arXiv subjects

Matt Visser

Publications and source records attributed to Matt Visser.

375 records · Page 21Linked to original sources

arXiv1996

Schwinger's Dynamical Casimir Effect: Bulk Energy Contribution

Schwinger's Dynamical Casimir Effect is one of several candidate explanations for sonoluminescence. Recently, several papers have claimed that Schwinger's estimate of the Casimir energy involved is grossly inaccurate. In this letter, we show that these calculations omit the crucial volume term. When the missing term is correctly included one finds full agreement with Schwinger's result for the Dynamical Casimir Effect. We have nothing new to say about sonoluminescence itself except to affirm that the Casimir effect is energetically adequate as a candidate explanation.

hep-th↗

arXiv1996

Gravitational vacuum polarization I: Energy conditions in the Hartle--Hawking vacuum

It is well-known that gravitationally induced vacuum polarization often violates the point-wise energy conditions and sometimes violates the averaged energy conditions. In this paper I begin a systematic attack on the question of where and by how much the various energy conditions are violated. I work in the test-field limit, and focus on conformally coupled massless scalar fields in Schwarzschild spacetime, using the Hartle--Hawking vacuum. I invoke a mixture of analytical and numerical techniques, and critically compare the qualitative behaviour to be expected from the Page approximation with that adduced from the numerical calculations of Anderson, Hiscock, and Samuel. I show that the various point-wise energy conditions are violated in a series of onion-like layers located between the unstable photon orbit and the event horizon, the sequence of violations being DEC, WEC, and (NEC+SEC). Furthermore the ANEC is violated for *some* of the null geodesics trapped in this region. Having established the basic machinery in this paper, the Boulware vacuum will be treated in a companion paper, while other exensions should be straightforward.

gr-qc↗

arXiv1996

Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum

I show that in the Boulware vacuum (1) all standard (point-wise and averaged) energy conditions are violated throughout the exterior region---all the way from spatial infinity down to the event horizon, and (2) outside the event horizon the standard point-wise energy conditions are violated in a maximal manner: they are violated at all points and for all null/timelike vectors. (The region inside the event horizon is considerably messier, and of dubious physical relevance. Nevertheless the standard point-wise energy conditions also seem to be violated even inside the event horizon.) This is rather different from the case of the Hartle--Hawking vacuum, wherein violations of the energy conditions were confined to the region inside the unstable photon orbit. These calculations are for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the Boulware vacuum. I work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. This *suggests* that general self-consistent solutions of semiclassical quantum gravity might *not* satisfy the energy conditions, and may in fact for certain quantum fields and certain quantum states violate *all* the energy conditions.

gr-qc↗

arXiv1996

Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime

Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC is violated everywhere in the spacetime (for any quantum state, not just the standard vacuum states).

gr-qc↗

arXiv1995

Thin-shell wormholes: Linearization stability

The class of spherically-symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat.

gr-qc↗

arXiv1994

Scale anomalies imply violation of the averaged null energy condition

Considerable interest has recently been expressed regarding the issue of whether or not quantum field theory on a fixed but curved background spacetime satisfies the averaged null energy condition (ANEC). A comment by Wald and Yurtsever [Phys. Rev. D43, 403 (1991)] indicates that in general the answer is no. In this note I explore this issue in more detail, and succeed in characterizing a broad class of spacetimes in which the ANEC is guaranteed to be violated. Finally, I add some comments regarding ANEC violation in Schwarzschild spacetime.

gr-qc↗

arXiv1994

Natural Wormholes as Gravitational Lenses

Visser has suggested traversable 3-dimensional wormholes that could plausibly form naturally during Big Bang inflation. A wormhole mouth embedded in high mass density might accrete mass, giving the other mouth a net *negative* mass of unusual gravitational properties. The lensing of such a gravitationally negative anomalous compact halo object (GNACHO) will enhance background stars with a time profile that is observable and qualitatively different from that recently observed for massive compact halo objects (MACHOs) of positive mass. We recommend that MACHO search data be analyzed for GNACHOs.

astro-ph↗

arXiv1993

Acoustic propagation in fluids: an unexpected example of Lorentzian geometry

It is a deceptively simple question to ask how acoustic disturbances propagate in a non--homogeneous flowing fluid. If the fluid is barotropic and inviscid, and the flow is irrotational (though it may have an arbitrary time dependence), then the equation of motion for the velocity potential describing a sound wave can be put in the (3+1)--dimensional form: d'Alembertian psi = 0. That is partial_mu(sqrt{-g} g^{mu nu} partial_nu psi)/sqrt{-g} = 0. The acoustic metric --- g_{mu nu}(t,x) --- governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. Even though the underlying fluid dynamics is Newtonian, non--relativistic, and takes place in flat space + time, the fluctuations (sound waves) are governed by a Lorentzian spacetime geometry.

gr-qc↗

arXiv1993

van Vleck determinants: traversable wormhole spacetimes

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.

gr-qc↗

arXiv1993

Dirty black holes: Entropy as a surface term

It is by now clear that the naive rule for the entropy of a black hole, {entropy} = 1/4 {area of event horizon}, is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, a rather different proof of this result is presented --- a proof based on Euclidean signature techniques. The total entropy is S = 1/4 {k A_H / l_P^2} + \int_H {S} \sqrt{g} d^2x. The integration runs over a spacelike cross-section of the event horizon H. The surface entropy density, {S}, is related to the behaviour of the matter Lagrangian under time dilations. Secondly, I shall consider the specific case of Einstein-Hilbert gravity coupled to an effective Lagrangian that is an arbitrary function of the Riemann tensor (though not of its derivatives). In this case a more explicit result is obtained S = 1/4 {k A_H / l_P^2} + 4 pi {k/hbar} \int_H {partial L / partial R_{μνλρ}} g^\perp_{μλ} g^\perp_{νρ} \sqrt{g} d^2x . The symbol $g^\perp_{μν}$ denotes the projection onto the two-dimensional subspace orthogonal to the event horizon.

hep-th↗

arXiv1993

Dirty black holes: Entropy versus area

Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\ell_P^2)} + {1/T_H} \int_Σ[rho - {L}_E ] K^μdΣ_μ + \int_Σs V^μdΣ_μ. (K^μis the timelike Killing vector, V^μthe four velocity of a co--rotating observer.) If no hair is present the validity of the ``entropy = (1/4) area'' law reduces to the question of whether or not the Lorentzian energy density for the system under consideration is formally equal to the Euclideanized Lagrangian. ****** To appear in Physical Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references updated, discussion of the Born-Infeld system excised]

hep-th↗

arXiv1993

Hawking's chronology protection conjecture: singularity structure of the quantum stress--energy tensor

The recent renaissance of wormhole physics has led to a very disturbing observation: If traversable wormholes exist then it appears to be rather easy to to transform such wormholes into time machines. This extremely disturbing state of affairs has lead Hawking to promulgate his chronology protection conjecture. This paper continues a program begun in an earlier paper [Physical Review {\bf D47}, 554--565 (1993), hepth@xxx/9202090]. An explicit calculation of the vacuum expectation value of the renormalized stress--energy tensor in wormhole spacetimes is presented. Point--splitting techniques are utilized. Particular attention is paid to computation of the Green function [in its Hadamard form], and the structural form of the stress-energy tensor near short closed spacelike geodesics. Detailed comparisons with previous calculations are presented, leading to a pleasingly unified overview of the situation.

hep-th↗

arXiv1993

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.

hep-th↗

arXiv1992

Dirty blackholes: Thermodynamics and horizon structure

Considerable interest has recently been expressed in (static spherically symmetric) blackholes in interaction with various classical matter fields (such as electromagnetic fields, dilaton fields, axion fields, Abelian Higgs fields, non--Abelian gauge fields, {\sl etc}). A common feature of these investigations that has not previously been remarked upon is that the Hawking temperature of such systems appears to be suppressed relative to that of a vacuum blackhole of equal horizon area. That is: $k T_H \leq \hbar/(4πr_H) \equiv \hbar/\sqrt{4πA_H}$. This paper will argue that this suppression is generic. Specifically, it will be shown that \[ k T_H = {\hbar\over4πr_H} \; e^{-ϕ(r_H)} \; \left( 1 - 8πG \; ρ_H \; r_H^2 \right). \] Here $ϕ(r_H)$ is an integral quantity, depending on the distribution of matter, that is guaranteed to be positive if the Weak Energy Condition is satisfied. Several examples of this behaviour will be discussed. Generalizations of this behaviour to non--symmetric non--static blackholes are conjectured.

hep-th↗

arXiv1992

Hawking radiation: a particle physics perspective

It has recently become fashionable to regard black holes as elementary particles. By taking this suggestion seriously it is possible to cobble together an elementary particle physics based estimate for the decay rate $(\hbox{black hole})_i \to (\hbox{black hole})_f + (\hbox{massless quantum})$. This estimate of the spontaneous emission rate contains two free parameters which may be fixed by demanding that the high energy end of the spectrum of emitted quanta match a blackbody spectrum at the Hawking temperature. The calculation, though technically trivial, has important conceptual implications: (1) The existence of Hawking radiation from black holes is ultimately dependent only on the fact that massless quanta (and all other forms of matter) couple to gravity. (2) The thermal nature of the Hawking spectrum depends only on the fact that the number of internal states of a large mass black hole is enormous. (3) Remarkably, the resulting formula for the decay rate gives meaningful answers even when extrapolated to low mass black holes. The analysis strongly supports the scenario of complete evaporation as the endpoint of the Hawking radiation process (no naked singularity, no stable massive remnant).

hep-th↗