5

I remember reading something about Stephen Hawking denying the fact you can't make CTC's (Closed Timelike Curves) without weak energy condition violation. If this is true, where do the light cones point to in the $t$ direction?

enter image description here

On the end of the right and left, the cone points up (future) but near the cylinder it tilts. In a region with negative energy density, do the cones tilt all the way to the $-t$ direction?

Qmechanic
  • 201,751
user122083
  • 527
  • Where do what light cones point to? Is there a specific scenario you are referring to? I assume T is timelike. Perhaps include more information? – Jim Jun 06 '14 at 19:45
  • Like in this image, http://inspirehep.net/record/1262683/files/Tipler2.png On the end of the right and left, the cone points up (future) but near the cylinder it tilts. In a region with negative energy density, do the cones tilt all the way to the -t direction? – user122083 Jun 06 '14 at 19:56
  • Weak energy condition is a property of the stress energy tensor, which you should get by computing the Einstein Tensor. All you gave in the question is a picture, from which is not possible to answer if it does violate or not WEC. On the other hand, you don't need to have the future directed light cones pointing in the $-t$ direction if you want closed causal curves, as the picture shows. – cesaruliana Jun 07 '14 at 18:09
  • very good question! – William Martens Jan 11 '23 at 13:06

2 Answers2

6

Stephen Hawking proved that closed timelike curves cannot be created in a finite system without using exotic matter. The Tippler cylinder doesn't use exotic matter, but it can create CTCs because it's infinite in length and therefore isn't a finite system.

I think the proof was in his paper on the Chronology Protection Conjecture.

John Rennie
  • 355,118
1

The theorem mentioned here, that in a finite range exotic matter, violating the energy conditions is necessary to form CTCs, i.e. that spacetime is suitable for time travel, is simply not true. Whoever supposedly proved it.

It has long been known that regular counterexamples, i.e. finite time machine spacetimes with normal matter, satisfying the energy conditions, are possible. For example this:
https://arxiv.org/pdf/gr-qc/0503077.pdf

Attila Janos Kovacs
  • 330