We address chronology protection in stationary, rotationally symmetric spacetimes in 2+1 dimensional gravity, focusing on the case of negative cosmological constant. We show that, if such spacetimes contain closed timelike curves, they belong to one of the following two classes: (i) bad asymptotics: the boundary itself contains closed timelike curves, or (ii) unphysical stress tensor in the bulk: the matter stress tensor violates the null energy condition. We illustrate these properties in a class of examples involving rotating dust in anti-de Sitter space and comment on the use of the AdS/CFT correspondence to study chronology protection.
The effective action of a free scalar field propagating in the generalized Godel spacetime is evaluated by the zeta-function regularization method. From the result we show that the renormalized stress energy tensor may be divergent at the chronology horizon. This gives a support to the chronology protection conjecture.
This is a brief survey of the current status of Stephen Hawking's ``chronology protection conjecture''. That is: ``Why does nature abhor a time machine?'' I'll discuss a few examples of spacetimes containing ``time machines'' (closed causal curves), the sorts of peculiarities that arise, and the reactions of the physics community. While pointing out other possibilities, this article concentrates on the possibility of ``chronology protection''. As Stephen puts it: ``It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the uni…
Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.
We give a simple nonsupersymmetric example in which chronology protection follows from unitarity and the AdS/CFT correspondence. We consider a ball of homogeneous, rotating dust in global AdS3 whose backreaction produces a region of Goedel space inside the ball. We solve the Israel matching conditions to find the geometry outside of the dust ball and compute its quantum numbers in the dual CFT. When the radius of the dust ball exceeds a certain critical value, the spacetime will contain closed timelike curves. Our main observation is that precisely when this critical radius is exceeded, a unit…
We study chronology protection in stationary, rotationally symmetric spacetimes in 2+1 dimensional gravity, focusing especially on the case of negative cosmological constant. We show that in such spacetimes closed timelike curves must either exist all the way to the boundary or, alternatively, the matter stress tensor must violate the null energy condition in the bulk. We also show that the matter in the closed timelike curve region gives a negative contribution to the conformal weight from the point of view of the dual conformal field theory. We illustrate these properties in a class of examp…
The recent renaissance of wormhole physics has led to a very disturbing observation: If traversable wormholes exist then it appears to be rather easy to to transform such wormholes into time machines. This extremely disturbing state of affairs has lead Hawking to promulgate his chronology protection conjecture. This paper continues a program begun in an earlier paper [Physical Review {\bf D47}, 554--565 (1993), hepth@xxx/9202090]. An explicit calculation of the vacuum expectation value of the renormalized stress--energy tensor in wormhole spacetimes is presented. Point--splitting techniques ar…
Many solutions of General Relativity appear to allow the possibility of time travel. This was initially a fascinating discovery, but geometries of this type violate causality, a basic physical law which is believed to be fundamental. Although string theory is a proposed fundamental theory of quantum gravity, geometries with closed timelike curves have resurfaced as solutions to its low energy equations of motion. In this paper, we will study the class of solutions to low energy effective supergravity theories related to the BMPV black hole and the rotating Wave--D1--D5--brane system. Time trav…
A massless scalar field is quantized in the background of a spinning string with cosmic dislocation. By increasing the spin density toward the dislocation parameter, a region containing closed timelike curves (CTCs) eventually forms around the defect. Correspondingly, the propagator tends to the ordinary cosmic string propagator, leading therefore to a mean-square field fluctuation, which remains well behaved throughout the process, unlike the vacuum expectation value of the energy-momentum tensor, which diverges due to a subtle mechanism. These results suggest that back reaction leads to the …
We consider 1/2 BPS excitations of AdS(5)xS(5) geometries in type IIB string theory that can be mapped into free fermion configurations according to the prescription of Lin, Lunin and Maldacena (LLM). It is shown that whenever the fermionic probability density exceeds one or is negative, closed timelike curves appear in the bulk. A violation of the Pauli exclusion principle in the phase space of the fermions is thus intimately related to causality violation in the dual geometries.
We review the issue of chronology protection and show how string theory can solve it in the half BPS sector of AdS/CFT. According to the LLM prescription, half BPS excitations of AdS_5 x S^5 geometries in type IIB string theory can be mapped into free fermion configurations. We show that unitarity of the theory describing these fermions is intimately related to the protection of the chronology in the dual geometries.
Analogue gravity systems offer many insights into gravitational phenomena, both at the classical and at the semiclassical level. The existence of an underlying Minkowskian structure (or Galilean in the non-relativistic limit) in the laboratory has been argued to directly forbid the simulation of geometries with Closed Timelike Curves (CTCs) within analogue systems. We will show that this is not strictly the case. In principle, it is possible to simulate spacetimes with CTCs whenever this does not entail the presence of a chronological horizon separating regions with CTCs from regions that do n…
We conjecture chronology is protected in string theory due to the condensation of light winding strings near closed null curves. This condensation triggers a Hagedorn phase transition, whose end-point target space geometry should be chronological. Contrary to conventional arguments, chronology is protected by an infrared effect. We support this conjecture by studying strings in the O-plane orbifold, where we show that some winding string states are unstable and condense in the non-causal region of spacetime. The one-loop string partition function has infrared divergences associated to the cond…
The global structure of 1 + 1 dimensional compact Universe is studied in two-dimensional model of dilaton gravity. First we give a classical solution corresponding to the spacetime in which a closed time-like curve appears, and show the instability of this spacetime due to the existence of matters. We also observe quantum version of such a spacetime having closed timelike curves never reappear unless the parameters are fine-tuned.
We extend in two directions our recent investigation of strongly interacting quantum fields in a class of spacetimes with chronology horizons (Misner spacetimes). First, we generalize to arbitrary dimensions the holographic mechanism of chronology protection in the absence of gravitational backreaction. The AdS geometry dual to a conformal field theory in these spacetimes shows, in every dimension, an entire separation between the bulk duals of the chronal and non-chronal regions, with the former being complete, regular geometries. In some instances the protection requires the inclusion of non…
A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analysed and is found that, away from the strings, the space is identical to a generalised Misner space. The vacuum expectation value of the energy momentum tensor for a conformally coupled scalar field is calculated on this generalised Misner space. It is found to diverge very weakly on the Chronology horizon, but more strongly on the polarised hypersurfaces. The divergence on the polarised hypersurfaces is strong enough that…
The recent interest in ``time machines'' has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings. This rather disturbing state of affairs has led Hawking to formulate his Chronology Protection Conjecture, whereby the formation of ``time machines'' is forbidden. This paper will use several simple examples to argue that the universe appears to exhibit a ``defense in depth'' strategy in this regard. For appropriate parameter regi…
We construct a family of supersymmetric solutions to AdS supergravity in three dimensions, that correspond to type IIB seven branes wrapped on an internal S3xT4. These solutions are generalizations of the three dimensional Goedel universe and have closed timelike curves. We propose an enhancon-like mechanism for excising the closed timelike curve region by including the effects of additional light degrees of freedom. These take the form of tensionless 7-brane probes, effectively described through the backreaction of a smeared domain wall. The absence of closed timelike curves in the asymptotic…
In the attempts toward a quantum gravity theory, general relativity faces a serious difficulty since it is non-renormalizable theory. Hořava-Lifshitz gravity offers a framework to circumvent this difficulty, by sacrificing the local Lorentz invariance at ultra-high energy scales in exchange of power-counting renormalizability. The Lorentz symmetry is expected to be recovered at low and medium energy scales. If gravitation is to be described by a Hořava-Lifshitz gravity theory there are a number of issues that ought to be reexamined in its context, including the question as to whether this grav…
We analyze the structure of supersymmetric Godel-like cosmological solutions of string theory. Just as the original four-dimensional Godel universe, these solutions represent rotating, topologically trivial cosmologies with a homogeneous metric and closed timelike curves. First we focus on "phenomenological" aspects of holography, and identify the preferred holographic screens associated with inertial comoving observers in Godel universes. We find that holography can serve as a chronology protection agency: The closed timelike curves are either hidden behind the holographic screen, or broken b…
We show that a Goedel-like deformation of AdS3 in heterotic string theory can be realized as an exact string background. Indeed this class of solutions is obtained as an exactly marginal deformation of the conformal field theory describing the NS5/F1 heterotic background. It can also be embedded in type II superstrings as a Kaluza-Klein reduction. We compute the spectrum of this model as well as the genus one modular invariant partition function. We discuss the issue of closed timelike curves and the propagation of long strings. They destabilize completely the background, although we construct…
We show that the null Melvin map applied to a rotational isometry of global anti-de Sitter space produces a spacetime with properties analogous to both the Godel and Schrodinger geometries. The isometry group of this Godel-Schrodinger spacetime is appropriate to provide a holographic dual for the same non-relativistic conformal theory as the ordinary Schrodinger geometry, but defined on a sphere. This spacetime also possesses closed timelike curves outside a certain critical radius. We show that a holographic preferred screen for an observer at the origin sits at an interior radius, suggesting…
Galileon models are a class of effective field theories that have recently received much attention. They arise in the decoupling limit of theories of massive gravity, and in some cases they have been treated in their own right as scalar field theories with a specific nonlinearly realized global symmetry (Galilean transformation). It is well known that in the presence of a source, these Galileon theories admit superluminal propagating solutions, implying that as quantum field theories they must admit a different notion of causality than standard local Lorentz invariant theories. We show that in…
Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single…
In this note, a brief review of the consistent state approach to systems containing closed timelike curves or similar devices is given, and applied to the well known thermodynamic problem of Maxwell's demon. The 'third party paradox' for acausal systems is defined and applied to CTC censorship and black hole evaporation. Some traditional arguments for chronology protection are re-examined.
To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The (1+3) timelike threading approach involves restrictions on the gravitational potentials $(g_{μν})$, while the (3+1) spacelike slicing approach involves restrictions on $(g^{μν})$. These latter coordinate conditions protect chronology within any such coordinate patch. While the threading coordinate conditions can be naturally integrated into the structure of Lorentzian geometry and constitute the standard coordinate conditions in general relativity, this circumstance …
We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner-Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.
We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like naked singularity. We study the general features of these metrics and prove that there are actually just two generic classes of space-times - those with null singularities are in the same class as the non-singular metrics. AdS/CFT seems to provide a dual description only for the first of these two types of space-time in terms of a unitary CFT indicating the p…
In this article, we explore the relationship between the existence of closed timelike curves and energy conditions that occur in the Kerr-Newman spacetime. To quantify the dependence, we define a correlation index between energy conditions and closed timelike curves. Based on the inputs from Hawking's chronology protection conjecture, we analyze two popular variants of Kerr-Newman spacetime: Non-commutative and Rastall Kerr-Newman spacetimes. These two models provide complementary scenarios that aid in analyzing Hawking's statements regarding the correlation of closed timelike curves and energ…
We study supersymmetric charged rotating black holes in AdS$_5$, and show that closed timelike curves occur outside the event horizon. Also upon lifting to rotating D3 brane solutions of type IIB supergravity in ten dimensions, closed timelike curves are still present. We believe that these causal anomalies correspond to loss of unitarity in the dual ${\cal N}=4$, D=4 super Yang-Mills theory, i.e. the chronology protection conjecture in the AdS bulk is related to unitarity bounds in the boundary CFT. We show that no charged or uncharged geodesic can penetrate the horizon, so that the exterior …
We discuss plane wave backgrounds of string theory and their relation to Goedel-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 Goedel-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,…
In asymmetrically warped spacetimes different warp factors are assigned to space and to time. We discuss causality properties of these warped brane universes and argue that scenarios with two extra dimensions may allow for timelike curves which can be closed via paths in the extra-dimensional bulk. In particular, necessary and sufficient conditions on the metric for the existence of closed timelike curves are presented. We find a six-dimensional warped metric which satisfies the CTC conditions, and where the null, weak and dominant energy conditions are satisfied on the brane (although only th…
