Recent content by cianfa72

Ah ok, so you (mistakenly) thought you had found a (counter) example consisting of a geodesic of ##E^4## which is not a geodesic of the 3-sphere (embedded within ##E^4##) that contains it. Ok, good.

Ok, therefore, according the today standard physics, there is no way to take a CTC journey or reach some (remote) region of spacetime via a whormhole or something like that..

Do physicists think that Gödel or Kerr-Gödel-type solutions could be plausible models for our Universe ?

Ok, this is actually an example of the other way around. Namely geodesics of that 3-sphere's contained surface fail to be a geodesics of the ##E^4##. Ah ok, yes. Actually in my post #48 I was thinking of spacelike hypersurfaces, though.

Well, then, for instance in Gödel's universe, by following a suitable timelike path, one could came back to the event where the journey began. Does the geometry/topology of Gödel's spacetime allow CTCs without having regions of infinite curvature or something like that (e.g. black holes) ?

Hi, I'm curious about the following: taking the point of view of the standard physics of spacetime including EFE's solutions, are there solutions that admit Closed Timelike Curves (CTC) ? In other words: do exist global topologies and Lorentzian metrics solutions of the EFE that support CTCs ...

No, maybe I wasn't clear. For any geodesic of the 4D Euclidean space you can always find an hypersurface containing it (on this hypersurface that curve is a geodesic of the induced metric).

This raises the following point. Let's take a spacelike geodesic of the 4D Lorentzian spacetime. There exists a spacelike hypersurface containing it, hence it is a (spacelike) geodesic on that hypersurface with the (Riemmanian) induced metric. What about the other way around. Under which...

You mean, taking a spacelike hypersurface (endowed with the induced metric) is basically a recipe to build a 3D Riemannian manifold.

As far as I can understand, in GR, the spacelike geodesics are (always) saddle points when considering them in the overall 4D spacetime. On the other hand, if you take a spacelike hypersurface and restrict yourself to consider only the (spacelike) geodesics w.r.t. the induced Riemannian metric...

Ok, this is similar to the Langevin congruence: take the worldline at the center of the rotating disk as "reference/fiducial" worldline. The neighboring worldlines of the Langevin observers in the congruence are described by a nonzero vorticity, yet they rotate around thanks to a suitable force...

Yes the vorticity is small, however it suffices to provide the rotation of the ISS w.r.t. the gyroscope's axis.

Better, I'd say the angular momentum is a bi-vector -- https://en.wikipedia.org/wiki/Angular_momentum

I was taking the more advanced viewpoint in which the momentum ##\boldsymbol p## is actually a co-vector (see for instance MTW chapter 2.5).

I mean the frame in which the system's CoM stays always at rest (zero total ##\vec P## w.r.t. it). Basically it shares the system's CoM velocity. If the system is under some non-zero external net (real) force then such a system's CoM rest frame will be non inertial. You mean that under some...