Energy Density of Non-Minimally Coupled Scalar Field Cosmologies

Scalar fields coupled to gravity via $\xi R {\Phi}^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective scalar mass becomes an explicit function of $\xi$ and the scale factor. The scalar quartic self-coupling gets shifted and can vanish for a particular choice of $\xi$. Gravitationally induced symmetry breaking and de-stabilization are possible in this theory.Comment: 18 pages in standard Late

Effective Potential of a Black Hole in Thermal Equilibrium with Quantum Fields

Expectation values of one-loop renormalized thermal equilibrium stress-energy tensors of free conformal scalars, spin-${1 \over 2}$ fermions and U(1) gauge fields on a Schwarzschild black hole background are used as sources in the semi-classical Einstein equation. The back-reaction and new equilibrium metric are solved for at $O({\hbar})$ for each spin field. The nature of the modified black hole spacetime is revealed through calculations of the effective potential for null and timelike orbits. Significant novel features affecting the motions of both massive and massless test particles show up at lowest order in $\epsilon= (M_{Pl}/M)^2 < 1$, where $M$ is the renormalized black hole mass, and $M_{Pl}$ is the Planck mass. Specifically, we find the tendency for \underline{stable} circular photon orbits, an increase in the black hole capture cross sections, and the existence of a gravitationally repulsive region associated with the black hole which is generated from the U(1) back-reaction. We also consider the back-reaction arising from multiple fields, which will be useful for treating a black hole in thermal equilibrium with field ensembles belonging to gauge theories.Comment: 25 pages (not including seven figures), VAND-TH-93-6. Typed in Latex, uses RevTex macro

On a class of stable, traversable Lorentzian wormholes in classical general relativity

It is known that Lorentzian wormholes must be threaded by matter that violates the null energy condition. We phenomenologically characterize such exotic matter by a general class of microscopic scalar field Lagrangians and formulate the necessary conditions that the existence of Lorentzian wormholes imposes on them. Under rather general assumptions, these conditions turn out to be strongly restrictive. The most simple Lagrangian that satisfies all of them describes a minimally coupled massless scalar field with a reversed sign kinetic term. Exact, non-singular, spherically symmetric solutions of Einstein's equations sourced by such a field indeed describe traversable wormhole geometries. These wormholes are characterized by two parameters: their mass and charge. Among them, the zero mass ones are particularly simple, allowing us to analytically prove their stability under arbitrary space-time dependent perturbations. We extend our arguments to non-zero mass solutions and conclude that at least a non-zero measure set of these solutions is stable.Comment: 23 pages, 4 figures, uses RevTeX4. v2: Changes to accommodate added references. Statement about masses of the wormhole correcte

Wormhole Cosmology and the Horizon Problem

We construct an explicit class of dynamic lorentzian wormholes connecting Friedmann-Robertson-Walker (FRW) spacetimes. These wormholes can allow two-way transmission of signals between spatially separated regions of spacetime and could permit such regions to come into thermal contact. The cosmology of a network of early Universe wormholes is discussed.Comment: 13 pages, in RevTe

Notes on wormhole existence in scalar-tensor and F(R) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G_eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant \omega > -3/2, except for the case \omega = 0; in the latter case, G_eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G_eff changes its sign.Comment: 7 two-column pages, no figures, to appear in Grav. Cosmol. A misprint corrected, references update

No realistic wormholes from ghost-free scalar-tensor phantom dark energy

It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(\Phi)$ is everywhere positive and the scalar field $\Phi$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(\Phi)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions require severe fine tuning and a very peculiar kind of model. If $f < 0$ is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under non-static perturbations, the instability appearing right near transition surfaces to negative $f$.Comment: 8 pages, late

On thin-shell wormholes evolving in flat FRW spacetimes

We analize the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state $\mathcal{P}=w\sigma$ and have a physical radius equal to $aR$, where $a$ is a time-dependent function describing the dynamics of the throat and $R$ is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.Comment: 8 pages; to appear in MPL

Brans-Dicke wormholes in the Jordan and Einstein frames

We examine the possibility of static wormhole solutions in the vacuum Brans-Dicke theory both in the original (Jordan) frame and in the conformally rescaled (Einstein) frame. It turns out that, in the former frame, wormholes exist only in a very narrow interval of the coupling parameter, viz., -3/2<omega<-4/3. It is shown that these wormholes are not traversable in practice. In the latter frame, wormhole solutions do not exist at all unless energy conditions are violated by hand.Comment: Minor errors corrected, uploaded for the benefit of the researcher

New Features of Extended Wormhole Solutions in the Scalar Field Gravity Theories

The present paper reports interesting new features that wormhole solutions in the scalar field gravity theory have. To demonstrate these, we obtain, by using a slightly modified form of the Matos-Nunez algorithm, an extended class of asymptotically flat wormhole solutions belonging to Einstein minimally coupled scalar field theory. Generally, solutions in these theories do not represent traversable wormholes due to the occurrence of curvature singularities. However, the Ellis I solution of the Einstein minimally coupled theory, when Wick rotated, yields Ellis class III solution, the latter representing a singularity-free traversable wormhole. We see that Ellis I and III are not essentially independent solutions. The Wick rotated seed solutions, extended by the algorithm, contain two new parameters a and \delta;. The effect of the parameter a on the geodesic motion of test particles reveals some remarkable features. By arguing for Sagnac effect in the extended Wick rotated solution, we find that the parameter a can indeed be interpreted as a rotation parameter of the wormhole. The analyses reported here have wider applicability in that they can very well be adopted in other theories, including in the string theory.Comment: 19 page

Cylindrical thin-shell wormholes

A general formalism for the dynamics of non rotating cylindrical thin-shell wormholes is developed. The time evolution of the throat is explicitly obtained for thin-shell wormholes whose metric has the form associated to local cosmic strings. It is found that the throat collapses to zero radius, remains static or expands forever, depending only on the sign of its initial velocity.Comment: 10 page