Geodesics in the static Mallett spacetime

Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.Comment: 5 page

Averaged null energy condition violation in a conformally flat spacetime

We show that the averaged null energy condition can be violated by a conformally coupled scalar field in a conformally flat spacetime in 3+1 dimensions. The violation is dependent on the quantum state and can be made as large as desired. It does not arise from the presence of anomalies, although anomalous violations are also possible. Since all geodesics in conformally flat spacetimes are achronal, the achronal averaged null energy condition is likewise violated.Comment: 11 page

Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape

We consider the cosmological dynamics associated with volume weighted measures of eternal inflation, in the Bousso-Polchinski model of the string theory landscape. We find that this measure predicts that observers are most likely to find themselves in low energy vacua with one flux considerably larger than the rest. Furthermore, it allows for a satisfactory anthropic explanation of the cosmological constant problem by producing a smooth, and approximately constant, distribution of potentially observable values of Lambda. The low energy vacua selected by this measure are often short lived. If we require anthropically acceptable vacua to have a minimum life-time of 10 billion years, then for reasonable parameters a typical observer should expect their vacuum to have a life-time of approximately 12 billion years. This prediction is model dependent, but may point toward a solution to the coincidence problem of cosmology.Comment: 35 pages, 8 figure

Quantum inequality for a scalar field with a background potential

Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background potential (i.e., a mass that varies with spacetime position) in Minkowski space. We treat the potential as a perturbation and explicitly calculate the first-order correction to a quantum inequality with an arbitrary sampling function, using general results of Fewster and Smith. For an arbitrary potential, we give bounds on the correction in terms of the maximum values of the potential and its first three derivatives. The techniques we develop here will also be applicable to quantum inequalities in general spacetimes with small curvature, which are necessary to rule out exotic phenomena

Can a circulating light beam produce a time machine?

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC's occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett's solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.Comment: 5 pages, RevTe

The quantum inequalities do not forbid spacetime shortcuts

A class of spacetimes (comprising the Alcubierre bubble, Krasnikov tube, and a certain type of wormholes) is considered that admits `superluminal travel' in a strictly defined sense. Such spacetimes (they are called `shortcuts' in this paper) were suspected to be impossible because calculations based on `quantum inequalities' suggest that their existence would involve Planck-scale energy densities and hence unphysically large values of the `total amount of negative energy' E_tot. I argue that the spacetimes of this type may not be unphysical at all. By explicit examples I prove that: 1) the relevant quantum inequality does not (always) imply large energy densities; 2) large densities may not lead to large values of E_tot; 3) large E_tot, being physically meaningless in some relevant situations, does not necessarily exclude shortcuts.Comment: Minor corrections and addition

The form of cosmic string cusps

We classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts. A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp. The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation. We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation. We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core. The result is that the energy scales as $\sqrt {rL}$ instead of the usual value of $r^{1/3} L^{2/3}$, where $r$ is the string radius and $L$ and is the typical length scale of the string. Since $r << L$ for cosmological strings, the radiation is strongly suppressed and could not be observed.Comment: 15 pages, ReVTex, 2 postscript figures with eps

Self sustained traversable wormholes and the equation of state

We compute the graviton one loop contribution to a classical energy in a \textit{traversable} wormhole background. The form of the shape function considered is obtained by the equation of state $p=\omega\rho$. We investigate the size of the wormhole as a function of the parameter $\omega$. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals. A zeta function regularization is involved to handle with divergences. A renormalization procedure is introduced and the finite one loop energy is considered as a \textit{self-consistent} source for the traversable wormhole.The case of the phantom region is briefly discussed.Comment: Uses RevTeX 4. 21 pages. Submitted to Classical and Quantum Gravity. Extended version of the talk given at ERE2006 (Palma de Mallorca, September 4-8, 2006) and of the talk given at MG11-GT5, Berlin, 23-29 July, 200

Averaged null energy condition in a classical curved background

The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. Exotic spacetimes, such as those allow wormholes or the construction of time machines are possible in general relativity only if ANEC is violated along achronal geodesics. Starting from a conjecture that flat-space quantum inequalities apply with small corrections in spacetimes with small curvature, we prove that ANEC is obeyed by a minimally-coupled, free quantum scalar field on any achronal null geodesic surrounded by a tubular neighborhood whose curvature is produced by a classical source

Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality

Quantum inequalities are constraints on how negative the weighted average of the renormalized stress-energy tensor of a quantum field can be. A null-projected quantum inequality can be used to prove the averaged null energy condition (ANEC), which would then rule out exotic phenomena such as wormholes and time machines. In this work we derive such an inequality for a massless minimally coupled scalar field, working to first order of the Riemann tensor and its derivatives. We then use this inequality to prove ANEC on achronal geodesics in a curved background that obeys the null convergence condition