A Lemaitre-Tolman-Bondi cosmological wormhole

We present a new analytical solution of the Einstein field equations describing a wormhole shell of zero thickness joining two Lema{\i}tre-Tolman-Bondi universes, with no radial accretion. The material on the shell satisfies the energy conditions and, at late times, the shell becomes comoving with the dust-dominated cosmic substratum.Comment: 5 pages, latex, no figures, to appear in Phys. Rev.

From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture

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 regimes Casimir effects, wormhole disruption effects, and gravitational back reaction effects all contribute to the fight against time travel. Particular attention is paid to the role of the quantum gravity cutoff. For the class of model problems considered it is shown that the gravitational back reaction becomes large before the Planck scale quantum gravity cutoff is reached, thus supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision

Gravastars must have anisotropic pressures

One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the "gravastar" model developed by Mazur and Mottola; and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure -- without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluids -- anisotropic pressures in the "crust" of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation.Comment: V1: 15 pages; 4 figures; uses iopart.cls; V2: 16 pages; added 3 references and brief discussio

Energetics in Condensate Star and Wormholes

It is known that the total gravitational energy in localized sources having static spherical symmetry and satisfying energy conditions is negative (attractive gravity). A natural query is how the gravitational energy behaves under circumstances where energy conditions are violated. To answer this, the known expression for the gravitational energy is suitably modified to account for situations like the ones occurring in wormhole spacetime. It is then exemplified that in many cases the modified expression yields desirable answers. The implications are discussed.Comment: 16 pages, 1 figure, references added, To appear in PR

Zeta functions, renormalization group equations, and the effective action

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.

Scharnhorst effect at oblique incidence

We consider the Scharnhorst effect (anomalous photon propagation in the Casimir vacuum) at oblique incidence, calculating both photon speed and polarization states as functions of angle. The analysis is performed in the framework of nonlinear electrodynamics and we show that many features of the situation can be extracted solely on the basis of symmetry considerations. Although birefringence is common in nonlinear electrodynamics it is not universal; in particular we verify that the Casimir vacuum is not birefringent at any incidence angle. On the other hand, group velocity is typically not equal to phase velocity, though the distinction vanishes for special directions or if one is only working to second order in the fine structure constant. We obtain an ``effective metric'' that is subtly different from previous results. The disagreement is due to the way that ``polarization sums'' are implemented in the extant literature, and we demonstrate that a fully consistent polarization sum must be implemented via a bootstrap procedure using the effective metric one is attempting to define. Furthermore, in the case of birefringence, we show that the polarization sum technique is intrinsically an approximation.Comment: 11 pages double-column format, 2 figures, RevTeX 4.0 (beta 2). Final versio

Horizon effects with surface waves on moving water

Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.Comment: 30 pages, 15 figures. Minor change

Shaping Robust System through Evolution

Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network's robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is derived, akin to the fluctuation-dissipation relationship known in physics

Homogeneous singularities inside collapsing wormholes

We analyze analytically and numerically the origin of the singularity in the course of the collapse of a wormhole with the exotic scalar field Psi with negative energy density, and with this field Psi together with the ordered magnetic field H. We do this under the simplifying assumptions of the spherical symmetry and that in the vicinity of the singularity the solution of the Einstein equations depends only on one coordinate (the homogeneous approximation). In the framework of these assumptions we found the principal difference between the case of the collapse of the ordinary scalar field Phi with the positive energy density together with an ordered magnetic field H and the collapse of the exotic scalar field Psi together with the magnetic field H. The later case is important for the possible astrophysical manifestation of the wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To be published in "Physical review. D, Particles, fields, gravitation, and cosmology

Gravastar Solutions with Continuous Pressures and Equation of State

We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.Comment: 19 pages, 9 figures. Latest version contains new and updated references along with some clarifying remarks in the stability analysi