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.

Entanglement entropy in curved spacetimes with event horizons

We consider the computation of the entanglement entropy in curved backgrounds with event horizons. We use a Hamiltonian approach to the problem and perform numerical computations on a spherical lattice of spacing $a$. We study the cosmological case and make explicit computations for the Friedmann-Robertson-Walker universe. Our results for a massless, minimally coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which resembles the flat space formula, although here the horizon radius, $r_H$, is time-dependent.Comment: 12 pages, RevTex 3.0, 2 figures as uuencoded compressed Postscript file

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

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

Entropy of Lovelock Black Holes

A general formula for the entropy of stationary black holes in Lovelock gravity theories is obtained by integrating the first law of black hole mechanics, which is derived by Hamiltonian methods. The entropy is not simply one quarter of the surface area of the horizon, but also includes a sum of intrinsic curvature invariants integrated over a cross section of the horizon.Comment: 15 pages, plain Latex, NSF-ITP-93-4

Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff

As a simple model for unknown Planck scale physics, we assume that the quantum modes responsible for producing primordial curvature perturbations during inflation are placed in their instantaneous adiabatic vacuum when their proper momentum reaches a fixed high energy scale M. The resulting power spectrum is derived and presented in a form that exhibits the amplitude and frequency of the superimposed oscillations in terms of H/M and the slow roll parameter epsilon. The amplitude of the oscillations is proportional to the third power of H/M. We argue that these small oscillations give the lower bound of the modifications of the power spectrum if the notion of free mode propagation ceases to exist above the critical energy scale M.Comment: 10 pages; matches version accepted by PR

Quantum Correlation in One-dimensional Extend Quantum Compass Model

We study the correlations in the one-dimensional extended quantum compass model in a transverse magnetic field. By exactly solving the Hamiltonian, we find that the quantum correlation of the ground state of one-dimensional quantum compass model is vanishing. We show that quantum discord can not only locate the quantum critical points, but also discern the orders of phase transitions. Furthermore, entanglement quantified by concurrence is also compared.Comment: 8 pages, 14 figures, to appear in Eur. Phys. J.

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde

Could supermassive black holes be quintessential primordial black holes?

There is growing observational evidence for a population of supermassive black holes (SMBHs) in galactic bulges. We examine in detail the conditions under which these black holes must have originated from primordial black holes (PBHs). We consider the merging and accretion history experienced by SMBHs to find that, whereas it is possible that they were formed by purely astrophysical processes, this is unlikely and most probably a populations of primordial progenitors is necessary. We identify the mass distribution and comoving density of this population and then propose a cosmological scenario producing PBHs with the right properties. Although this is not essential we consider PBHs produced at the end of a period of inflation with a blue spectrum of fluctuations. We constrain the value of the spectral tilt in order to obtain the required PBH comoving density. We then assume that PBHs grow by accreting quintessence showing that their mass scales like the horizon mass while the quintessence field itself is scaling. We find that if scaling is broken just before nucleosynthesis (as is the case with some attractive non-minimally coupled models) we obtain the appropriate PBH mass distribution. Hawking evaporation is negligible in most cases, but we also discuss situations in which the interplay of accretion and evaporation is relevant.Comment: 11 pages, 12 figure