The disinformation problem for black holes (conference version)

Basic properties of black holes are explained in terms of trapping horizons. It is shown that matter and information will escape from an evaporating black hole. A general scenario is outlined whereby a black hole evaporates completely without singularity, event horizon or loss of energy or information.Comment: 4 latex pages, 12 eps figures. Presented at the 14th Workshop on General Relativity and Gravitation, Kyoto Universit

Signature Change at Material Layers and Step Potentials

For a contravariant 4-metric which changes signature from Lorentzian to Riemannian across a spatial hypersurface, the mixed Einstein tensor is manifestly non-singular. In Gaussian normal coordinates, the metric contains a step function and the Einstein tensor contains the Dirac delta function with support at the junction. The coefficient of the Dirac function is a linear combination of the second fundamental form (extrinsic curvature) of the junction. Thus, unless the junction has vanishing extrinsic curvature, the physical interpretation of the metric is that it describes a layer of matter (with stresses but no energy or momentum) at the junction. In particular, such metrics do not satisfy the vacuum Einstein equations, nor the Einstein-Klein-Gordon equations and so on. Similarly, the d'Alembertian of a Klein-Gordon field contains the Dirac function with coefficient given by the momentum of the field. Thus, if the momentum of the field does not vanish at the junction, the physical interpretation is that there is a source (with step potential) at the junction. In particular, such fields do not satisfy the massless Klein-Gordon equation. These facts contradict claims in the literature.Comment: 7 pages; Te

COMMENT ON ``BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE''

Fundamental errors exist in the above-mentioned article, which attempts to justify previous erroneous claims concerning signature change. In the simplest example, the authors' proposed ``solutions'' do not satisfy the relevant equation, as may be checked by substitution. These ``solutions'' are also different to the authors' originally proposed ``solutions'', which also do not satisfy the equation. The variational equations obtained from the authors' ``actions'' are singular at the change of signature. The authors' ``distributional field equations'' are manifestly ill defined.Comment: 4 pages. TeX

Gravitational energy as Noether charge

A definition of gravitational energy is proposed for any theory described by a diffeomorphism-invariant Lagrangian. The mathematical structure is a Noether- current construction of Wald involving the boundary term in the action, but here it is argued that the physical interpretation of current conservation is conservation of energy. This leads to a quasi-local energy defined for compact spatial surfaces. The energy also depends on a vector generating a flow of time. Angular momentum may be similarly defined, depending on a choice of axial vector. For Einstein gravity: for the usual vector generating asymptotic time translations, the energy is the Bondi energy; for a stationary Killing vector, the energy is the Komar energy; in spherical symmetry, for the Kodama vector, the energy is the Misner-Sharp energy. In general, the lack of a preferred time indicates the lack of a preferred energy, reminiscent of the energy-time duality of quantum theory.Comment: 4 pages, revte

Involute, minimal, outer and increasingly trapped spheres

Seven different refinements of trapped surfaces are proposed, each intended as potential stability conditions. This article concerns spherical symmetry, but each condition can be generalized. Involute trapped spheres satisfy a similar condition to minimal trapped spheres, which are are strictly minimal with respect to the Kodama vector. There is also a weaker version of involute trapped. Outer trapped spheres have positive surface gravity. Increasingly (future, respectively past) trapped spheres generate spheres which are more trapped in a (future, respectively past) causal direction, with three types: in any such causal direction, along the dual Kodama vector, and in some such causal direction. Assuming the null energy condition, the seven conditions form a strict hierarchy, in the above order. In static space-times, they reduce to three inequivalent definitions, namely minimal, outer and increasingly trapped spheres. For a widely considered class of so-called nice (or non-dirty) black holes, minimal trapped and outer trapped become equivalent. Reissner-Nordstr\"om black holes provide examples of this, and that increasingly trapped differs. Examples where all three refinements differ are provided by a simple family of dirty black holes parameterized by mass and singularity area.Comment: Substantially extended to include detailed study of static space-times. 10 REVTeX4 page

Formation and evaporation of non-singular black holes

Regular (non-singular) space-times are given which describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region. The static region is Bardeen-like, supported by finite density and pressures, vanishing rapidly at large radius and behaving as a cosmological constant at small radius. The dynamic regions are Vaidya-like, with ingoing radiation of positive energy flux during collapse and negative energy flux during evaporation, the latter balanced by outgoing radiation of positive energy flux and a surface pressure at a pair creation surface. The black hole consists of a compact space-time region of trapped surfaces, with inner and outer boundaries which join circularly as a single smooth trapping horizon.Comment: 4 revtex4 pages, 5 eps figures. Correction concerning surface layer, revised discussion, title chang

Recent progress in wormhole dynamics

Space-time wormholes were introduced in Wheeler's idea of space-time foam. Traversible wormholes as defined by Morris & Thorne became popular as potential short cuts across the universe and even time machines. More recently, the author proposed a general theory of wormhole dynamics, unified with black-hole dynamics. This article gives a brief review of the above ideas and summarizes progress on wormhole dynamics in the last year. Firstly, a numerical study of dynamical perturbations of the first Morris-Thorne wormhole showed it to be unstable, either collapsing to a black hole or exploding to an inflationary universe. This provides a mechanism for inflating a wormhole from space-time foam to usable size. Intriguing critical behaviour was also discovered. Secondly, a wormhole solution supported by pure radiation was discovered and used to find analytic examples of dynamic wormhole processes which were also recently found in a two-dimensional dilaton gravity model: the construction of a traversible wormhole from a Schwarzschild black hole and vice versa, and the enlargement or reduction of the wormhole.Comment: 4 latex pages, 6 ps/eps figures. Presented at the 12th Workshop on General Relativity and Gravitation, University of Toky

Spatial and null infinity via advanced and retarded conformal factors

A new approach to space-time asymptotics is presented, refining Penrose's idea of conformal transformations with infinity represented by the conformal boundary of space-time. Generalizing examples such as flat and Schwarzschild space-times, it is proposed that the Penrose conformal factor be a product of advanced and retarded conformal factors, which asymptotically relate physical and conformal null (light-like) coordinates and vanish at future and past null infinity respectively, with both vanishing at spatial infinity. A correspondingly refined definition of asymptotic flatness at both spatial and null infinity is given, including that the conformal boundary is locally a light cone, with spatial infinity as the vertex. It is shown how to choose the conformal factors so that this asymptotic light cone is locally a metric light cone. The theory is implemented in the spin-coefficient (or null-tetrad) formalism by a simple joint transformation of the spin-metric and spin-basis (or metric and tetrad). The advanced and retarded conformal factors may be used as expansion parameters near the respective null infinity, together with a dependent expansion parameter for both spatial and null infinity, essentially inverse radius. Asymptotic regularity conditions on the spin-coefficients are proposed, based on the conformal boundary locally being a smoothly embedded metric light cone. These conditions ensure that the Bondi-Sachs energy-flux integrals of ingoing and outgoing gravitational radiation decay at spatial infinity such that the total radiated energy is finite, and that the Bondi-Sachs energy-momentum has a unique limit at spatial infinity, coinciding with the uniquely rendered ADM energy-momentum.Comment: 11 revtex4 pages, 1 eps figure, correcting typos etc, unabridged (abridged version to be published

Confinement by Black Holes

The question of whether an observer can escape from a black hole is addressed, using a recent general definition of a black hole in the form of a future outer trapping horizon. An observer on a future outer trapping horizon must enter the neighbouring trapped region. It is possible for the observer to subsequently escape from the trapped region. However, if the horizon separates the space-time into two disjoint components, inside and outside the horizon, then an observer inside a future outer trapping horizon cannot get outside, assuming the null energy condition. A similar confinement property holds for trapped, locally area-preserving cylinders, as suggested by Israel.Comment: 5 pages. Figures not include

The disinformation problem for black holes (pop version)

The supposed information paradox for black holes is based on the fundamental misunderstanding that black holes are usefully defined by event horizons. Understood in terms of locally defined trapping horizons, the paradox disappears: information will escape from an evaporating black hole. According to classical properties of trapping horizons, a general scenario is outlined whereby a black hole evaporates completely without singularity, event horizon or loss of energy or information.Comment: 6 revtex4 page