0
votes
0answers
20 views

How to express “curvature scalars” in terms of "discrete curvature values $\kappa_n$?

We know from MTW [1] and Synge [2] how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
1
vote
0answers
59 views

Wick rotation and relativity

CMIIW, but as I understand it, Wick rotation replaces the Minkowski basis (t,x,y,z) with the Euclidean basis (it,x,y,z). Suppose that $t_2=t_1 cosh \beta+x_1 sinh \beta$ and $x_2=t_1 sinh \beta+x_1 ...
3
votes
1answer
66 views

Are there any restrictions on building the topology of spacetime out of the complement of open balls?

I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point ...
3
votes
1answer
115 views

An issue about the compactness and the existence of CTCs

There is a well known fact that a compact spacetime necessarily contains a closed timelike curve (CTC). Proof can be found in several books on GR (e.g. Hawking, Ellis, Proposition 6.4.2), and in ...
2
votes
1answer
375 views

Orientability of spacetime

In many theoretical setups it is implicitly assumed that the underlying manifold (i.e. spacetime) is orientable. Then our analysis depends on this implicit assumption. For example, Stokes' theorem ...
2
votes
2answers
186 views

Is the assumption of space time to be a continuum is just a matter of mathematical taste?

Is the assumption of space time to be a continuum is just a matter of mathematical taste ? Isn't there any physical significance associated with it.
9
votes
5answers
1k views

Hubble's law and conservation of energy

If all distances are constantly increasing, as Hubble's law say, then lots of potential energies of form ~$\frac{1}{r}$ changes, so how is the total energy of the Universe conserved with Hubble's ...