All Questions
Tagged with spacetime general-relativity
1,867
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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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0
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64
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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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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 ...
- 87
2
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43
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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 ...
- 2,613
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81
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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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2
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1
answer
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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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1
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Question on spatiotemporal dimensionality about the contradictions of time being a dimension
We can axiomatically see that all spatial dimensions have a fundamental rule where they can either move back or forwards infinitely. However, the temporal dimension started when the universe began and ...
2
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Under what circumstances can a 4D singularity occur in General Relativity?
I've tried to find on the literature about 4D (single point) singularities, but most of the theorems about singularities pertain to either space-like or time-like singularities, which always have some ...
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Does gravity accelerate you towards the geodesic of light between you and the mass?
If there's a planet far away, you will accelerate straight towards it due to gravity. If you place a Schwarzschild black hole right in the middle between you and the planet (the distance between the ...
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1
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Do satellites in orbit create Relativity paradoxes? [closed]
Can someone point out the flaw in this very realistic scenario below?
I will start by stating established first principles of the applicable orbital and relativistic conditions.
Then I will describe ...
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5
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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 ...
- 171
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68
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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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4
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659
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Understanding expansion of the Universe as things flying apart
Say that we have a Universe uniformly filled just with matter (let's not bring dark energy into this). And say that we fill it with very light particles (so that the gravitational interaction between ...
2
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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 ...
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1
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Confusion about local Minkowski frames
This is sort of a follow-up to the question I asked here:
Confusion about timelike spatial coordinates
The important context is that we imagine a metric that, as $t\rightarrow\infty$, approaches the ...
- 160
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1
answer
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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
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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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1
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When you are in a gravitational field, do object far away get physically closer to you as you get closer to the mass?
An observer A is close to a black hole and an observer B one light year away. They are both remaining at constant radial distance from the black hole. A is at 2 Rs away from the center of the black ...
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1
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Time component of four-velocity
While reading through Spacetime and Geometry by Sean Carroll, I came across the following passage:
"Don't get tricked into thinking that the timelike component of the four velocity of a particle ...
- 442
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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 ...
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2
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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 ...
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2
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How do we account for the 'one way' drag of moving space?
As I understand it, the rotating space outside a Kerr black hole drags radially falling particles into circular motion. Similarly the river model posits that the inward flow of space ensures particles ...
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2
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Are $i^\pm$ and $i^0$ codimension 1 surfaces?
Standard textbooks like Carroll's say that spatial and temporal infinities in Minkowski space Penrose diagram are points. But on the footnote in pg. 3 of some draft notes on Celestial holography by ...
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Time function as a function of energy (from velocity and gravity)?
Is there any formula, preferably in terms of energy, for the time dilation an object experiences taking both relativistic velocity and mass into account? I see both formulas frequently, but haven't ...
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1
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What objects are solutions to the Einstein Field Equations?
The usual way the solutions of the Einstien Field Equations are introduced is by saying they are (pseudo-) riemannian metrics that satiafy the diff equations for a given EM Tensor. My question is: ...
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1
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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. ...
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2
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What is $r$ in a metric signature in general relativity? If $v$ and $p$ are the time and spatial coordinates?
The Wikipedia article on metric signatures says that the signature of a metric can be written $(v,p,r)$, where $v$ is the number of positive eigenvalues, $p$ is the number of negative eigenvalues, and ...
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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, ...
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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 ...
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5
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Vacuum solutions in presence of mass?
Here is the page I will be referencing: Vacuum solution (general relativity) - Wikipedia
My point is: if $T_{\mu\nu}=0$ implies that there is no mass, how can Schwarzschild vacuum be a solution, if ...
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51
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Does it make sense to talk about time in absence of matter? [duplicate]
The equations of general relativity should predict (although I might be wrong) that in absence of mass the spacetime is everywhere flat. That is, time is the same everywhere. However, I'm not sure ...
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1
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Does dark matter have mass?
When trying to understand what dark matter is, it is helpful to know that some properties of it can already be derived from various observations, such as, it only interacting via gravity and no other ...
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1
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Does time arising from entropy agree with GR?
There's a theory that the direction of time arises from entropy and the correlations (interactions) between bodies. However, I don't see how this would incorporate the effects of General Relativity, ...
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1
answer
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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 ...
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1
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Time required to reach Black Hole's Event Horizon from outsider perspective?
Let's imagine a pair of particles that is entangled. One (call it $P_1$) is released and then falls to a black hole from a distant $x_0$, (for example $x_0=5r_s$) and velocity $v_0(=1/2c)$, while the ...
-7
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1
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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 ...
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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 ...
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6
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If gravity is not a force, what makes massive objects spheroid?
For most of my life, the explanation given for why celestial bodies like stars, planets, etc. are round is due to gravitational force. Simply put, if an object has enough mass, it will, in turn, have ...
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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 ...
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How does gravity act and propagate in a 2+1D universe?—Newtonian versus general relativity
In a hypothetical 2+1D universe:
if we apply the Newtonian concept of gravity, we might expect that the gravitational force between two mass points with a distance of $r$ would diminish linearly with ...
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2
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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 ...
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2
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If a weak light source is attached to a string, and someone swing this light source in circle. It seems that this light source is brighter. Yes or no
It may be truly a question of life and death.
You know those glow sticks.
As a sailor it is a good idea to carry one on our lifevest.
Falling into the sea, those glow stick make a light source that ...
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2
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What is the manifold topology of a spinning Cosmic String?
Given the following metric which is that of a rotating Cosmic String:
$$g=-c^2 dt^2 + d\rho^2 + (\kappa^2 \rho^2 - a^2) d\phi^2 - 2ac d \phi dt + dz^2.$$
can one determine the manifold topology ...
- 1,268
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Relativistic force correction factor for time-dilated continuous entities
How does gravitational time dilation affect the transmission of mechanical forces in a hypothetical scenario where a tether extends from a less gravitationally influenced region, like the edge of the ...
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Nature of the spacetime trajectory (worldline) described by $\frac{d^2x^\mu}{d\tau^2}=0$
The covariant equation of motion of a free particle, in flat Minkowski spacetime and Cartesian coordinates, reads
$$
\frac{d^2x^\mu}{d\tau^2}=0, \tag{1}
$$
with $\mu=0,1,2,3$, and has the solution
$$
...
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How to motivate that in presence of gravity the spacetime metric must be modified to $ds^2=g_{ab}(x)dx^adx^b$?
In the presence of a gravitational field, the spacetime metric, $$ds^2=\eta_{ab}dx^a dx^b,$$ should be changed to, $$ds^2=g_{ab}(x)dx^adx^b.$$ What are the convincing physical arguments that motivate ...
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Is there a location in the universe with the minimum rate of time dilation?
According to general relativity, time dilation occurs due to strong gravitational fields and high relative velocities, causing time to pass more slowly compared to observers in weaker gravitational ...
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1
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Apparent paradox in general relativity wrt relative gravity, spacetime curvature and time dilation [closed]
Imagine Alice is near a massive black hole and Bob is on the Earth.
Obviously their gravitational fields are different for each other. In other words, their spacetime is flat for themselves but curved ...
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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 ...
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2
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111
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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 ...
