All Questions
589
questions
0
votes
0
answers
5
views
Spinning top moving in curved spacetime
If I have a spinning top in empty space, it would take work to change the orientation of the angular momentum vector of the top. Suppose I throw a spinning top in flat space such that the direction of ...
- 1,222
-3
votes
0
answers
64
views
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 ...
- 87
0
votes
0
answers
40
views
Extrinsic Curvature in a conformally-flat spacetime that is also asymptotically-flat spacetime
I would appreciate if someone can confirm or correct my understanding of extrinsic-curvature (as in the ADM 3+1 decomposition of spacetime) when dealing with a conformally-flat spacetime.
(I updated ...
- 21
-3
votes
3
answers
76
views
Does Matter Cause Curvature or Vice-Versa [closed]
From the way explanations about gravity-acceleration-curvature equivalence are usually phrased here or elsewhere, it would appear many or most think that matter causes space-time curvature.
I cannot ...
- 115
5
votes
3
answers
239
views
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 ...
- 131
2
votes
2
answers
917
views
Theoretically, can perfectly flat space exist in the universe?
According to general relativity, mass and energy cause the curvature of space. To have perfectly flat space, there must be a completely empty vacuum state with no mass or energy.
Theoretically, is it ...
- 305
2
votes
1
answer
68
views
Understanding Wormholes Geometrically
Is the folding sheet analogy really that good for understanding what a wormhole is? After all, space-time curvature doesn't require any ambient space (it's intrinsic), as such a picture would suggest. ...
- 323
26
votes
10
answers
13k
views
How do black holes move if they are just regions in spacetime?
If black holes are just regions of spacetime, how can black holes even move? When matter moves through spacetime, it bends the spacetime around it, but if black holes are just regions of spacetime, ...
- 403
1
vote
0
answers
48
views
How can you use gravity while trying to model gravity? [duplicate]
So consider the usual pop-science spacetime model, a bowling ball on a trampoline. Apparently, the ball should sink into the trampoline, causing a dip in the fabric which causes nearby objects to fall ...
- 141
-7
votes
1
answer
138
views
So just because gravity "merely" bends space and isn't "really" a force at a distance - isn't it still a thing at a distance? [closed]
As a preamble, just for clarity as far as I can remember (I was awfully drunk) I have a degree in physics, math and comp sci: my point is "here's a probably stupid question at the level of person ...
- 994
-1
votes
1
answer
53
views
If an area in 2D cannot be curved and finite is the same regarding the space of our pressumed 3D universe?
Is the sentence in the title right that our universe is infinite? And if so does it mean that stars are not evenly distributed along our universe but they all move from a populated centre to a fairly ...
- 2,255
1
vote
1
answer
57
views
Does the Weyl tensor amount to tidal effects of gravity?
The Ricci tensor, for the spacetime surrounding the Earth, is zero, so the spacetime around the Earth is Ricci-flat.
The Riemann tensor though is not zero since spacetime certainly is curved. This ...
- 450
2
votes
2
answers
111
views
Why does the warping of spacetime make objects move closer together?
I understand why the warping of spacetime affects moving objects, but why would it affect stationary ones if it even does? Would two completely stationary objects not move closer together because they ...
18
votes
2
answers
3k
views
How does spacetime curve around an object in superposition?
I'm trying to learn quantum mechanics and this is a question that came to mind. I tried searching for it online, but I couldn't find a good answer (or at least one I could understand). From what I ...
- 191
0
votes
1
answer
59
views
Are gravitons suggested as the cause of matter curving space?
My understand is that GR says that mass curves space but it does not say why or how this occurs. Is the idea of gravitons that they are the entities that actually affect space?
- 2,238
0
votes
0
answers
72
views
How to mathematically describe the process of spacetime curvature?
I guess as a result of the energy-momentum tensor $T_{\mu\nu}$ coupling to a flat Minkowski metric, $\eta_{\mu\nu}$, the flat metric can become that of a curved spacetime, $g_{\mu\nu}$. How can one ...
- 357
1
vote
1
answer
67
views
How would objects move in a linear gravitational field?
In General Relativity, gravity is described as the curvature of spacetime caused by mass. This curvature is often visualized as a straight path bending due to a warped surface. My question is: If, ...
- 87
0
votes
1
answer
33
views
Measuring distances between the stars
If we know how far away are the two known stars from Earth, then is it a safe bet that we can know how far apart those two stars are from each other using sine rules? Does that mean we must first ...
- 13k
0
votes
0
answers
73
views
Are there any ways to conceptualize the relationship between gravity and space-time other than curvatures?
This might sound like a random question, but it came to me while I was trying to conceptualize the size of the universe and started thinking of entire galaxies resembling grands of sand floating ...
1
vote
1
answer
67
views
Why does trajectory in the space curved by gravity, depend on the speed?
I am sorry about the probably naiive nature of this question (I am a software eng, not a physics student):
I (think I) understand the popular curved "trampoline" model of 2-dimensional space,...
- 13
1
vote
2
answers
85
views
What is Dirac's reasoning when saying parallel displacement creates vector field with vanishing covariant derivative?
Section 12 of Dirac's book "General Theory of Relativity" is called "The condition for flat space", and he is proving that a space is flat if and only if the curvature tensor $R_{\...
- 43
0
votes
2
answers
77
views
Gravitational field of the star changes the paths of light rays, how is this observed during eclipse?
The gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. I understand that the light cones are bend slightly ...
- 103
0
votes
0
answers
46
views
How does Einstein's spacetime curvature theory for gravity actually makes sense? [duplicate]
I have a lot of confusion understanding the concept that a mass creates a curvature in the space time and other small masses gets attracted towards big masses since they starts falling inside that ...
1
vote
1
answer
97
views
Limit of gravity
Is there any limit to the bending of spacetime due to gravity?
I have been reading about wormholes and how they bend spacetime and connect two systems. But if there is no limit to gravity, we can ...
0
votes
3
answers
133
views
What is spacetime like according to general relativity? [duplicate]
It is often said that matter curves space (or rather spacetime) in general relativity.
But why should matter curve space one way and not the other way? So it seems like a metaphor, I guess.
I read ...
- 15
0
votes
1
answer
102
views
Flat space between colliding black holes
When 2 black holes approach each other, they both bend space in an opposite direction. There must always be a flat space between 2 colliding black holes.
However, I heard that they actually merge, ...
- 187
4
votes
4
answers
826
views
Why do we call the Riemann curvature tensor the curvature of spacetime rather than the curvature tensor of its tangent bundle?
I was studying the mathematical description of gauge theories (in terms of bundle, connection, curvature,...) and something bothers me in the terminology when I compare it with general relativity.
In ...
- 123
1
vote
1
answer
71
views
Does the variation of $I$ yield Bach tensor？
For $$I_1=\int \sqrt{-g}C_{abcd}C^{abcd}d^4x,$$ where $C_{abcd}$ is the Weyl tensor. If we neglect the Gauss-Bonnet term this can be reduced to $$I_2=2\int \sqrt{-g}(R^{ab}R_{ab}-\frac {1}{3} R^2)d^4x....
- 75
1
vote
0
answers
84
views
Definition of asymptotically flat spacetime
Following the definition in Wald's book on general relativity, in page 276 asymptotically flat spacetimes are defined using conformal isometry with conformal factor $Ω$.
Then one of the requirements ...
- 1,734
1
vote
0
answers
86
views
How does a curvature in time equate to Newtonian gravity? [duplicate]
I often read that a curvature in time (the rate at which clocks tick) near a massive object, is considered to be the source of Newtonian gravity.
This got me wondering, does General Relativity use the ...
2
votes
7
answers
1k
views
I can't wrap my head around the idea of matter interacting with spacetime. How is the interaction taking place? [closed]
I have tried Googling this for a long time. I have read many forums on this. But still, it doesn't make sense.
General relativity says that space-time is bent/changes when a massive object is there. ...
1
vote
0
answers
60
views
Is the universe closed or flat?
Apparently there is a tension in the measuring of the curvature of the universe (https://arxiv.org/abs/2307.07475) as apparently in 2018 the Planck collaboration got a series of results consistent ...
- 2,472
2
votes
2
answers
189
views
Can $\mathbb{R}^4$ be globally equipped with a non-trivial non-singular Ricci-flat metric?
I'm self-studying general relativity. I just learned the Schwarzschild metric, which is defined on $\mathbb{R}\times (E^3-O)$. So I got a natural question: does there exist a nontrivial solution (...
- 107
0
votes
0
answers
28
views
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 ...
1
vote
1
answer
99
views
The apparent dilatation of time in General Relativity
Maybe this a dumb question, but, is the gravitational dilatation of time caused because a particle travelling through a geodesic in a curved space-time must cover a larger distance than the one ...
- 1,525
6
votes
3
answers
2k
views
Is source of space-time curvature necessary?
Einstein field equations have vacuum solutions that (probably) assumes the source of curvature (either energy-momentum tensor or the cosmological constant term or both) is elsewhere. Like, in ...
- 1,161
4
votes
1
answer
156
views
Do neutron stars (or really dense stars) contain more volume inside of them than the expected $V=\frac{4}{3}\pi r^3$?
If I understand correctly neutron stars are so dense that general relativistic effects are not negligible anymore. Does this mean that the volume inside of neutron stars is bigger than we would expect ...
- 2,035
0
votes
0
answers
50
views
How the equivalence principle leads to the idea of curved spacetime? [duplicate]
In wikipedia https://en.wikipedia.org/wiki/Equivalence_principle, there are three forms of equivalence principle ( equivalence of gravitational and inertial mass ) :
Weak version (Galilean) :
The ...
- 317
1
vote
1
answer
464
views
Einstein tensor in 2d [duplicate]
Is the Einstein tensor in 2D or 1+1D always zero? If so, why?
I recently installed EinsteinPy and started playing wing different metrics - for the 2D cases the result turned out to be always zero.
- 1,161
0
votes
0
answers
38
views
Expressing curvature invariants ($K_1, I_1, ... $), at any one event, through Synge's WF $\sigma$ (given of each event pair, in a suitable region)
Considering a set $\mathcal S$ of events such that for each pair $p, q \in \mathcal S$ Synge's world function $\sigma$ is defined and the corresponding value $\sigma[ ~ p, q ~ ]$ is given, and such ...
- 4,306
0
votes
1
answer
106
views
Another dimensions [closed]
Just a science ponderer, and pretty much interested in physics. Please guide me if I am wrong.
There have been many statements made by the physicists about the existence of other dimensions (...
- 19
-1
votes
1
answer
106
views
When doing general relativity in practice, how do we choose the appropriate manifold describing the scenario?
The theory only deals with the local curvatures, not the global topology. Hence any manifold with an allowed metric is allowed. These can be infinitely many, especially for negative curvature space-...
- 7,980
2
votes
6
answers
2k
views
Is it possible to describe every possible spacetime in Cartesian coordinates? [duplicate]
Curvature of space-time (in General Relativity) is described using the metric tensor. The metric tensor, however, relies on the choice of coordinates, which is totally arbitrary.
See for example ...
- 93
-1
votes
1
answer
129
views
According the theory of general relativity, what is the role of causality in the changes of the curvature of spacetime? [closed]
In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes ...
- 41
0
votes
1
answer
71
views
Is curvature localised in General Relativity?
Is the curvature of spacetime in General Relativy localised?
- 476
8
votes
2
answers
826
views
How does the covariant derivative satisfy the Leibniz rule?
In Carroll's "Spacetime and Geometry", he states on page 95 (section 3.2) that the covariant derivative, $\nabla$, is a map from $\left(k, l\right)$ tensor fields to $\left(k, l+1\right)$ ...
- 103
9
votes
3
answers
6k
views
Why is Spacetime described as flat even though we live in 3 dimensions of space?
I’ve always heard and seen diagrams that show spacetime as being “flat” or in 2 dimensions with curvature. How does this correspond to the 3 spacial dimensions that we perceive to exist in?
- 135
0
votes
0
answers
53
views
Question on gravity and spacetime curvature [duplicate]
In General Theory of Relativity, it is explained that the fabric of reality i.e. spacetime bends around objects with mass, and that curvature causes other objects to come close to/ fall towards the ...
1
vote
3
answers
2k
views
Why does mass make curvature in spacetime? [duplicate]
According to Einstein's general relativity theory, matter with mass makes curvature in spacetime. The greater the mass, the curvature in spacetime will be greater.
My questions:
Why will mass make ...
- 19
2
votes
1
answer
135
views
How do you relate $\Omega_{k}$, the curvature term in the FLRW metric, to the radius of curvature?
I have assumed, for reasons a bit too detailed to go into here, that if $\Omega_{k}$, the curvature term in the FLRW metric, is equal to 1, then the radius of curvature is equal to 13.8 billion light ...
- 371