113 research outputs found
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
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
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
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
instead of the usual value of , where is the
string radius and and is the typical length scale of the string. Since 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 . We investigate
the size of the wormhole as a function of the parameter . 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
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
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
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