All Questions
22
questions
1
vote
1
answer
164
views
How does null infinity differ from ordinary infinity?
Null infinity is the diagonal lines on the edge of a Penrose diagram. It seems to be the place where beams of light go if they never bump into anything, but only light can go there. It appears to be ...
- 278
3
votes
2
answers
612
views
Null infinity reachable by timelike worldlines?
Usually, Penrose diagrams are marked with points and segments being named past/future timelike infinity $i^{-,+}$, past/future null infinity $\mathscr{I}^{-,+}$ and spacelike infinity $i^0$ -- see for ...
- 743
2
votes
1
answer
85
views
Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed
This is one of the exercises on Wald's General Relativity:
Chapter 8, Problem 8.b Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed. (Hint: ...
- 22.1k
5
votes
1
answer
209
views
Why should a Cauchy surface be closed?
A Cauchy surface is defined on any spacetime $M$ as a subset $S$ which is closed, achronal, and whose domain of dependence $D(S) = M$.
Why do we include the "closed" condition in the above ...
- 1,588
1
vote
1
answer
63
views
Non-Compactness in Penrose Singularity
I've been studying singularities in GR, and (obviously), came across PST.
Let us state it as the following:
Let $(M, g)$ be a connected globally hyperbolic
spacetime with a noncompact Cauchy ...
- 487
1
vote
1
answer
111
views
Topology of Time
I came across the concept of topology of time and causality in Reichenbach book, "Philosophy of Space and Time". It would be nice to have list of references of recent developments of the ...
1
vote
1
answer
96
views
When a curve is future (past) inextendible?
Future (past) endpoint: We say that $p\in M$ is a future (past) endpoint of a curve $\lambda$ if for every neighborhood $O$ of $p$ there exists a $t_0$ such that
$\lambda(t)\in O$ for all $t>t_0$ (...
- 27
2
votes
0
answers
55
views
Why is the edge of a closed achronal set equal to the edge of its future Cauchy horizon?
This question is related to Proposition 6.5.2 of Hawking & Ellis. It states that
$$\text{edge}(H^+(\mathscr S))=\text{edge}(\mathscr S),$$
for a closed achronal set $\mathscr S$.
Of course, ...
- 1,487
1
vote
1
answer
319
views
How to show that the interior of the causal future is contained in the chronological future?
I want to show that $int[J^+(S)\subset I^+(S)$ for an arbitrary set S. I've done most of it I think but not up to the level of rigor that I would like. Here's what I have:
Let $p \in int[J^+(S)]$. ...
- 61
3
votes
1
answer
157
views
Characterizing compactness of the Alexandrov topology in a spacetime
This is perhaps more of a soft question and on the mathematical side of things, but I'm struggling to find references and to formulate a precise argument. There's of course the chance that what I'm ...
- 545
2
votes
1
answer
177
views
Penrose diagrams for non-spherically symmetric spacetimes
As far as I have seen, Penrose diagrams are composed for spacetimes where there is spherical symmetry. The angular degrees of freedom are suppressed so as to understand the causal properties of ...
- 1,200
3
votes
1
answer
115
views
Quantum Field Theory on non-globally hyperbolic spacetimes?
In all the references I have found on QFT in curved spacetime, they treat only globally hyperbolic Lorentzian spacetimes, not Lorentzian spacetimes in general. Are there any references which discuss ...
1
vote
0
answers
90
views
Any problem creating a global time function given known spacetime topology?
Gödel says the absence of a global time function
seems to imply an absurdity. For it enables one e.g., to travel into the near past of those places where he has himself
lived.
But is it not true ...
- 383
1
vote
0
answers
73
views
Should time be a loop or a line?
It's interesting to see that torus was so popular in physics, that it worked so well. There was famous Gauss–Bonnet theorem which stated basically
$$\oint_S K dS= 2\pi \chi(S)$$
where K was the ...
- 3,256
3
votes
1
answer
466
views
Can you conformally map the Lorentzian cylinder to the Lorentzian plane?
When studying CFT in Euclidean signature, for the purpose of radial quantization, we conformally map the Euclidean cylinder to the Euclidean plane (minus the origin, which I ignore).
Can one also ...
- 684