Questions tagged [spacetime]
Within relativity (both special and general), changes of reference frames can change both the notions of space and of time, with one depending on the other as well. As a consequence, it is necessary to treat both concepts in a unified manner. Hence the term spacetime.
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Is it possible to express various nonlinear motions as straight lines in transformed spacetime?
I am trying to understand simple examples of space-time curvature.
Assume for the moment that $c$ is infinite (classical curvature due to Newton's laws). Also, I will only consider 1+1-dimensional ...
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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
$$\delta S = \int_{\mathcal{...
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Could Space-Time Displace or Distort Itself? [closed]
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Could space-time distort and displace space-time?
If space-time can interact with surrounding space-time, then which ...
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Does Mass Actually Displace Space-Time, or does Mass only Distort it?
1. Question
Given the plethora of space-time illustrations, there is a sense that space-time is actually being displaced by mass, (planets). But on its face, this doesn't really make sense because ...
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is $LT$ a Lorentz invariant?
We know the relations of time dilation and length contraction
$$L=\frac{L_0}\gamma\\
T=\gamma T_0$$
If we multiply them together, we get
$$LT=L_0T_0.$$
This holds for all $L$ and $T.$
So, is $LT=L'T'$ ...
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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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What is meant by "spontaneous creation" in this paper?
I have some questions in regard to the paper "Spontaneous creation of the universe from nothing". If I am not mistaken it is akin to Alexander Vilenkin's proposed cosmological model that has the ...
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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 ...
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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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As I read an article on this website that light cannot warp space time fabric [closed]
But actually we know that energy is equals to mass then light energy can act like mass and it can create a black hole made up of light .
As per Einstein equation E=mc² then why there is no black hole ...
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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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How can we have motion through time with Relativity? [closed]
How can anything actually move through time if Relativity is correct? It seems everything is just a Lorentz Transformation to a different reference frame and 4D spacetime keeps track of all of these ...
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Spinors, Spacetime and Clifford algebra
I'm looking to understand the intrinsic connection that Clifford algebra allows one to make between spin space and spacetime. For a while now I've trying to wrap my head around how the Clifford ...
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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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Question on special relativity
I am trying to learn special relativity. If we consider two inertial reference frames with spacetime co-ordinates $(t,x,y,z)$ and $(t',x',y',z')$ and let there be 2 observers who measure the speed of ...
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Looking for papers that claim that spacetime is emergent
This article states:
It’s really striking that for most of the plausible theories of quantum gravity that we have, in some sense their message is, yeah, general relativistic spacetime isn’t in there ...
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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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Lorentz invariance of the Klein-Gordon equation action
What I will say is not exclusively true for the KG equation, but let's take it as a simple example.
When proving the invariance of its action under a Lorentz transformation, it suffices to show that ...
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How does brain perceive time dilation due to gravity?
Einstein's General Relativity says gravity warps spacetime. Consider a hypothetical scenario:
A person travels into space from Earth.
He landed on a different planet in some far off galaxy where time ...
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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 ...
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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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What happens if we differentiate spacetime with respect to time? [closed]
Essentially, what would differentiating space-time with respect to time provide us with? What are the constraints associated with such operations? Is it possible to obtain a useful physical quantity ...
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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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Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?
The spatial part of the Minkowski metric, written in the Cartesian coordinates, $$d\vec{ x}^2=dx^2+dy^2+dz^2,$$ is invariant under spatial translations: $\vec{x}\to \vec{x}+\vec{a}$, where $\vec{a}$ ...
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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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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 ...
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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 ...
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Can part of space be causally disconnected from the rest of the universe by being surrounded by black holes? [duplicate]
Is it possible for black hole event horizons to overlap and form a spherical wall around an island of space (that's not inside a black hole) while still being causally disconnected from the rest of ...
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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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How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?
Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
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Does time dilation cause gravity as explained in this video?
Watch it around 2:00 minutes. https://youtu.be/gcvq1DAM-DE
Do objects move closer to Earth because they experience time at different rates, really? Does it make sense? The video also represents the ...
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Length Contraction: is $t'$ or $t = 0$?
To demonstrate my confusion - let's say there is a rod traveling with velocity +v relative to S, and in S, the length of the rod is measured to be $L$.
If I want to go from S to S', the frame where a ...
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Does the universe have a center? [duplicate]
If the big bang was the birth of everything, and the big bang was an event in the sense that it had a location and a time (time 0), wouldn't that mean that our universe has a center?
Where was the ...
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Is the observable universe analogous to a white hole?
My instinct is no, but my lack of understanding with respects to white holes doesn't tell me why. My thinking is this: The universe is expanding and the further away from us the faster it is expanding....
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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 ...
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Spin connection raise and lower flat indices
The spin connection $\omega^a_{b\nu}$ is used to define the covariant derivative of a spinor in curved spacetime. I want to explicitly calculate the covariant derivative:
$$\nabla_\nu\Psi=(\partial_\...
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Can there be a theoretical synchronised ‘now’ moment at all points across the universe?
Einstein’s relativity rejects the notion of a universal ‘now’ moment. It underlines how the concept of ‘now’ is compromised due to time passing at differing rates in differing frames of reference, ...
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Deriving the Minkowski Metric from homogeneity of space-time and the isotropy of space
In this wikipedia page, it says that one can derive the spacetime interval between 2 arbitrary events from the second postulate of special relativity, together with the homogeneity of spacetime and ...
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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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What is the problem with this method to measure one-way speed of light? [closed]
I am having a hard time grasping the idea that one-way speed of light is immeasurable. I have watched several videos (including the Veritasium one), read the Wikipedia article, and read some questions ...
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Killing tensor in the Kerr metric
It was famously shown by Carter that the Kerr metric possesses a 4th non-obvious constant of the motion, derived from the separability of the Hamiltonian. This constant is related to a Killing tensor.
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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 ...
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Why would speed of light be directional if spacetime is discrete?
In Feynman's Simulating Physics with Computers, Feynman states that
"we might change the idea that space is
continuous to the idea that space perhaps is a simple lattice and everything
is ...
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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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Local inertial frames, and locally flat geometry, taylor expanding metric coefficients
In general relativity, if there is a line element of the form $$ds^2 = [f(u, v)]du^2 + [h(u, v)]dvdu + [w(u, v)]dv^2$$ which I believe corresponds to metric coefficients $$g_{00} = f(u, v)$$ $$g_{01} =...
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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 ...
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