Closed timelike curves and holography in compact plane waves

Abstract

We discuss plane wave backgrounds of string theory and their relation to Gödel-like universes. This involves a twisted compactification along the direction of propagation of the wave, which induces closed timelike curves. We show, however, that no such curves are geodesic. The particle geodesics and the preferred holographic screens we find are qualitatively different from those in the Gödel-like universes. Of the two types of preferred screen, only one is suited to dimensional reduction and/or T-duality, and this provides a "holographic protection" of chronology. The other type of screen, relevant to an observer localized in all directions, is constructed both for the compact and non-compact plane waves, a result of possible independent interest. We comment on the consistency of field theory in such spaces, in which there are closed timelike (and null) curves but no closed timelike (or null) geodesics.The four-dimensional Gödel universe [1] is a topologically trivial homogeneous space with non-zero rotation. This gives rise to some unusual properties: not only do all observers see themselves as the centre of rotation, but there exist closed timelike curves (CTCs) through every point. As an example of a space with CTCs for all times, it is unclear as to what extent Hawking's chronology protection conjecture [2], concerning the impossibility of forming a CTC in nature, is applicable.For this reason, the discussion of the physics of chronology protection (see, e.g., [3] for a recent review), has mostly avoided the Gödel universe. However, the discovery [4] of supersymmetric Gödel-like solutions to five-dimensional minimal supergravity, and to its eleven-dimensional M-theoretic lift, has forced the issue, at least within the string theory community. Surprisingly, these solutions to string and M-theory turn out [5,6] to be related to another supersymmetric space of much recent interest, namely the plane wave [7,8,9], and this is the relation of interest to us here. We should also note that supergravity solutions describing supersymmetric deformations of the extreme five-dimensional Reissner-Nordstrom black hole have been studied in this context. Both of the deformations discussed in [10] -one corresponding to the rotating black hole of [11], the other to a black hole in a Gödel-like universe -have CTCs, the precise nature of which has been examined in some detail [12,13,10,14,15]. Other non-supersymmetric solutions of interest, describing black holes in a Gödel-like universe, have recently been discussed in [16].It turns out that these Gödel-like universes (GLUs) are related to compactified plane waves (CPWs) in two different ways. The eleven-dimensional CPW, dimensionally reduced on an everywhere spacelike circle, yields a ten-dimensional GLU [6]. On the other hand, a CPW in type II string theory is T-dual to a GLU times a transverse circle [5]. Depending on the specific plane wave we start with, these procedures give rise to a large variety of GLUs. In addition to the R-R fluxes typically supporting the CPW solutio...

Holographic dual of a time machine

“…So these results can be considered as a very accurate and nice supporting evidence in favor of the Hawking conjecture. On the other hand in [19][20][21][22], it was demonstrated that the Gödel type solutions can be smoothly embedded in the context of string theory. Closed timelike curves in that case are hidden behind the so-called holographic screens and do not violate causality in the rest of the space-time.…”

Boundary states for supertubes in flat spacetime and Gödel universe

“…Considering the Euclidean world-sheet, i.e., treating t as a real one in the second line in eq. (2.18), the second line corresponds to taking the following gauge in the open string channel 20) where τ E is the Euclidean time. Under the open closed duality τ E ↔ tσ, this changes to the gauge X + = Rwσ in the closed string channel.…”

“…Especially they are useful in studying closed timelike curves (CTCs) in Gödel universe [12]. The main motivation of studying Gödel universe is to find out fates of backgrounds with CTCs and it is interesting to study this problem in the string theory [13,14,15,16,17,18,19,20,21,22,23,24]. In this sense, the supersymmetric type IIA Gödel universe [15] will be a good example.…”

Velocity and velocity bounds in static spherically symmetric metrics

“…An open question is whether or not naked singularities and backgrounds with CTCs can be solved by quantum effects in a theory of quantum gravity. Related to this point we would like to emphasize that examples of how naked singularities and CTCs can be solved appear in string theory (see for instance [5][6][7][8][9][10]). As we will demonstrate in the case of naked singularities, the radial velocity of a massless particle exceeds the value 1 in the Schwarzschild coordinates in certain space regions, i.e.…”