All Questions
Tagged with spacetime general-relativity
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Hawking and Ellis Lemma 4.3.1 Proof
I have a few questions about Hawking and Ellis' proof of this lemma (pages 92-93):
Write the $(2, 0)$ stress-energy tensor in coordinates as
$\mathbf{T} = T^{ab} \partial_a \otimes \partial_b$ and ...
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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 $p \in int[J^+(S)]$. ...
CommunityBot
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Action principle dependent on spacetime-topology?
Consider the Lagrangian density
$$L(\phi, \nabla \phi, g) = g^{\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi$$
If one varies the action as usual, then one finds the equation
$$\delta S = \int_{\mathcal{...
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Could Space-Time Displace or Distort Itself? [closed]
1. Question
Could space-time distort and displace space-time?
If space-time can interact with surrounding space-time, then which ...
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Does Mass Actually Displace Space-Time, or does Mass only Distort it?
1. Question
Given the plethora of space-time illustrations, there is a sense that space-time is actually being displaced by mass, (planets). But on its face, this doesn't really make sense because ...
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Boundary conditions on transition maps on general relativity
On the initial courses of topology and differential geometry, we learn again and again about charts, and atlas, and transition maps. I feel that transition maps are a very powerful idea, because they ...
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Does time exist without Gravity?
If you travel the universe and move into an area where there is negligible gravitational influence, does time stop? As an observer, would this be like watching someone cross the event horizon of a ...
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What is the geometry of light cones if space is curved/non-Euclidean?
In light cone diagrams, the plane corresponding to the present is always the Euclidean one, but what if space is curved? Now, I've also seen diagrams where spacetime is supposed to be regarded as ...
CommunityBot
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We know there is no aether, so what is being dragged in frame dragging?
I have read this question:
In stellar frame dragging what is the 'frame'?
There are several questions on this site about frame dragging, all of them take the frame that is being dragged as an ...
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On time arrow and coordinate change in General relativity
This may be a silly question but I would like to have things cleared up once and for all in my head.
I will take the example of a Schwarzschild black hole as a solution to vacuum Einstein Field ...
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How exactly does curved space-time describe the force of gravity?
I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or ...
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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 ...
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3
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How did Einstein figure out mass (and hence energy) bends spacetime?
I can understand that once I fix the velocity of light at $c$, there is a relative variation in space-time based on special relativity (inertial frame of reference). It's not clear to me how Einstein ...
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Do you always experience the gravitational influence of other mass as you see them in your frame?
You see a galaxy far away. That galaxy is attracting you with a certain amount of gravity. I'm wondering if the gravity influence of the galaxy on you, as measured by you, always ends up being what ...
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Diameter of a sphere in the regime of general relativity
Lets start naive: empty space, define the origin somewhere, start putting mirrors in a distance of $r$ in many directions so that they roughly sample the surface of a ball of radius $r$.
Someone ...
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