Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes

We will discuss selected physical effects of spacetime geometry fluctuations, especially the operational signatures of geometry fluctuations and their effects on black hole horizons. The operational signatures which we discuss involve the effects of the fluctuations on images, and include luminosity variations, spectral line broadening and angular blurring. Our main interest will be in black hole horizon fluctuations, especially horizon fluctuations which have been enhanced above the vacuum level by gravitons or matter in squeezed states. We investigate whether these fluctuations can alter the thermal character of a black hole. We find that this thermal character is remarkably robust, and that Hawking's original derivation using transplanckian modes does not seem to be sensitive even to enhanced horizon fluctuations.Comment: 13 pages, 3 figures, based on a talk presented at the Peyresq 12 worksho

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

Quantum Inequalities and Singular Energy Densities

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps

Scalar Field Quantum Inequalities in Static Spacetimes

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum inequality for a static observer in terms of a Euclidean two-point function. In a short sampling time limit, the quantum inequality can be written as the flat space form plus subdominant correction terms dependent upon the geometric properties of the spacetime. This supports the use of flat space quantum inequalities to constrain negative energy effects in curved spacetime. Using the exact Euclidean two-point function method, we develop the quantum inequalities for perfectly reflecting planar mirrors in flat spacetime. We then look at the quantum inequalities in static de~Sitter spacetime, Rindler spacetime and two- and four-dimensional black holes. In the case of a four-dimensional Schwarzschild black hole, explicit forms of the inequality are found for static observers near the horizon and at large distances. It is show that there is a quantum averaged weak energy condition (QAWEC), which states that the energy density averaged over the entire worldline of a static observer is bounded below by the vacuum energy of the spacetime. In particular, for an observer at a fixed radial distance away from a black hole, the QAWEC says that the averaged energy density can never be less than the Boulware vacuum energy density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset in RevTe

A Third Planet Orbiting HIP 14810

We present new precision radial velocities and a three-planet Keplerian orbit fit for the V = 8.5, G5 V star HIP 14810. We began observing this star at Keck Observatory as part of the N2K Planet Search Project. Wright et al. (2007) announced the inner two planets to this system, and subsequent observations have revealed the outer planet planet and the proper orbital solution for the middle planet. The planets have minimum masses of 3.9, 1.3, and 0.6 M_Jup and orbital periods of 6.67, 147.7, and 952 d, respectively. We have numerically integrated the family of orbital solutions consistent with the data and find that they are stable for at least 10^6 yr. Our photometric search shows that the inner planet does not transit.Comment: ApJL, accepte

Sexual healthcare professionals’ views on HPV vaccination for men in the UK

Background: Human Papillomavirus (HPV) vaccination for men could prevent anal cancers amongst men who have sex with men (MSM). Methods: An e-survey of attitudes towards vaccination for men in the UK was conducted in July–August 2014. Results: Among 325 sexual health professionals, 14% were already vaccinating men against HPV, 83% recommended genderneutral HPV vaccination and 65% recommended targeting MSM. Over 50% reported having poor knowledge about the use of HPV vaccine for MSM and the skills to identify MSM likely to benefit from HPV vaccination. Conclusions: Clear advice and guidelines on HPV vaccine use for men at sexual health clinics are required to ensure equitable opportunities for vaccination

The history of mass assembly of faint red galaxies in 28 galaxy clusters since z=1.3

We measure the relative evolution of the number of bright and faint (as faint as 0.05 L*) red galaxies in a sample of 28 clusters, of which 16 are at 0.50<= z<=1.27, all observed through a pair of filters bracketing the 4000 Angstrom break rest-frame. The abundance of red galaxies, relative to bright ones, is constant over all the studied redshift range, 0<z<1.3, and rules out a differential evolution between bright and faint red galaxies as large as claimed in some past works. Faint red galaxies are largely assembled and in place at z=1.3 and their deficit does not depend on cluster mass, parametrized by velocity dispersion or X-ray luminosity. Our analysis, with respect to previous one, samples a wider redshift range, minimizes systematics and put a more attention to statistical issues, keeping at the same time a large number of clusters.Comment: MNRAS, 386, 1045. Half a single sentence (in sec 4.4) change