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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88 views

Is it known what the necessary and sufficient conditions are for the existence of a “3+1 split” (by means of a foliation) of a (Lorentzian) manifold?

When trying to do physics on a more general pseudo-Riemannian manifold we want to require that there is a foliation of this manifold into three-dimensional subspaces. By this I mean we would like to ...
5
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129 views

Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
4
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0answers
53 views

Energy of a particle as measured by an observer at infinity

I'm wondering if it is possible to make a definition for the energy of a particle as measured by an observer at infinity. I've looked through Wald for this but wasn't able to find anything - I may be ...
4
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0answers
25 views

Gravitational lensing and cosmic strings

Say we have a straight cosmic string lying along the $z$-axis, with energy-momentum tensor $$T_{\mu\nu}=\mu\delta(x)\delta(y)\operatorname{diag}(1,0,0,-1)\tag{1}\label{1}$$ for some small positive ...
4
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0answers
27 views

Parity and Time reversal when the number of space or time dimensions is even

There's a side remark in the middle of section 2.6 of Weinberg I that I find a bit unclear. Suppose that $L(p)$ is a boost that carries the four momentum $k^\mu=(0,0,0,M)$ to $p^\mu$, and that ${\bf ...
4
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0answers
89 views

Aren't black holes required to exist forever in our frame of reference?

I know that for an observer far away, nothing ever crosses a black hole horizon (due to time dilation), while in the frame of reference of a falling observer the horizon is nothing special on its way ...
4
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0answers
79 views

Question about $\alpha-$plane in twistor theory

In twistor theory, given the complexified Minkowski space $CM$ and the projective twistor space $PT$, an $\alpha-$plane is defined as the correspondence in $CM$ wit a point $Z \in PT$. But I found ...
4
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122 views

Coincidence of spacetime events & Lorentz invariance

Am I correct in thinking that if two spacetime events are coincident in one frame of reference, then they are coincident in all frames of reference, i.e. coincidence of spacetime events is a Lorentz ...
4
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95 views

Does a mass gain inertia against movement in all directions as it approaches the speed of light?

If a mass moves along the x axis at near the speed of light, does it take as much energy to additionally accelerate the mass along the y axis as it does to accelerate it along the x axis by the same ...
4
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236 views

Nature of Microscopic space-time

I am going through the introductory chapter's of Schwinger's Source theory. He writes, It [Source Theory] is a phenomenological theory, designed to describe the observed particles. No speculations ...
3
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39 views

Why do some stars actually produce “Gamma ray bursts”?

I looked it up but I haven't found any explanation as to why some stars produce them, I understand that collapsing and merging stars produce them, but my question is why is the energy concentrated in ...
3
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48 views

Looking out from the inside of an Alcubierre bubble

Disregarding the difficulties in achieving a warp "bubble" as per Alcubierre's theoretical warp drive, as far as I understand it the geometry of the spacetime that arises is mathematically sound. ...
3
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72 views

Asymtotically flat spacetime applicable for spacetimes which are not diffeomorphic to $\mathbb{R}^4$

I wanted to investigate changes on a compact 4-manifold $M$. More specifically it is the K3-surface. I follow a paper by Asselmeyer-Maluga from 2012. The idea there was to make sure that the manifold ...
3
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0answers
115 views

What Would Negative Mass Do To Spacetime?

It's known that positive mass bends space-time to create a curvature. But if something had negative mass what would it do? Make it flat or like a crest?
3
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167 views

Curvature and spacetime

Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
3
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281 views

Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
2
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0answers
55 views

Closed timelike curves in the Kerr metric

I just read in Landau-Lifshitz that the Kerr metric admits closed timelike curves in the region $r \in (0, r_{hor})$ where $r_{hor}$ is the event-horizon ( I am talking about the case $|M|>|a|$ ...
2
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69 views

Should we consider space and time as separate entity?

In general relativity, we think of space and time in spacetime framework. As some people say, metric tensor sign difference, along with our inability to go backward in time suggests that space and ...
2
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0answers
42 views

Does entropy flatten spacetime?

Forgive me if this is a non-question, but I could not find anything regarding this. I only know parts of GR, and I am not familiar with the math. Since energy and matter density curve spacetime, ...
2
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0answers
88 views

Black Hole - Between event horizon and singularity

Dear Physics Board Users What is between the singularity and the event horizon? If the gravitation gets bigger and bigger coming nearer to a black hole, is then the gravition inside even bigger that ...
2
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0answers
138 views

Kleppner derivation of Lorentz transformation

I am reading Kleppner.(Lorentz transformations) He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form $$x'=Ax +Bt, y'=y, z'=z, ...
2
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0answers
103 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...
2
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0answers
114 views

Examples of warped product manifolds?

Bishop and O'Neil defined warped product manifolds. Space-times are good examples of such warped product manifolds. Is there a famous and important example of space-times $I×M$ where $M$ is itself a ...
2
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28 views

Can isotropy (or anisotropy) be expressed in terms of intervals ($s^2$) between pairs of events?

Considering a set $\mathcal S$ of events and given the values of intervals $s^2[~P, Q~] \in \mathbb R$ for all pairs of events $P, Q \in \mathcal S$ (up to a common non-zero scale factor): how can ...
2
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96 views

Examples of manifolds (not) being: flat, homogeneous and isotropic

I am looking for (at least) one example of the following manifolds: Flat, homogeneous and isotropic Curved, homogeneous and isotropic Flat, non-homogeneous and isotropic Flat, homogeneous and ...
2
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170 views

Does quantum entanglement imply the existence of a non-causal structure connecting space-time together?

In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together ...
2
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50 views

Hierachies of AdS/CFT holographies

One of the most disturbing aspects of General Relativity is the 'Marble versus Wood' duality of the theory: Matter creates curvature, and curvature doesn't create curvature (at least not directly) ...
2
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0answers
165 views

If tachyons exist, what would they do to spacetime?

Mass (Positive) bends space-time generating gravity. If Tachyons are supposed to have imaginary mass, what would they do to spacetime (if they do exist).
2
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152 views

Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
2
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0answers
92 views

When spacetime expands to the point where galaxy clusters are not observable, will there by any interaction?

It's my understanding that in a few billion years, clusters of galaxies won't be able to directly observe one another due to the expansion of spacetime overcoming gravity between those clusters. ...
2
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0answers
108 views

Car parking special-relavity puzzle

Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution? Let's suppose a car is going to park to a garage and the garage is ...
2
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258 views

Higher dimensions

1) How we determine whether the higher dimensions are Unstable or Unpredictable? Or on the basis of what assumption we make this prediction? (Source of Image: Max Tegmark. See also this Wikipedia ...
2
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802 views

de Sitter and anti de Sitter metric

Is the following correct for the distance $d$ from the origin $(0,0)$ to point $(t,x)$ in the 2-dimensional de-Sitter and anti de-Sitter spaces? Here, $t$ is time and the distance may be called the ...
1
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76 views

The path that a light beam takes in empty space

First excuse me if this question is very simple for you but for me and for my friend is not. Recently we were discussing what path a light beam will follow in a box moving at a constant velocity in ...
1
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0answers
66 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
1
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0answers
96 views

What is the justification for continuing to model space-time as a manifold in string theory?

Background The question I have arises from taking seriously the idea that, in a physical theory, one should first define all physical quantities via (thought) experiment. Justification and ...
1
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47 views

Can a photon be captured in a grid space representation at a fractional Planck position?

Consider a photon, positioned in space in a finite portion of a grid. Any point of the grid is vertically or horizontally aligned, each distanced by a Planck unit. $l_P = 1.616 199(97) × 10−35 m$ ...
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0answers
48 views

What is conformal symmetry physically?

I'm reading a paper by t'Hooft http://arxiv.org/abs/1410.6675. There is an argument in the paper that I could not understand: "Now that system, described by Maxwell’s equations, does have conformal ...
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43 views

Could time consistently flow in reverse?

Could time consistently flow in reverse? Here is an article about the subject of quantum asymmetry of time and space. Thoughts?
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58 views

Could a perfect vacuum exist at the boundary of the universe?

Space is not truly a vacuum because of our observation of quantum foam, but if causality does not exist outside our universe, could that mean that quantum foam cannot exist outside our observable ...
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47 views

If black hole is equivalent to a planet of same mass for a distant observer, then why does 'excess radius formula' require uniform mass density?

I understand that the spacetime curvature of a non-rotating, uncharged black hole is identical to that of a planet with same mass/energy for an observer at a distance farther than the radius of the ...
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0answers
149 views

If gravity is due to curvature, how does gravity work in situations with no curvature?

The strength of the gravitational field falls off as the inverse square of the distance from a spherical source. It only falls off as the inverse of the distance from an extended cylindrical or line ...
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44 views

Spacetime as a coset of a symmetry group

In the introduction to his nice PNAS paper on symmetry, David Gross said Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of ...
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46 views

Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question: If the proper time $\tau$ is infinite for a timelike geodesic, does it mean ...
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0answers
29 views

Fixed background theories which feature lorentz invariance?

Are there fixed background theories that also display lorentz invariance? Could be with lorentz invariance being true only approximately at some limit... Realized we can still arrive at time-dilation ...
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63 views

Is there a model of the universe with the transfinite (space)time?

In mathematics there is a concept of ordinal numbers where one can count to infinity and beyond. For example the least number that is greater than all the finite numbers is denoted by $\omega$. Such ...
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71 views

Compactly generated vs. compactly constructed causality violating region?

I am currently trying to grasp the nuance between a compactly generated future Cauchy horizon (as per Hawking's chronological protection conjecture) and a compactly constructed causality violating ...
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53 views

In discrete models of spacetime, what are some implications of the Einstein equation

We have several models of discrete spacetime. Sorkin has a causal growth dynamics, there's spin foams, Panangaden showed a correspondence between interval domains and spacetimes. I am looking for ...
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107 views

Does negative mass reverse the arrow of time?

General relativity predicts that normal mass (positive mass) results in the curvature of spacetime which in return leads to gravitation. Since space and time are bonded together, any change on the ...
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64 views

Can you communicate future information through the event horizon?

According to Hawking on "Particle Creation by Black Holes", there exists a relationship between the entropy outside of an event horizon, flux within the event horizon, and the area of that same event ...