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There will be spoilers if you keep reading Firstly, he is shown surviving inside black holes. From where did he got oxygen? Perhaps from oxygen bottles. But, in an intense gravitational pull, how he survives? He would have got torn apart! am I right? The popular press says the word black hole and it is a bit vague what they mean because there are some ...


7

The closest thing in mainstream theoretical physics is "closed timelike curves", paths along which you can travel and thereby return to the same place and time as you started, provided your velocity varies as the path requires. (Shortcuts through spacetime called Einstein-Rosen bridges or "wormholes" can be a part of the setup.) Whether such paths exist ...


5

There's four simple-ish models to generate closed timelike curves : The timelike cylinder/torus (Minkowski space where $t = 0$ and $t = T$ are identified, and also possibly spatial dimensions) Misner space (Minkowski space identified along a boost) The Deutsch-Politzer spacetime (two spacelike cuts in Minkowski space identified) Thin-shell wormholes (...


4

Since you have linked to Wikipedia for both CTC and Wormhole I'll try not to repeat what they say and address the distinction you are seeking. A CTC is a curve along which something e.g. an observer may travel, starting at time $t_0$, always moving "forward" in time from its own perspective but nonetheless finding itself back where it started at some ...


4

Closed timelike curves can be geodesics. In some spacetimes it's even possible that every geodesic is a closed timelike curve. What I think you're refering to is the chronology protection theorem, which states that closed causal geodesics will cause a divergence in the energy of the vacuum. A rather suggestive form for the propagator of quantum field is ...


4

First, consider the set of open sets formed by the chronological future at every point, ie $$\{ I^{+}(p) | p \in M \}$$ You can show easily enough that this is an open cover of the manifold (just consider the convex normal neighbourhood of every point, you'll be able to show that for any point $q \in M$, there exists a point $p$ such that $q \in I^+(p)$). ...


3

No, there is no experimental evidence for closed time-like curves.


3

Space and time are only "sort of" on the same dimensional footing. Space and time are physically inseparable, but within four-dimensional spacetime, some directions are "spacelike", and some directions are "timelike". ("Lightlike" a.k.a. "null" is a third type of direction in spacetime.) And if you choose four orthogonal directions in spacetime, with no "...


3

A closed, space-like curve (CSC) would have to return to its original point in (t,x,y,z) to be considered truly closed in GR. Of course, you can draw such a curve, but a massive particle (or even photon) could never traverse it, as the definition of space-like means that it cannot be the trajectory of a physical particle. So really, even open space-like ...


3

Suppose a spacetime has a global time function: a globally defined difference between past and future. Then we can divide timelike curves into two classes. When the proper time along a "future-pointing" curve advances, so does the global time. When the proper time along a "past-pointing" curve advances, the global time goes backwards. In the Kerr-Carter ...


3

While there are probably a lot more problems with that statements, here are a few : A Tipler cylinder is infinitely long, hence it would require the nucleus to stretch infinitely far (and due to limitations on the speed of light, for eternity) before actually qualifying as one. I am not quite sure a nucleus would even survive such a stretching. It is a ...


3

The Thorne time machine, a wormhole with one opening accelerated or Lorentz boosted outwards and then conversely brought back, does not permit time travel prior to the Cauchy horizon. This is the point where the time machine is "turned on." This Cauchy horizon has in regions of spacetime prior to its formation a set of curves winding through the wormhole ...


2

If you want to make a flat space theory for a topologically trivial manifold you can do it in the standard ways if your metric was very very close to the Minkowski metric. Yours is not. So for instance you aren't going to be able to ignore higher order terms in $h$ since in one of the $y$ directions your $h$ blows up. You can still compute an $h$ field by ...


2

I am writing my Ph.D. thesis and wanted to address the same question. The best demonstration I found is at page 133 of "A First Course in General Relativity (Second Edition)" by Bernard Schutz. It goes like this: Let us consider a photon at a radius $r$, moving in an equatorial orbit ($\theta=\pi/2$ and ${\rm d}\theta=0$) around the Black Hole (BH). The ...


2

Time loops are a part of spacetime physics. They are though probably not causally connected to our observable world n a direct way. Probably the best example is the anti-de Sitter spacetime. The anti-de Sitter spacetime in $n$ dimensions is topologically $\mathbb R^{n-1}\times\mathbb S^1$, where the one sphere or circle is the time direction. This is by way ...


2

I can't say that I have ever seen any attempts at simulating non-causal spacetimes (the closest I've seen is the simulation of fields upon such spacetimes). A few non-causal spacetimes do admit a time slicing, by the way, although by definition not all of these slices are achronal. Just solving it like any other PDE might be an avenue worth exploring, but ...


2

A causal loop is, as far as I'm aware (it's not 100% a standard term), a sequence of events that form a loop. It is not quite a physical concept (it's more likely to pop up in the philosophy of physics, like in the books of Reichenbach or Earman), but it does apply to a variety of physical theories. For instance, a basic one would be that given two events $A$...


1

I wondered whether it is possible to interpret a pair creation of electron and positron followed by pair annihilation as one electron moving in a timeloop continuously absorbing and emitting photons. This phenomenon actually exists and is called vacuum polarization. You can imagine it as one electron moving in a loop, as visualized by the following ...


1

Short of having actual experimental evidence, it is hard to say what physical laws may differ in the presence of non-globally hyperbolic spacetimes, so for the most part, in the analysis of non-globally hyperbolic spacetimes, it is assumed that the same laws apply. Of course, this doesn't mean that the behaviours are similar to globally hyperbolic spacetimes,...


1

I have 2 questions plus an optional third, as I’m not sure I’ve fully understood the problem: 1) what does it mean that the probability of second apparatus to shoot a photon from C depends on the detection of a photon in B? Do you mean that there the emission from the second device is not causal and the second photon “sees” the future of the detection in B ...


1

The simplest models I have seen are classical mechanics treatments of the billiard problem with time machines, e.g. https://arxiv.org/abs/gr-qc/9506087, https://arxiv.org/abs/gr-qc/9607063, https://arxiv.org/abs/gr-qc/0007064


1

A Lorentzian manifold is a manifold on which a "Lorentzian" metric is defined. A Lorentzian metric is a Riemannian metric with the positive definiteness requirement (that for a metric $g$, $g(u,u)\gt 0~\forall ~u\neq 0$) removed and instead of having (in 4-D) signature $(+,+,+,+)$, it has signature $(-,+,+,+)$ or $(+,-,-,-)$ depending on what sign ...


1

A diagram is the best way to illustrate this. This diagram has time in the vertical direction. At the bottom are two observers in a comoving frame. Then one observer moves to enter a "tube" colored red. This could be a wormhole boosted into a time machine, or a Kraznikov tube so a "star gate of some sort. The red region is considered isolated from the ...


1

I don't see how to do this using mod 2 intersection, but I believe it can be done over $\mathbb{Z}$ in the following way. Since $\mathbb{R}^4$ is simply-connected, it's time-orientable, i.e. we can continuously choose at every point the positive half of the light cone. Similarly, it is space-orientable: any 3-dimensional space-like submanifold is orientable....


1

First, you realize that there isn't ANY a mechanism allowing to travel back in time, so a real answer doesn't really exist. But, I were to go ahead and assume that such a mechanism existed, then I would imagine that the answer would most probably be: If the mechanism would send the traveler back 100 years into the past without changing his position and ...


1

Let me write down the metric in the equatorial plane ($\vartheta = \pi/2$) of the Kerr space-time in Boyer-Lindquist coordinates: $$ d s^2 = -\left(1 - \frac{2M r}{r^2 + a^2}\right) d t^2 + \frac{r^2+a^2}{r^2 - 2Mr + a^2} d r^2 + \left(r^2 + a^2 + \frac{2M r a^2 }{r^2 + a^2}\right) d \varphi^2 - \frac{2 M r a}{r^2 + a^2} dt d \varphi $$ Now you have to trust ...


1

See section 3.19 of Black Holes: An Introduction By Derek J. Raine, Edwin George Thomas https://books.google.ca/books?id=O3puAMw5U3UC&pg=PA103&lpg=PA103&dq=kerr+schild+closed+timelike&source=bl&ots=elnzJu2ySm&sig=B4cWXIkib4fqbs0D7yA2YlZKE8A&hl=en&sa=X&redir_esc=y#v=onepage&q=kerr%20schild%20closed%20timelike&f=...


1

Most effects on matter that are associated with closed timelike curves are also the kind of effects that usually are supposed to prevent them. But here's a few experimental ways some people have proposed to detect CTCs and various physical consequences : The most obvious consequence is that, in a non-causal spacetime, curves are not required to cross every ...


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