The hidden horizon and black hole unitarity

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic "exclusive backgrounds" to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such "inclusive background" presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes 3 and 5

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

Meta-analysis on studies with heterogeneous and partially observed covariates.

Individual participant data meta-analysis is a commonly used alternative to the traditional aggregate data meta-analysis. It is popular because it avoids relying on published results and enables direct adjustment for relevant covariates. However, a practical challenge is that the studies being combined often vary in terms of the potential confounders that were measured. Furthermore, it will inevitably be the case that some individuals have missing values for some of those covariates. In this paper, we demonstrate how these challenges can be resolved using a propensity score approach, combined with multiple imputation, as a strategy to adjust for covariates in the context of individual participant data meta-analysis. To illustrate, we analyze data from the Bill and Melinda Gates Foundation-funded Healthy Birth, Growth, and Development Knowledge Integration project to investigate the relationship between physical growth rate in the first year of life and cognition measured later during childhood. We found that the overall effect of average growth velocity on cognitive outcome is slightly, but significantly, positive with an estimated effect size of 0.36 (95% CI 0.18, 0.55)

Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes

Generalized Painleve-Gullstrand metrics are explicitly constructed for the Kerr-Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass M, charge Q, angular momentum aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities are eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman black holes are analysed and discussed; and it is revealed that some of these descriptions are actually not related by physical Lorentz transformations to the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is the reason complex components appear (for certain ranges of the radial coordinate) in these metrics. As an application of our constructions the correct effective Hawking temperature for Kerr black holes is derived with the method of Parikh and Wilczek.Comment: 5 pages; extended to include application to derivation of Hawking radiation for Kerr black holes with Parikh-Wilczek metho

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa

Isolated and dynamical horizons and their applications

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.Comment: 77 pages, 12 figures. Typos and references correcte

The Weak Gravity Conjecture and the Viscosity Bound with Six-Derivative Corrections

The weak gravity conjecture and the shear viscosity to entropy density bound place constraints on low energy effective field theories that may help to distinguish which theories can be UV completed. Recently, there have been suggestions of a possible correlation between the two constraints. In some interesting cases, the behavior was precisely such that the conjectures were mutually exclusive. Motivated by these works, we study the mass to charge and shear viscosity to entropy density ratios for charged AdS5 black branes, which are holographically dual to four-dimensional CFTs at finite temperature. We study a family of four-derivative and six-derivative perturbative corrections to these backgrounds. We identify the region in parameter space where the two constraints are satisfied and in particular find that the inclusion of the next-to-leading perturbative correction introduces wider possibilities for the satisfaction of both constraints.Comment: 24 pages, 6 figures, v2: published version, refs added, minor clarificatio

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum Calculations 5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living Reviews of Relativit

Semi-parametric benchmark dose analysis with monotone additive models.

Benchmark dose analysis aims to estimate the level of exposure to a toxin associated with a clinically significant adverse outcome and quantifies uncertainty using the lower limit of a confidence interval for this level. We develop a novel framework for benchmark dose analysis based on monotone additive dose-response models. We first introduce a flexible approach for fitting monotone additive models via penalized B-splines and Laplace-approximate marginal likelihood. A reflective Newton method is then developed that employs de Boor's algorithm for computing splines and their derivatives for efficient estimation of the benchmark dose. Finally, we develop a novel approach for calculating benchmark dose lower limits based on an approximate pivot for the nonlinear equation solved by the estimated benchmark dose. The favorable properties of this approach compared to the Delta method and a parameteric bootstrap are discussed. We apply the new methods to make inferences about the level of prenatal alcohol exposure associated with clinically significant cognitive defects in children using data from six NIH-funded longitudinal cohort studies. Software to reproduce the results in this paper is available online and makes use of the novel semibmd  R package, which implements the methods in this paper

Lovelock gravity from entropic force

In this paper, we first generalize the formulation of entropic gravity to (n+1)-dimensional spacetime. Then, we propose an entropic origin for Gauss-Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton's law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory. PACS: 04.20.Cv, 04.50.-h, 04.70.Dy.Comment: 10 pages, new versio