Hawking Spectrum and High Frequency Dispersion

We study the spectrum of created particles in two-dimensional black hole geometries for a linear, hermitian scalar field satisfying a Lorentz non-invariant field equation with higher spatial derivative terms that are suppressed by powers of a fundamental momentum scale $k_0$. The preferred frame is the ``free-fall frame" of the black hole. This model is a variation of Unruh's sonic black hole analogy. We find that there are two qualitatively different types of particle production in this model: a thermal Hawking flux generated by ``mode conversion" at the black hole horizon, and a non-thermal spectrum generated via scattering off the background into negative free-fall frequency modes. This second process has nothing to do with black holes and does not occur for the ordinary wave equation because such modes do not propagate outside the horizon with positive Killing frequency. The horizon component of the radiation is astonishingly close to a perfect thermal spectrum: for the smoothest metric studied, with Hawking temperature $T_H\simeq0.0008k_0$, agreement is of order $(T_H/k_0)^3$ at frequency $\omega=T_H$, and agreement to order $T_H/k_0$ persists out to $\omega/T_H\simeq 45$ where the thermal number flux is $O(10^{-20}$). The flux from scattering dominates at large $\omega$ and becomes many orders of magnitude larger than the horizon component for metrics with a ``kink", i.e. a region of high curvature localized on a static worldline outside the horizon. This non-thermal flux amounts to roughly 10\% of the total luminosity for the kinkier metrics considered. The flux exhibits oscillations as a function of frequency which can be explained by interference between the various contributions to the flux.Comment: 32 pages, plain latex, 16 figures included using psfi

Formation and Evaporation of Charged Black Holes

We investigate the dynamical formation and evaporation of a spherically symmetric charged black hole. We study the self-consistent one loop order semiclassical back-reaction problem. To this end the mass-evaporation is modeled by an expectation value of the stress-energy tensor of a neutral massless scalar field, while the charge is not radiated away. We observe the formation of an initially non extremal black hole which tends toward the extremal black hole $M=Q$, emitting Hawking radiation. If also the discharge due to the instability of vacuum to pair creation in strong electric fields occurs, then the black hole discharges and evaporates simultaneously and decays regularly until the scale where the semiclassical approximation breaks down. We calculate the rates of the mass and the charge loss and estimate the life-time of the decaying black holes.Comment: 23 pages, 7 eps figures, RevTex, accepted for publication in Phys. Rev.

Black Hole Evaporation in the Presence of a Short Distance Cutoff

A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.Comment: 35 pages, plain LaTeX, UMDGR93-32, NSF-ITP-93-2

Supercurrent flow through an effective double barrier structure

Supercurrent flow is studied in a structure that in the Ginzburg-Landau regime can be described in terms of an effective double barrier potential. In the limit of strongly reflecting barriers, the passage of Cooper pairs through such a structure may be viewed as a realization of resonant tunneling with a rigid wave function. For interbarrier distances smaller than $d_0=\pi\xi(T)$ no current-carrying solutions exist. For distances between $d_0$ and $2d_0$, four solutions exist. The two symmetric solutions obey a current-phase relation of $\sin(\Delta\varphi/2)$, while the two asymmetric solutions satisfy $\Delta\varphi=\pi$ for all allowed values of the current. As the distance exceeds $nd_0$, a new group of four solutions appears, each contaning $(n-1)$ soliton-type oscillations between the barriers. We prove the inexistence of a continuous crossover between the physical solutions of the nonlinear Ginzburg-Landau equation and those of the corresponding linearized Schr\"odinger equation. We also show that under certain conditions a repulsive delta function barrier may quantitatively describe a SNS structure. We are thus able to predict that the critical current of a SNSNS structure vanishes as $\sqrt{T'_c-T}$, where $T'_c$ is lower than the bulk critical temperature.Comment: 20 pages, RevTex, to appear in Phys. Rev. B, 6 figures on request at [email protected]

Linking the trans-Planckian and the information loss problems in black hole physics

The trans-Planckian and information loss problems are usually discussed in the literature as separate issues concerning the nature of Hawking radiation. Here we instead argue that they are intimately linked, and can be understood as "two sides of the same coin" once it is accepted that general relativity is an effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in General Relativity and Gravitatio

Black Hole Entropy without Brick Walls

We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, S=\A/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.Comment: 15 pages, plain LaTex minor additions including some references; version accepted for publicatio

On Slow Light as a Black Hole Analogue

Although slow light (electromagnetically induced transparency) would seem an ideal medium in which to institute a ``dumb hole'' (black hole analog), it suffers from a number of problems. We show that the high phase velocity in the slow light regime ensures that the system cannot be used as an analog displaying Hawking radiation. Even though an appropriately designed slow-light set-up may simulate classical features of black holes -- such as horizon, mode mixing, Bogoliubov coefficients, etc. -- it does not reproduce the related quantum effects. PACS: 04.70.Dy, 04.80.-y, 42.50.Gy, 04.60.-m.Comment: 14 pages RevTeX, 5 figure

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.Comment: 47 pages, 5 figures. v2: See end of introduction for an important note adde

On the Origin of Entropic Gravity and Inertia

It was recently suggested that quantum field theory is not fundamental but emerges from the loss of phase space information about matter crossing causal horizons. Possible connections between this formalism and Verlinde's entropic gravity and Jacobson's thermodynamic gravity are proposed. The holographic screen in Verlinde's formalism can be identified as local Rindler horizons and its entropy as that of the bulk fields beyond the horizons. This naturally resolves some issues on entropic gravity. The quantum fluctuation of the fields is the origin of the thermodynamic nature of entropic gravity. It is also suggested that inertia is related to dragging Rindler horizons.Comment: 9 pages, revtex4-1, 3 figures, accepted for publication in Foundations of Physic

Observable Effects of Scalar Fields and Varying Constants

We show by using the method of matched asymptotic expansions that a sufficient condition can be derived which determines when a local experiment will detect the cosmological variation of a scalar field which is driving the spacetime variation of a supposed constant of Nature. We extend our earlier analyses of this problem by including the possibility that the local region is undergoing collapse inside a virialised structure, like a galaxy or galaxy cluster. We show by direct calculation that the sufficient condition is met to high precision in our own local region and we can therefore legitimately use local observations to place constraints upon the variation of "constants" of Nature on cosmological scales.Comment: Invited Festscrift Articl