Thermal gravity, black holes and cosmological entropy

Taking seriously the interpretation of black hole entropy as the logarithm of the number of microstates, we argue that thermal gravitons may undergo a phase transition to a kind of black hole condensate. The phase transition proceeds via nucleation of black holes at a rate governed by a saddlepoint configuration whose free energy is of order the inverse temperature in Planck units. Whether the universe remains in a low entropy state as opposed to the high entropy black hole condensate depends sensitively on its thermal history. Our results may clarify an old observation of Penrose regarding the very low entropy state of the universe.Comment: 5 pages, 2 figures, RevTex. v4: to appear in Phys. Rev.

Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits

Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-motion binary orbits. We use black hole perturbation theory, so our results assume extreme mass ratios. We develop tools to compute the distortion to a black hole's curvature for any spin parameter, and for tidal fields arising from any bound orbit, in the frequency domain. We also develop tools to visualize the horizon's distortion for black hole spin $a/M \le \sqrt{3}/2$ (leaving the more complicated $a/M > \sqrt{3}/2$ case to a future analysis). We then study how a Kerr black hole's event horizon is distorted by a small body in a circular, equatorial orbit. We find that the connection between the geometry of tidal distortion and the orbit's evolution is not as simple as in the Newtonian limit.Comment: 37 pages, 8 figures. Accepted for publication to Physical Review D. This version corrects a number of typographical errors found when reviewing the page proof

Black hole entropy, curved space and monsters

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than their area in Planck units. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter $S < A^{3/4}$. This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states.Comment: 5 pages, revtex. Final version to appear Physics Letters

Minimum Length from Quantum Mechanics and Classical General Relativity

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a {\it device independent} limit on possible position measurements.Comment: 8 pages, latex, to appear in the Physical Review Letter

Monsters, black holes and the statistical mechanics of gravity

We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality. In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics -- essentially, the geometry of Hilbert space -- and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.Comment: 9 pages, 4 figures, revtex; invited Brief Review to be published in Modern Physics Letters

Long-term effects of allergen sensitization and exposure in adult asthma: a prospective study.

BACKGROUND: : We investigated the effects of sensitization and exposure to common domestic allergens on longitudinal changes in lung function and bronchial hyperresponsiveness. METHODS: : Subjects attended 2 visits that were 4 years apart. Skin prick testing was performed and household dust samples were collected for quantification of mite, dog, and cat allergens at baseline. Measurements of lung function, exhaled nitric oxide, and bronchial hyperresponsiveness were completed at both visits. RESULTS: : Dust samples were collected in 165 of the 200 subjects completing both visits. Mean length of follow-up was 47 months. Bronchial hyperresponsiveness, measured at both visits in 86 subjects, deteriorated in those exposed to high mite allergen levels compared with those not exposed [mean (95% CI) doubling dose change PD20 = -0.44 (-1.07 to 0.19) vs 0.82 (0.27 to 1.36)], but improved in those exposed to high dog allergen levels compared with those not exposed [1.10 (0.33 to 1.86) vs 0.10 (-0.39 to 0.58)]. The associations were significant in the multivariate models. Cat allergen exposure was not associated with any changes in lung function, exhaled nitric oxide, or bronchial hyperresponsiveness. CONCLUSIONS: : In a 4-year prospective cohort of persons with asthma, exposure to high levels of dust mite allergens at baseline was associated with a subsequent increase in bronchial hyperresponsiveness