq 0 (a-1)^2+(b-0)^2 \geq 1 so circle radius 1 centre (1,0)?

What's the set \{ z \in \mathbb{C}| |z|^2 \geq z+ \bar{z} \}? I've set z=a+ib and found a^2 + b^2 \geq 2a \Rightarrow b^2 \geq a(2-a) I'm not sure how to interpret this geometrically ie what it looks like? I suppose it is the set of vectors whose length is bigger than twice their real part. I...

Hi, I'm curious as to the differences between gauged and ungauged SUSY and gauged and ungauged SUGRA. Perhaps I can break down my problems into the following few questions: (i) I understand that to go from SUSY to SUGRA, one must make the supersymmetry local. What does this mean? I've read...

Yeah that's what I did and I'm fairly sure the technique is correct and I just cannot see the mistake that's giving me the wrong number. The Einstein eqn should be -\frac{1}{2} R_{\mu \nu} + \delta_{ab} \partial_\mu q^a \partial_\nu q^b + \frac{1}{2H} g_{\mu \nu} V(q)=0 Now when I vary with...

I have a 3d system with Lagrangian e_3^{-1} L_3 = -\frac{1}{2} R_3 + \delta_{ab} \partial_\rho q^a \partial^\rho q^b + \frac{1}{2H} V(q) From this I want to calculate the Einstein equation by performing the Euler-Lagrange procedure. First of all, I move the 3d dreibein to the RHS and then I...

So the correct defn is the hypersurface stuff because it is coordinate invariant. Is it correct to say that if it's static then it's always possible to find a coordinate system with g_{tx}=0?

Why do you have a square root? This would correspond to "ds" rather than ds^2 and I though ds was an infinitesimal line element i.e. a measure of distance? If the metric is just a statement about orthogonality, how is it connected to length? Or is it only a statement about orthogonality when...

Static spacetimes can be defined as having no g_{tx} component of the metric. Alternatively we can say that they are foliated by a bunch of spacelike hypersurfaces to which the Killing vector field \frac{\partial}{\partial t} is orthogonal. How are these two statements consistent...

Your eqns are lacking any first order derivatives. How did you get them? Even accepting your dispute with my \ddot{t} equation, I don't see how you get a \tanh{r} in the \ddot{r} equation?

I disagree. I find \Gamma^t_{tt} = \frac{1}{2} g^{tt} g_{tt,t} = - \frac{1}{2 \cosh^2{(r(\tau))}} \left( -2 \cosh{r} \sinh{r} \frac{dr(\tau)}{dt} \right) = \tanh{r} \frac{dr}{d \tau} \frac{d \tau}{dt} = \tanh{r} \frac{\dot{r}}{\dot{t}} Does that make sense?

Actually I realize I made a mistake in my above answer. I now find \ln{u} = -2 \ln{\cosh{r}} + C \Rightarrow u = A ( \cosh{r})^{-2} Substituting into the other geodesic equation gives \ddot{r} + A^2 \frac{\sinh{r}}{\cosh^3{r}} =0 I don't know how to solve this and am now thinking that...

Yes I have read through it but I'm afraid the connection between the path and the quotient manifold is not clear to me. Is it to do with post #3 that you make. You pick a frame where the clocks are at rest (equivalent to quotient manifold) and set up the clocks on a path \gamma and say the...

So the synchronisation gap is due to SR effects eg time dilation. That seems fair enough. But what's the connection to lack of hypersurface orthogonality? Is it just that lack of orthogonality means the spacetime is stationary and therefore allowed to rotate which introduces these SR effects? Or...