All Questions
107
questions
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End points of event horizon
I am reading The Nature of Space and Time by S. W. Hawking. In the last paragraph on page 16 he said that:
event horizon may have past end points but don't have any future end points
I understand ...
- 59
2
votes
1
answer
79
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A few doubts regarding the geometry and representations of spacetime diagrams [closed]
I had a couple questions regarding the geometry of space-time diagrams, and I believe that this specific example in Hartle's book will help me understand.
However, I am unable to wrap my head around ...
- 23
2
votes
1
answer
89
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Confusion about timelike spatial coordinates
I'm pretty new to general relativity, and I'm self-studying it using Sean M. Carroll's text on the subject. In Section 2.7, he introduces the notion of closed timelike curves. He gives the example of ...
- 160
3
votes
1
answer
79
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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
2
votes
1
answer
44
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Are non-point spacetime events partially ordered?
When describing events in spacetime, we usually use points. We then phrase the relation between points as a trichotomy: either they are timelike, spacelike, or lightlike separated, based on the ...
- 180
4
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answers
91
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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
1
vote
2
answers
71
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How do I interpret the time axis in a diagram with multiple light cones?
Light cones are often drawn on a spacetime diagram that has a directional time axis like the fourth one on this page:
There is a time axis, and all of the light cones are align with it because this ...
- 113
1
vote
1
answer
109
views
Carter-Robinson Theorem
There are uniqueness theorems that classify Black holes according to its mass, angular momentum and charge. One of the theorem is Carter-Robinson theorem which has many assumptions and then it says ...
- 59
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1
answer
54
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In Relativity theory, is chronological relation an order relation?
Let $(M,g)$ be a (Lorentz) spacetime, i.e a connected smooth manifold $M$ with a metric tensor field $g$ and a time orientation called future direction which is defined by a smooth timelike vector ...
- 143
1
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0
answers
44
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Global Hyperbolicity and Timelike Boundary
I am trying to understand and show that asymptotically Anti-de Sitter spacetimes are not globally hyperbolic.
Now, I have found papers that talk about global hyperbolic spacetimes with timelike ...
- 743
2
votes
0
answers
63
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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
2
answers
161
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If I were to drop my phone into a black hole, would I be able to catch it?
Say, for the sake of argument, I am outside the event horizon of a black hole and accidentally drop my phone (or some other object) into the hole. If I were to enter the black hole, would I ever be ...
- 121
3
votes
2
answers
612
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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
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28
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Same curvature but different orientation of light cones? [duplicate]
Can there be two regions of spacetime which have the same curvature, but with their light cones oriented in different directions?
In the Stack Exchange question "General Relativity via light ...
7
votes
2
answers
2k
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Do the Einstein Field Equations force the metric to be Lorentzian?
In GR, we are working with Lorentzian metrics, which are examples of a pseudo-Riemannian metrics. That is, we are trying to find pseudo-Riemannian $g_{\mu\nu}$ that are solutions to the field equation ...
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