cianfa72's latest activity

Can you formally prove it ?

As far as I know, there are two definitions of tensor field on a differential manifold ##M##. Just to fix ideas consider the two-times...

To me, the idea is that formalizing the notion of global isotropy and homogeneity leads to both topological constraints and geometric...

Ah yes, definitely. Indeed in those lectures maximally symmetric condition enter later to write down the metric in RW form.

My goal was to better understand the point he made there. At minue 37:30 he claims that in 4D, the global hyperbolicity condition (i.e...

It's worth noting that this is not purely a topological restriction; the concept of a "maximally symmetric manifold" requires a metric...

The lecturer claims that, to write down EFE's solutions in a simplified form (like RW metric), the spacetime must be globally...

So why does the lecturer (D. Giulini) claim that condition/restriction on the (global) topology of spacetime in that lecture ?

I'm keep watching the lectures on GR from F.P. Shuller and D. Giulini -- International Winter School on Gravity and Light. As far as I...

The two formal defintions of born rigidity I'm aware of apply to timelike congruence which I will denote as ##u^a##. I believe the...

Back to the Langevin congruence: it is a timelike stationary congruence. Which is the definition of timelike stationary congruence ...

$$g_{\mu\nu}g^{\nu\rho}=g_{\mu}^{\ \ \ \rho}$$ $$g_{\mu\nu}g^{\rho\nu}=g_{\mu}^{\rho}$$ $$g_{\nu\mu}g^{\rho\nu}=g_{\ \ \ \mu}^{\rho}$$...

But only ##g## can be used to raise and lower indices, and ##g## is symmetric.

So your point is: in the second case ##g_{\mu \nu} g^{\rho \nu}## seen as ##g_{\mu \nu} (g^{\rho \nu})##, before calculating the...

Yes, it doesn't matter at all since ##g## is symmetric. However, from the formal viewpoint of tensor calculus, the results in the second...