# Questions tagged [spacetime]

As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.

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### Could Spacetime have a more General Geometry than just a Metric Field?

In standard general relativity the fundamental structure of spacetime is given through the six tuple $({M},\mathcal{O},\mathcal{A},{g},\nabla, {W}[\Phi,{g}])$, where ${M}$ is a smooth four-dimensional ...
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### How do we figure out what is the right geometry of space?

In page-319 of Visual Differential Geometry, the following is written: When we speak of a solution to Einstein's equation, we mean a geometry of space time (defined by it's metric) that satisfies the ...
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### Is the gravitational tidal force equivalent to expanding space?

If you fall towards a black hole, the particles in front and the back of you, in the direction of the center, are accelerating away from you. So, seen from a freely frame, can we say that space is ...
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### Is it possible the Black Holes to be pure deformations in the fabric of spacetime and not an effect of super-dense matter?

Is there any theory in the literature that supports this hypothesis that BHs in their center do not have a super-dense matter singularity but are pure deformations in the fabric of spacetime itself or ...
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### Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?

The action of a relativistic free particle is $$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$ for $$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$ I understand that a particle will follow the trajectory of ...
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### How does it make sense for the universe to have started from a big bang?

It has been said that the Big Bang started from a singularity. Think about a balloon radially growing over time. Fix a time $t_0, t_1 > 0$, and let $M_0, M_1$ be two balloons at time $t_0, t_1$ ...
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### Linear Momentum in General Relativity

My question is, does a particle moving in a straight line at constant velocity through empty space create "frame dragging" that would tend to entrain other bodies in the direction of its ...
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### Will a light come back within finite years?

In this answer Javier said Imagine the universe was the inside of a ball. We're 3D now, so no one is hiding any dimensions. This ball has a border, except it's not really a border. You should think ...
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### What does a black hole accretion disk look like edge on?

We have images of two black holes so far, with representations showing a deep black center where in-falling matter vanishes- how would that look side on? Would it be possible to even obtain an image ...
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### A synchronous clock problem in a rigid frame with constant proper acceleration

I am a beginner of general relativity. I read and follow the notation in Andrew Steane's book, Relativity Made Relatively Easy, chap 9.2. Suppose there is an rigid accelerating frame with constant ...
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### The space of the universe is expanding. Is there any corresponding universal phenomenon for time (contraction/dilation)? [duplicate]

Just like how electric and magnetic fields are complimentary, space and time are complimentary as they share the same "fabric". We observe that space in the universe is expanding at about a ...
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### Constraining the metric on the boundary of space-time to get rid of unwanted equation of motion

I've posted this question on maths.stackexchange discussing the action I'm working with, which is (in Dirichlet boundary conditions) just the effective action of a minimally coupled free massive ...
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### What is space? Does it curve around itself? [closed]

Update for focus: Learning about spacetime curvature and general relativity years back, i've come to a question that still no one has answered me. Does space curves in itself? when we say "space ...
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### Invariance of spacetime interval by Schutz

I am reading the book on General Relativity by Bernard Schutz. In it he proves the invariance of the interval in special relativity using the following argument. $S^2=0$ for all light-like paths. This ...
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### Is this line of thought compatible with current physics thinking?

The closer we get to the max speed of light, the faster time is moving from the perspective of the people "stationary" on Earth. This time speeding value is henceforth 'A'. The closer we get ...
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### How do you define present from physics point of view [closed]

So how would you exactly define present, aside from fact that time is an illusion; is it the age of the universe in this sector that we experience subjectively as present, does it have to do anything ...
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### Is length contraction just a rotation in spacetime? [duplicate]

I am trying to understand length contraction in special relativity, in an intuitive way. So I am trying to visualize this phenomenon in the following way, and I would like to know if my example has ...
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### Post flagged as duplicate but I still don't know the answer to my question! [migrated]

This post was flagged as duplicate to this but I couldn't understand all the replies very well. Mr John Rennie's reply seems to agree with my initial thought process, but I could be wrong; Is the ...
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### Help me understand length contraction in an intuitive way—length contraction as four-dimensional rotations? [duplicate]

I am trying to understand length contraction in special relativity, in an intuitive way. So I am trying to visualize this phenomenon in the following way, and I would like to know if my example has ...
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### What is there at a point the universe hasn't expanded past yet? [duplicate]

(Please don't mark as a duplicate) If the universe is constantly expanding that means that there is a point the univese hasn't expanded past, with that what would be past that point? This isn't about ...
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### What is at the edge of space? [duplicate]

if the universe is constantly expanding that means that there is an end where the universe hasn't expanded yet if you could be at that before it was to expand more, or go past/into that edge, what ...
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### How would the following image look like, if we didn't use $ct$ for time?

I just wonder how spacetime would look like if we didn't use $ct$ for $t$ and we just used $t$ instead? I guess the $t$-axis would just scale. Would that mean that, the hyperbolas would be very hard ...
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### Does the curvature of spacetime resulting from the mass of an object imply acceleration [closed]

I recently saw a video about general relativity, to help improve my understanding of the curvature of spacetime and gravitational acceleration. From the video, I have made the following conclusions: ...
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### Dark matter and un-smoothness in spacetime [duplicate]

Since dark matter currently is only observable with its gravitational effects and nothing else can we theorize that dark matter is only non-smoothness in spacetime that has been there from the Big ...
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### Is it really true that time stops for matter moving at the speed of light? [duplicate]

If time stops when you achieve the speed of light, then how can photons ever change frequency, or how are Green lasers possible through additive synthesis in a crystal, if photons move at the speed of ...
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### If I moved in a straight line forever, would I hit something?

Say you could move infinitely fast/gravity doesn't affect you. You move in a straight line. Do you hit anything, like stars or black holes? Not talking about cosmic dust.
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### Could the universe be a 4-ball?

I recently thought of the idea that the universe could be an infinite 4-ball. The Big Bang would be its centre, and time would be outward from its centre (one layer would be one point in time). I ...
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### Question from Einstein's original paper on special relativity

Just for fun, I started reading the original paper by Einstein on the special theory of relativity. Well, what do you know? I got stuck in a place because he jumped a few steps. See if anyone can help ...
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### Perception of light speed when traveling between two light sources

I'm struggling with a fundamental understanding of time dilation and special relativity (if I'm correct). Many online sources explain it as the following: With the ship moving away from the lightbeam ...
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### Space-time continuum expansion

I still don't understand how the expansion of the universe works. If the universe is made up of an infinite number of points that make up space-time, then how can space expand or stretch. Common sense ...
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### Can any other manifold be used for compactifying the 6 extra dimensions of string theory? [duplicate]

I'm a layman interested in string theory. I read about how the 6 extra dimensions of superstring theory are compactified into 3-dimensional complex manifolds (so real dimension 6?) called Calabi-yau ...
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### Does the spacetime curvature in the vicinity of a massive body increase, decrease or remain unchanged with the increasing velocity of an observer?

Does the spacetime curvature in the vicinity of a massive body such as the sun increase, decrease or remain unchanged with respect to an observer's increasing velocity relative to that massive body?
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### Why is a Lorentzian metric still Lorentzian after a general coordinate transformation?

In my GR course, we define a lorentzian metric $g_{\mu\nu}(x)$ as a symmetric $(0,2)$ tensor field having 3 positive and 1 negative eigenvalue. Now given a general coordinate transformation described ...
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### How is the divergence of a unit timelike vector related to expanding space?

Just for fun I'm trying to understand spacetime with an expanding universe from a 3+1 point of view (yes, similarly to the ADM formalism). If I consider our spatial 3-surface $\Sigma$ as embedded ...
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### Using embedding and identity or Minkowski metric instead of complicated metric [duplicate]

The Einstein's equation describes how the metric changes in presence of a mass. If we consider a spherically symmetric mass, the solution to it is given by the Schwarzschild metric. By complicated ...
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### Looking back to Earth via general relativity [duplicate]

Based on Eddington experiment proving the effect of gravity on light, would it be conceivable that some light emitted from our sun bounce back on earth and continued in the universe. During this ...
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### Are there any symmetries in the Mixmaster model?

The Mixmaster model is usually presented as one example of chaotic models in physics and cosmology. Usually, "chaos" or "randomness" may be related to a complete lack of symmetries ...
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### How can an observer observe the metric of spacetime?

I don't mean how can we measure the metric in practice. I only mean in principle. Suppose you are an omnipresent being, no experimental limitations. What measurements do you need to measure the metric ...
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### What's the physical content in the invariance of spacetime interval in GR?

Spacetime interval in one co-ordinate system is given by : $$g_{\mu \nu} dx^{\mu} dx^{\nu} \tag{1}$$ $dx$ is some infinitesimal displacement vector between two events. Spacetime interval after a ...
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### Can space only be infinite? [closed]

I have read before that if you could just go fast enough, as a thought experiment, and you move in a straight line, in any direction, that you eventually might reach the spot from which you started. I ...
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### Derivation of the Hypersurface Deformation Algebra

Let $({M},{g})$ be a smooth $4d$ spacetime manifold with lorentzian metric $g$ and local coordinates $\xi^{\alpha}$ and let further $({N},{q})$ be a smooth $3d$ manifold with metric $q$ and local ...
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### A projectile in a rocket with constant proper acceleration

I am a beginner in general relativity. I read the chapter 9.2 in Relativity make relatively easy vol 1 by Andrew Steane. There is a rocket which accelerates upwards with constant proper acceleration. ...
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### EINSTEIN THEORY OF SPACETIME [closed]

CAN SOMEBODY HELP ME ANSWERING THIS QUESTION. HOW WOULD YOU EXPLAIN SPACETIME TO AN UNSCHOOLED PERSON? I AM STILL A STUDENT AND THINKING AN EXACT EXAMPLE IS QUITE HARD FOR ME.
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### Would our orbit really remain the same if the sun were a black hole of equal mass?

There seems to be an idea floating around that the sun could be replaced by anything of equal mass with no consequence to our orbit. It seems to me that if the mass of the sun were confined to a ...
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### Constant speed of light violates accelerating expansion of universe?

My question regards the following: One of the most fundamental principles of Einstein's GR is that all free bodies move through spacetime with constant velocity $c=1$. However, in 1998 Hubble showed ...
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### Is the solar system sitting in the centre of curved spacetime and if so, are we viewing the rest of the universe from inside that "bubble"?

I read an article about a huge bubble being discovered in which the solar system sits bang in the middle. It got me thinking about the curvature of spacetime. The bubble was created by several ...
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### Spacetime Visual Aid Concept

How do you envision spacetime? What visual-aid(s) have helped you the most? We have all probably seen the “bowling ball on a trampoline” construct but the big problem with that is it represents ...
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### Measuring the Hubble Constant

Attempts to measure the expansion of the universe have come in various forms. The recent Cosmology Crisis (https://www.space.com/why-is-there-a-cosmology-crisis) has me pondering the expansion rate ...
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### About gravitational time dilation

Your clock run slower than the clocks on Earth?
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### Which class of metrics should I look at?

In the context of GR, I would like to consider a spherical body (or spherical inhomogeneity) with a time dependent energy-momentum tensor immersed in some fluid, for example radiation. So I am not ...
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