Tagged Questions
1
vote
1answer
77 views
Killing vector argument gone awry?
What has gone wrong with this argument?!
The original question
A space-time such that $$ds^2=-dt^2+t^2dx^2$$
has Killing vectors $(0,1),(-\exp(x),\frac{\exp(x)}{t}), ...
0
votes
1answer
42 views
Does the actual curvature of spacetime hold energy?
My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
1
vote
2answers
161 views
Excluding big bang itself, does spacetime have a boundary?
My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity).
Does this mean that ...
6
votes
1answer
131 views
Our Universe Can't be Looped? [duplicate]
With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
0
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0answers
33 views
metric extension outside the light cone
Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past ...
3
votes
1answer
76 views
The most general form of the metric for a homogeneous, isotropic and static space-time
What is the most general form of the metric for a homogeneous, isotropic and static space-time?
For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
1
vote
0answers
60 views
Do we expect that the universe is simply-connected? [duplicate]
I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the ...
2
votes
1answer
137 views
Space time a function of itself, objects in it, or both?
Is spacetime a function of itself, objects within it, or both? I am struggling to understand just what is spacetime without objects in it (or theoretical reference points) and thus no frame of ...
2
votes
3answers
124 views
Why are black holes special?
A black hole is where it's mass is great enough that light can't escape at a radius above the surface of the mass?
I've been told that strange things happen inside the event horizon such as ...
1
vote
0answers
46 views
When is spacetime homogenous and isotropic?
When is spacetime homogenous and isotropic?
For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric
$$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + ...
1
vote
0answers
45 views
Naked singularity and null coordinates
I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
2
votes
0answers
48 views
Naked singularity and extendable geodesics
I'm currently trying to understand the notion of a naked singularity. After consulting books by Wald and Choquet-Bruhat, it seems that for a naked singularity one must have that the causal curves can ...
2
votes
4answers
203 views
Time inside a Black hole
If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black ...
0
votes
1answer
81 views
Space time curvature real or theoretical (mathematical)?
Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
0
votes
2answers
105 views
Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? [duplicate]
The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't ...
1
vote
3answers
134 views
About gravity through space time curvature
Is it possible to produce virtual gravity? I mean gravity without the help of mass by curving spacetime with other effects like fast rotating objects?
1
vote
1answer
69 views
Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?
In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime.
If I ...
0
votes
2answers
123 views
If the universe is 3D, how is space-time like a “fabric”? [duplicate]
I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures ...
1
vote
2answers
136 views
How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?
The metric tensor for Fock-Lorentz space-time,
$$
\mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
0
votes
0answers
157 views
Spacetime around a Black Hole
If we consider the sun, then space-time is curve around it. My question is that what is the kind of curvature of space and time around the black hole. Is that space and time more curved around the ...
4
votes
1answer
141 views
Does the curvature of space-time cause objects to look smaller than they really are?
What's the difference between looking at a star from a black hole and looking at it from empty space?
My guess is that the curvature of space-time distorts the wavelength of light thus changing the ...
1
vote
2answers
71 views
Why can certain functions be absorbed into the Schwarzschild metric, while others can't?
Another question about the Schwarzschild solution of General Relativity:
In the derivation (shown below) of the Schwarzschild metric from the vacuum Einstein Equation, at the step marked "HERE," we ...
1
vote
2answers
90 views
about the 1D singularity of black hole
I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the ...
2
votes
2answers
114 views
Does gravitational redshift imply gravitation time dilation?
The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
3
votes
3answers
305 views
Why do clocks measure arc-length?
Apologies in advance for the long question.
My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
4
votes
3answers
155 views
Setting up a local-coordinate system in space-time using only a single clock and light beams
I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please ...
4
votes
3answers
231 views
Can spacetime exist in the absence of matter and energy?
I'm pretty sure Ernst Mach would have said that spacetime cannot exist without matter in it.
But I'm also pretty sure that a black hole can be described as a self-sustaining gravitational field, ...
2
votes
2answers
104 views
Does spacetime have momentum?
In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
0
votes
0answers
115 views
Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?
A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
-4
votes
3answers
175 views
How can mass affect spacetime?
In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?
2
votes
2answers
122 views
Curved space or curved spacetime?
As I understand it, you can have time + flat space = curved spacetime.
So, when one is trying to emphasise that there is a curvature to the space, is it more technically correct to say curved space ...
10
votes
4answers
342 views
The definition of an inertial reference frame in Einstein's relativity
I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
2
votes
3answers
181 views
Are the principles of space-time homogeneity and Isotropy independent of one another?
Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
3
votes
3answers
259 views
Could metric expansion create holes, or cavities in the fabric of spacetime?
Is it possible for metric expansion to create holes, or cavities in the fabric of spacetime?
According to the Schwarzschild metric, the metric expansion of space around a black hole goes to infinity ...
4
votes
2answers
208 views
Space-time geometry and metric
I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
3
votes
1answer
97 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 ...
8
votes
1answer
494 views
Is String Theory formulated in flat or curved spacetime?
String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with ...
3
votes
1answer
255 views
Problem with convergent geodesics at 2D sphere
There is a chapter on general relativity in the book Spacetime Physics Introduction To Special Relativity by Taylor and Wheeler, which qualitatively explains how attractive gravitational force can be ...
7
votes
1answer
153 views
Is spacetime flat inside a spherical shell?
In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
2
votes
1answer
202 views
What bends fabric of space-time?
I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it?
Other energy sources, forces ...
1
vote
1answer
129 views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
5
votes
0answers
156 views
Penrose Conformal diagram for flat 2-dim Lorentz space-time
I have the following metric
$$ds^2 ~=~ Tdv^2 + 2dTdv,$$
defined for
$$(v,T)~\in~ S^1\times \mathbb{R},$$
e.g. $v$ is periodic.
This is the according Penrose diagram:
Question 1) Is the ...
-3
votes
1answer
72 views
Is it fabric of space or fabric of space-time?
Very quick question, in the general relativity is it fabric of space, fabric of space-time or both mentioned?
1
vote
1answer
209 views
What is the general relativistic calculation of travel time to Proxima Centauri?
It has already been asked here how fast a probe would have to travel to reach Alpha Centauri within 60 years. NASA has done some research into a probe that would take 100 years to make the trip. But ...
-9
votes
1answer
200 views
Why are we talking about space curvature as if we know what space is? [closed]
1) Why are we talking about space curvature as if we know what space is?
Every question about gravity seems to evoke an answer involving "space curvature" which seems like an undefined placeholder ...
0
votes
3answers
142 views
The radius of the universe and time
Ok - fair warning - Non-physicist asking dumb-assed questions here again.
I've been reading a lot of Einstein, Feynmann, Ferris etc. I'm just loving this stuff.
But I suddenly found myself looking at ...
1
vote
1answer
117 views
Is it possible to describe the entire universe with the behavior of an $\mathbb{R}^n$ field?
Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as ...
2
votes
1answer
236 views
Does electric charge affect space time fabric?
I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the ...
5
votes
0answers
145 views
Energy balance of closed timelike curves in Gödel's universe
I recently read Palle Yourgrau's book "A World Without Time" about Gödel's contribution to the nature of time in general relativity.
Gödel published his discovery of closed timelike curves in 1949. ...
3
votes
7answers
1k views
According to General Relativity, Does The Past “Exist”?
I'm curious about just what is meant by time being another dimension, like the three (observable) spatial dimensions. Does this imply, according to General Relativity, that the past and the future ...
