The twin paradox in compact spaces

Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.Comment: to be published in PRA, 3 page

Note on Varying Speed of Light Cosmologies

The various requirements on a consistent varying speed of light (`VSL') theory are surveyed, giving a short check-list of issues that should be satisfactorily handled by such theories.Comment: 6 pages; to appear in the GRG Journa

Neutron Stars in a Varying Speed of Light Theory

We study neutron stars in a varying speed of light (VSL) theory of gravity in which the local speed of light depends upon the value of a scalar field $\phi$. We find that the masses and radii of the stars are strongly dependent on the strength of the coupling between $\phi$ and the matter field and that for certain choices of coupling parameters, the maximum neutron star mass can be arbitrarily small. We also discuss the phenomenon of cosmological evolution of VSL stars (analogous to the gravitational evolution in scalar-tensor theories) and we derive a relation showing how the fractional change in the energy of a star is related to the change in the cosmological value of the scalar field.Comment: 15 pages, 2 figures. Added solutions with a more realistic equation of state. To be published in PR

Stability of Closed Timelike Curves in Goedel Universe

We study, in some detail, the linear stability of closed timelike curves in the Goedel metric. We show that these curves are stable. We present a simple extension (deformation) of the Goedel metric that contains a class of closed timelike curves similar to the ones associated to the original Goedel metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in Goedel universe with or whithout the inclusion of regular or exotic matter are also stable under linear perturbations. We also find a sort of structural stability.Comment: 12 pages, 11 figures, RevTex, several typos corrected. GRG, in pres

Perturbation evolution with a non-minimally coupled scalar field

We recently proposed a simple dilaton-derived quintessence model in which the scalar field was non-minimally coupled to cold dark matter, but not to `visible' matter. Such couplings can be attributed to the dilaton in the low energy limit of string theory, beyond tree level. In this paper we discuss the implications of such a model on structure formation, looking at its impact on matter perturbations and CMB anisotropies. We find that the model only deviates from $\Lambda$CDM and minimally coupled theories at late times, and is well fitted to current observational data. The signature left by the coupling, when it breaks degeneracy at late times, presents a valuable opportunity to constrain non-minimal couplings given the wealth of new observational data promised in the near future.Comment: Version appearing in Physical Review D. 10 pages, 9 figs. Comparison with SN1a and projected MAP results, and appendix adde

Can inflationary models of cosmic perturbations evade the secondary oscillation test?

We consider the consequences of an observed Cosmic Microwave Background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum {\em can} be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and \pk satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models can {\em not} evade the secondary oscillation test.Comment: Final version accepted for publication in PRD. Minor improvements have been made to the discussion and new data has been included. The conclusions are unchagne

G\"odel Incompleteness and the Black Hole Information Paradox

Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization is to identify the G\"odel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement

STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.Comment: 19 pages, LaTe

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity

Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which remains in general arbitrary. Spacetimes for fluids fulfilling linear and polytropic state equations are explicitly derived; they describe, among others, stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate fermions, incoherent and pure radiation. As a by--product, we demonstrate the uniqueness of the constant energy density perfect fluid within the studied class of metrics. A full similarity of the perfect fluid solutions with constant energy density of the 2+1 and 3+1 gravities is established.Comment: revtex4, 8 page