Black Holes or Firewalls: A Theory of Horizons

We present a quantum theory of black hole (and other) horizons, in which the standard assumptions of complementarity are preserved without contradicting information theoretic considerations. After the scrambling time, the quantum mechanical structure of a black hole becomes that of an eternal black hole at the microscopic level. In particular, the stretched horizon degrees of freedom and the states entangled with them can be mapped into the near-horizon modes in the two exterior regions of an eternal black hole, whose mass is taken to be that of the evolving black hole at each moment. Salient features arising from this picture include: (i) the number of degrees of freedom needed to describe a black hole is e^{A/2 l_P^2}, where A is the area of the horizon; (ii) black hole states having smooth horizons span only an e^{A/4 l_P^2}-dimensional subspace of the relevant e^{A/2 l_P^2}-dimensional Hilbert space; (iii) internal dynamics of the horizon is such that an infalling observer finds a smooth horizon with probability 1 if a state stays in this subspace. We identify the structure of local operators in the exterior and interior spacetime regions, and show that this structure avoids firewall arguments---the horizon can keep being smooth throughout the evolution. We discuss the fate of falling observers under various circumstances, especially when they manipulate degrees of freedom before entering the horizon, and find that an observer can never see a firewall by making a measurement on early Hawking radiation. We also consider the framework in an infalling reference frame, and argue that Minkowski-like vacua are not unique. In particular, the number of true Minkowski vacua is infinite, although the label discriminating these vacua cannot be accessed in usual non-gravitational quantum field theory. An application to de Sitter horizons is also discussed.Comment: 24 pages, 1 figure; minor revision

Low Energy Description of Quantum Gravity and Complementarity

We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black hole complementarity. Our framework employs a "special relativistic" description of gravity; specifically, gravity is treated as a force measured by the observer tied to the coordinate system associated with a freely falling local Lorentz frame. We identify, in simple cases, regions of spacetime in which low energy local descriptions are applicable as viewed from the freely falling frame; in particular, we identify a surface called the gravitational observer horizon on which the local proper acceleration measured in the observer's coordinates becomes the cutoff (string) scale. This allows for separating between the "low-energy" local physics and "trans-Planckian" intrinsically quantum gravitational (stringy) physics, and allows for developing physical pictures of the origins of various effects. We explore the structure of the Hilbert space in which the proposed scheme is realized in a simple manner, and classify its elements according to certain horizons they possess. We also discuss implications of our framework on the firewall problem. We conjecture that the complementarity picture may persist due to properties of trans-Planckian physics.Comment: 18 pages, 1 figure; matches published versio

Spin liquid phase in a spatially anisotropic frustrated antiferromagnet

We explore the effect of the third nearest-neighbors on the magnetic properties of the Heisenberg model on an anisotropic triangular lattice. We obtain the phase diagram of the model using Schwinger-boson mean-field theory. Competition between N\'eel, spiral and collinear magnetically ordered phases is found as we vary the on the ratios of the nearest, J1, next-nearest, J2, and third-nearest, J_3, neighbor exchange couplings. A spin liquid phase is stabilized between the spiral and collinear ordered states when J2/J1 < 1.8 for rather small J3/J1 < 0.1. The lowest energy two-spinon dispersions relevant to neutron scattering experiments are analyzed and compared to semiclassical magnon dispersions finding significant differences in the spiral and collinear phases between the two approaches. The results are discussed in the context of the anisotropic triangular materials: Cs2CuCl4 and Cs2CuBr4 and layered organic materials, kappa-(BEDT-TTF)2X and Y[Pd(dmit)2]2.Comment: 11 pages, 9 figure

Spin liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice

Linear spin wave theory shows that ring exchange induces a quantum disordered region in the phase diagram of the title model. Spin wave spectra show that this is a direct manifestation of competing classical orders. A spin liquid is found in the `Goldilocks zone' of frustration, where the quantum fluctuations are large enough to cause strong competition between different classical orderings but not strong enough to stabilize spiral order. We note that the spin liquid phases of $\kappa$-(BEDT-TTF)${_2}X$ and $Y$[Pd(dmit)$_2$]$_2$ are found in this Goldilocks zone.Comment: 5 pages, 3 figure

Supersonic through-flow fan engine and aircraft mission performance

A study was made to evaluate potential improvement to a commercial supersonic transport by powering it with supersonic through-flow fan turbofan engines. A Mach 3.2 mission was considered. The three supersonic fan engines considered were designed to operate at bypass ratios of 0.25, 0.5, and 0.75 at supersonic cruise. For comparison a turbine bypass turbojet was included in the study. The engines were evaluated on the basis of aircraft takeoff gross weight with a payload of 250 passengers for a fixed range of 5000 N.MI. The installed specific fuel consumption of the supersonic fan engines was 7 to 8 percent lower than that of the turbine bypass engine. The aircraft powered by the supersonic fan engines had takeoff gross weights 9 to 13 percent lower than aircraft powered by turbine bypass engines

Interplay of frustration, magnetism, charge ordering, and covalency in a model of Na0.5CoO2

We investigate an effective Hamiltonian for Na0.5CoO2 that includes the electrostatic potential due to the ordered Na ions and strong electronic correlations. This model displays a subtle interplay between metallic and insulating phases and between charge and magnetic order. For realistic parameters, the model predicts an insulating phase with similarities to a covalent insulator. We show that this interpretation gives a consistent explanation of experiments on Na0.5CoO2, including the small degree of charge ordering, the small charge gap, the large moment, and the optical conductivity.Comment: 5 pages, 4 figures. Text revised making more emphasis on model properties. Figures compacte

Acoustical Behavior Of Churches: Mudejar-Gothic Churches

Christian churches have traditionally been considered to have very good acoustical behavior. This unfounded belief has led to important en-on in church rehabilitation works, especially when the church is to be used subsequently as an auditorium or theater; this is the case of many churches in Spain. Our research group has worked in acoustical analysis for more than ten years. We have participated in many cases of church rehabilitation and have had the opp&unity to achieve surprisingly good acwstical behavior in several. We deal with a very common type in southern Spain: Gothic-Mudejar churches, which have a small volume, a triple-nave layout, and wooden ceilings

The design and performance estimates for the propulsion module for the booster of a TSTO vehicle

A NASA study of the propulsion systems for possible low-risk replacements for the Space Shuttle is presented. Results of preliminary studies to define the USAF two-stage-to-orbit (TSTO) concept to deliver 10,000 pounds to low polar orbit are described. The booster engine module consists of an over/under turbine bypass engines/ramjet engine design for acceleration from takeoff to the staging point of Mach 6.5 and approximately 100,000 feet altitude. Propulsion system performance and weight are presented with preliminary mission study results of vehicle size