Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

We show that a gap exists in the allowed sizes of all zero temperature static spherically symmetric black holes in semiclassical gravity when only conformally invariant fields are present. The result holds for both charged and uncharged black holes. By size we mean the proper area of the event horizon. The range of sizes that do not occur depends on the numbers and types of quantized fields that are present. We also derive some general properties that both zero and nonzero temperature black holes have in all classical and semiclassical metric theories of gravity.Comment: 4 pages, ReVTeX, no figure

Dynamic wormholes, anti-trapped surfaces, and energy conditions

Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess two such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide, (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the ``flare-out'' condition for an arbitrary wormhole. We derive theorems regarding violations of the null energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time-dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations cannot be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats.Comment: 32 pages in plain LaTex, no figures. Additional text and references adde

Tolman wormholes violate the strong energy condition

For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a three-dimensional edgeless achronal spacelike hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions--theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example: even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

<Tνμ>ren<T^{\mu}_{\nu}>_{ren} of the quantized fields in the Unruh state in the Schwarzschild spacetime

The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Unruh state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in conformal space and utilizing the regularity conditions in the physical metric. The relations of obtained results to the existing approximations are analysed.Comment: 17 pages, REVTE

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

Semiclassical effects in black hole interiors

First-order semiclassical perturbations to the Schwarzschild black hole geometry are studied within the black hole interior. The source of the perturbations is taken to be the vacuum stress-energy of quantized scalar, spinor, and vector fields, evaluated using analytic approximations developed by Page and others (for massless fields) and the DeWitt-Schwinger approximation (for massive fields). Viewing the interior as an anisotropic collapsing cosmology, we find that minimally or conformally coupled scalar fields, and spinor fields, decrease the anisotropy as the singularity is approached, while vector fields increase the anisotropy. In addition, we find that massless fields of all spins, and massive vector fields, strengthen the singularity, while massive scalar and spinor fields tend to slow the growth of curvature.Comment: 29 pages, ReVTeX; 4 ps figure

Electromagnetic waves in a wormhole geometry

We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one-dimensional Schr\"odinger-like equation with a barrier-type potential. Using numerical methods, we calculate the transmission coefficient as a function of the energy. We also discuss the polarization of the outgoing radiation due to this gravitational scattering.Comment: LaTex file, 5 pages, 2 figures, one reference added, accepted for publication in PR

Rotating traversable wormholes

The general form of a stationary, axially symmetric traversable wormhole is discussed. This provides an explicit class of rotating wormholes that generalize the static, spherically symmetric ones first considered by Morris and Thorne. In agreement with general analyses, it is verified that such a wormhole generically violates the null energy condition at the throat. However, for suitable model wormholes, there can be classes of geodesics falling through it which do not encounter any energy-condition-violating matter. The possible presence of an ergoregion surrounding the throat is also noted.Comment: 15 pages, harvmac; 1 figure in PicTeX; minor changes; to appear in Phys. Rev.

A note on brain actuated spelling with the Berlin brain-computer interface

Brain-Computer Interfaces (BCIs) are systems capable of decoding neural activity in real time, thereby allowing a computer application to be directly controlled by the brain. Since the characteristics of such direct brain-tocomputer interaction are limited in several aspects, one major challenge in BCI research is intelligent front-end design. Here we present the mental text entry application ‘Hex-o-Spell’ which incorporates principles of Human-Computer Interaction research into BCI feedback design. The system utilises the high visual display bandwidth to help compensate for the extremely limited control bandwidth which operates with only two mental states, where the timing of the state changes encodes most of the information. The display is visually appealing, and control is robust. The effectiveness and robustness of the interface was demonstrated at the CeBIT 2006 (world’s largest IT fair) where two subjects operated the mental text entry system at a speed of up to 7.6 char/min