All Questions
38
questions with no upvoted or accepted answers
4
votes
0
answers
91
views
Is the causal structure completely determined by the Weyl tensor alone?
By causal/conformal structure I mean the context of Malament's 1977 theorem. If I understand correctly this means that any two spacetimes which agree about all of the future-directed continuous ...
- 151
4
votes
0
answers
84
views
Conformal Diagram for Astrophysical Black Hole
I have a question about the conformal diagram of an ‘astrophysical’ black hole which forms in finite time (but with no evaporation).
Usually I see the conformal diagram presented as something similar ...
- 55
4
votes
0
answers
84
views
The point of holedness
In general relativity there is a vaguely defined notion of a spacetime having "holes", with many different definitions. Many of those were cast off when it was realized that Minkowski space also has ...
- 16.5k
3
votes
1
answer
79
views
How to Understand Negative Energy in the Ergoregion?
I am trying to understand the Penrose process and having trouble explaining negative energy in the ergoregion.
How I interpret it is:
Energy is the dot product between the four momentum of the object ...
- 63
3
votes
0
answers
98
views
Can a timelike curve catch up to a causal curve?
In Wald's General Relativity, Lemma 8.1.4, he proves that if $\gamma$ is a causal, past-directed, inextendible curve passing through $p$, then through any $q \in I^+(p) = \{\text{all points reachable ...
- 31
3
votes
0
answers
322
views
Malament theorem in curved spacetime?
Malament's theorem roughly assert that given a very general theory of a point particle, characterized by some operator $P_D$ such that for a region of space $D$ at a given time $t$, $P_D | \Psi \...
- 16.5k
2
votes
0
answers
36
views
How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?
Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
- 31
2
votes
0
answers
35
views
Is there a general methodology for causal nets of observables regardless of kinematics?
The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
- 16.5k
2
votes
0
answers
63
views
Conjugate points on manifolds
My question is:
Why do conjugate points exist on globally hyperbolic manifolds, satisfying the strong energy condition?
We define M to be globally hyperbolic if it posseses a cauchy surface and a pair ...
user390166
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
2
votes
0
answers
110
views
Is the time dimension naturally linked to the real axis?
The real number axis is asymmetric against zero: for instance, multiplication of two negative or two positive numbers will produce a positive number, a square root of a negative number is not real, ...
- 11.2k
2
votes
0
answers
323
views
Spacelike, timelike, lightlike vectors and the light-cone structure
Consider a semi-Riemannian manifold which of these statements is false:
All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in ...
- 305
2
votes
0
answers
89
views
Hausdorff property in Minkowski spacetime
In the 4-dimensional Minkowski spacetime, for a given point $x = (x^0,x^1,x^2,x^3)$, its timelike future/past set is defined as,
$$ I^{\pm}(x) = \{y =(y^0,...,y^3) \in \mathbb{R}^4 : \eta_{\mu \nu}(y-...
- 21
2
votes
0
answers
99
views
Locality and relativity - a paradox?
The equations of nature are supposed to exhibit locality in the sense that the action depends on fields and their derivatives. i.e. comparing the values of fields at local points.
But two points on a ...
user84158
2
votes
0
answers
101
views
If microscopic dimensions were found in particle experiments, how do we determine whether it is spatial or temporal?
This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe ...
- 935