Spacetime Definition and 1000 Threads

I was just reading about de Sitter space and the following question occurred to me: de Sitter spacetime is curved despite containing no mass-energy, because it has a positive cosmological constant. Does it have a foliation into spatially flat, constant-time hypersurfaces though? Maybe it's...

This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is: ##A## has set up a space-time co-ordinate system with some arbitrary event along his...

I was looking at this chart and I didn't understand how increased angular momentum of the test particle curves the spacetime around the center mass. If that is how it's interpreted. Now the way it looks like is that the curvature is dependent on the angular momentum of the test particle.

In de Sitter-Schwarzschild spacetime things close to the black hole are falling towards it whereas in greater distance they are receding. So there should be a certain (unstable) ##r##-coordinate, where things are static. The de Sitter-Schwarzschild metric has according to Wikipedia...

For someone who have just finished the study of the (fundamentals) of Schwarzschild spacetime, what would be the next natural topic to study?

In a spacetime diagram the spatialized time direction is the vertical y-axis and the pure space direction is the horizontal x-axis, ct and x, respectively. The faster you go and therefore the more kinetic energy you have, you'll have a greater component of your spacetime vector in the...

Since it is nonlinear, the 3 leg lengths would be limited to differentials? But how would the metric coefficients be incorporated into those leg lengths? It seems like the leg differential lengths would have to vary inversely with the magnitudes of the metric coefficients? For example, near...

If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, placing it there with its length alligned in the radial direction of the black hole, would I see the rod close to the black hole with a length shorter...

I am trying to understand the basic conceptual ideas about the space-time diagrams. In spacetime diagrams we have events which are labeled as points on the diagram. Let us call we have an event on point ##A(0,0)##and another event on ##B(4,0)## measured by an inertial frame ##S##. This inertial...

I built the tool initially for myself to better understand how Lorentz Transforms and spacetime diagrams work. Then while trying to discuss it with a friend I need to put it online and it snowballed from there. Now I am wondering whether there is any value for others in what I have created...

I am reading this book and in there the spacetime defined as a manifold such that an affine space of dimension 4. I am having trouble to understand the affine space. I made some reasearch but I couldn't grasp the idea of it. In the books its also stated that " We are familiar with the structure...

I am still new to the theory of relativity (both SR and GR), but I've read few books which gave me an insight about the subject (not a mathematical insight though). There's a question that I really would like to know the answer of: Is there a time delay for the bending of spacetime to occur...

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Now that gravitational waves are more famous because of LIGO, it got me to thinking about what we (lay people) are usually told would happen, which is that the Earth will continue in a straight line at a tangent to its orbit at that moment that information arrives eight minutes later. Which is...

I know that the mathematical form of the line element of spacetime is invariant in all inertial reference frames, namely $$ds^2 = -(cdt^2) + dx^2 + dy^2 + dz^2$$ From what I understand, the actual spacetime distance between two events is the same numerical quantity in all reference frames...

Hi, reading the book "The Road to Reality" by Roger Penrose I was a bit confused about the notion of Galilean spacetime as fiber bundle (section 17.2). As explained there, each fiber over absolute time ##t## is a copy of ##\mathbf E^3## (an instance of it over each ##t##), there exist no...

I have been at this exercise for the past two days now, and I finally decided to get some help. I am learning General Relativity using Carrolls Spacetime and Geometry on my own, so I can't really ask a tutor or something. I think I have a solution, but I am really unsure about it and I found 6...

Okay, so, while discussing Rindler space with my professor, I was asked to prove that for a free-falling observer, proper time for passing through the Rindler horizon is finite. That is at least how the question is phrased. So, the professor obviously assumes that it is clear and trivial to me...

How can space time emerge from nothing, I mean nothing in the absolute case is voide of any thing, I can imagine the BB where there is a primordial plasma the expands and creates the matter and space, but space time from nothing is beyond me, me being stupid and uneducated.

Hi, starting from this very interesting thread I'm still a bit confused about the conclusions. The main point, as far as I can understand, is all about conditions for a quadrilateral to be considered a parallelogram. My first basic doubt is: the concept of 'parallel' applies just to geodesic...

My question comes from the following confusing aspect of the big bang theory. Since at different stages during development of the current universe, we know that fundamental particles, atoms and large masses started to form. And if all large masses are embedded in spacetime when during the...

Hi I have been reading Brian Cox/Jeff Forshaw book on Why does E=mc2 (highly recommend it) One thing I don't get (page 95) is when they say everything moves through spacetime at the same constant speed c?! I get why a person/object A at rest moves through space time with speed c - but say...

In Abner Shimony's paper "The Reality of the Quantum World", the choice between particle detector and wave interference detector is said to be made "after the photon had interacted with the beam splitter". A: Isn't it true that, at light speed, time is not passing for the photon? And so, with...

Consider a free particle with rest mass ##m## moving along a geodesic in some curved spacetime with metric ##g_{\mu\nu}##: $$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda$$...

Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime Sean Carroll https://www.amazon.com/dp/1524743011/?tag=pfamazon01-20 Review of the book by Matt Leifer Does the many-worlds interpretation hold the key to spacetime? https://physicstoday.scitation.org/doi/10.1063/PT.3.4366

Summary:: Strap a weight-measuring bathroom scale to your feet and jump on a trampoline: weight measurements at different points of each jump? What is the longest part of the cycle you are in the free-float frame? I am studying Spacetime Physics 2nd ed. by Taylor and Wheeler at the suggestion...

Let me begin by stating that I'm aware of the fact that this is a metric of de Sitter spacetime, aka I know the solution, my problem is getting there. My idea/approach so far: in the coordinates ##(u,v)## the metric is given by $$g_{\mu\nu}= \begin{pmatrix}1 & 0\\ 0 & -u^2\end{pmatrix}.$$ The...

If I understood well, cosmology makes a difference between matter moving in spacetime and the expansion of spacetime itself. Are these concepts experimentally distinguishable, or this distinction is only in our theories?

How would one plot the space-time continuum graphically(if it were possible,obviously)?

The current of fluid is the vector J^{\nu}. In free-falling laboratory due to Equivalence principle holds the know Continuity Equation J^{\nu}_{, \nu}=0, where the ordinary 4-divergence is used. Latter equation was derived in Minkowski spacetime, thus the Christoffel Symbols are all zero for...

The components of the energy tensor are defined sometimes as the flux of the ith component of the momentum vector across some component jth of constant surface. But isn't the tensor a function of points of spacetime just as the metric? How can you evaluate a surface of j when the tensor is a...

The empty FRW-universe with curvature parameter ##k = -1## and expanding linearly is well known. Also that it is mathematically equivalent (after a coordinate transformation) with the Milne universe which also expands linearly. I wonder if the Friedmann Equations have another solution (I...

Curious, is there any useful reason to translate the 4d curved Lorentzian manifold in GR to, if i read this right, either a 46 or 230 dimensional flat Euclidian space, depending whether the manifold is compact or not? (although another source listed a 39 dimensional flat embedding). ( from...

Does spacetime have elasticity ? I was reading this and they are talking about the stiffness of spacetime.

Summary: No answer could be more important to the assumptions and approach to cosmology. The overwhelming bias is a finite Universe, and could this be a mistake? The measurements across the observable universe strongly indicate a Gaussian Curvature of Zero(Flat). Does this prove that Spacetime...

Just wanted to point out that i have never seen a better depiction of Einsteinian gravity, if a little hard to swallow and somewhat baffling to human intuition. In the following experiment prof. Brian Cox(he used to be on this forum?) says: "Isaac Newton would say that the ball and the feather...

Hey everybody, Background: I'm currently working on a toy model for my master thesis, the massless Klein-Gordon equation in a rotating static Kerr-Schild metric. The partial differential equations are (see http://arxiv.org/abs/1705.01071, equation 27, with V'=0): $$ \partial_t\phi =...

I got the book "An Illustrated Guide To Relativity" by Tatsu Takeuchi, and have questions on how to understand spacetime diagrams from different reference points. Before I ask, please let me know how I can draw a spacetime diagram and post it on the forum. I will want to use different colors to...

I'm just a layperson with a keen interest a couple of notches above popular science. As far as I understand SpaceTime is an attribute where if you change one attribute (space or time) then the other attribute is affected. E.g. as you approach the speed of light, the time passing of other things...

I have been trying to study some differential geometry and some stuff about manifolds in my efforts to learn about closed timelike curves, but thus far it has been a lot of set theory and I have yet to see the "geometry" aspect. What I really want to know is this: We know how some spacetimes...

I have seen people using Einstein's comments on the geometrical description of spacetime to mean that he didn't believe in the curvature of spacetime. While I do not think this is true I cannot fully understand what his remarks mean.When reviewing a book on relativity by Emile Meyerson: La...

Edit: I'm leaving the original post as is, but after discussion I'm not confused over coordinate time having a physical meaning. I was confused over a particular use of a coordinate time difference to solve a problem, in which a particular coordinate time interval for a particular choice of...

I have some questions. Let us assume for these questions that I am using the (- + + +) sign convention. Firstly, we know that if you have a parameterized curve ξ(s), then you can find the proper time between two events at points s1 and s2 by using this formula (assuming that the curve is...

I've been trying to understand the following very interesting problem: "Julius Ceasar was murdered on March 15 in the year 44 B.C. at the age of 55 approximately 2000 years ago. Is there some way we can use the laws of relativity to save his life? Let Caesar's death be the reference event...

Hello, I’m not a physicist or studying physics in school; I’ve just read some books and have some questions that I was hoping someone could help with. Sorry if they’re a little basic. I’m trying to understand how tightly coupled matter is to spacetime. In other words, if you could look at a...

I suppose that that a spacetime geodesic of an object falling on Earth would a appear as straight line. But what I'd like to see is a whole bunch of relevant geodesics that would represent falling bodies all around the Earth such that one could zoom out and so see these straight line geodesics...

i am new at relativity, it said mass can curve spacetime, does this mean spacetime will curve to a new 5th dimension (1-3 for space dimension, 4 for time dimension)?

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Is it not Spacetime is akin to the Wave function in Quantum Mechanics where it is just a mathematical tool and no way to distinguish between different interpretations? Why is that there are countless professional debates about interpretations of quantum mechanics while there is very few or...

The presence of the cosmological constant produces a flat spacetime universe with Ω = 1. There is also the curvature index of space k, which can be +1, 0, -1. But it is possible to have any of these values of k with Λ > 0 or Λ < 0. How is the curvature of spacetime determined by Λ different from...