Quantum Structure of Space Near a Black Hole Horizon

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one at each spatial point. The corresponding operator at each point is the product of the outgoing and ingoing null convergences, and describes the scale invariant quantum mechanics of a particle moving in an attractive $1/X^2$ potential. The variable $X$ that is analoguous to particle position is the square root of the conformal mode of the metric. We quantize the theory via Bohr quantization, which by construction turns the Hamiltonian constraint eigenvalue equation into a finite difference equation. The resulting spectrum gives rise to a discrete spatial topology exterior to the horizon. The spectrum approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur

Quantum black holes from null expansion operators

Using a recently developed quantization of spherically symmetric gravity coupled to a scalar field, we give a construction of null expansion operators that allow a definition of general, fully dynamical quantum black holes. These operators capture the intuitive idea that classical black holes are defined by the presence of trapped surfaces, that is surfaces from which light cannot escape outward. They thus provide a mechanism for classifying quantum states of the system into those that describe quantum black holes and those that do not. We find that quantum horizons fluctuate, confirming long-held heuristic expectations. We also give explicit examples of quantum black hole states. The work sets a framework for addressing the puzzles of black hole physics in a fully quantized dynamical setting.Comment: 5 pages, version to appear in CQ

The information recovery problem

The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We~argue that some prominent cures are more troubling than the disease, demonstrate that their central element---forming of the event horizon before the evaporation begins---is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.Comment: 7 pages +1 fig Published versio

Probing entropy bounds with scalar field spacetimes

We study covariant entropy bounds in dynamical spacetimes with naked singularities. Specifically we study a spherically symmetric massless scalar field solution. The solution is an inhomogeneous cosmology with an initial spacelike singularity, and a naked timelike singularity at the origin. We construct the entropy flux 4-vector for the scalar field, and show by explicit computation that the generalized covariant bound $S_{L(B,B')}\le (A(B)-A(B'))/4$ is violated for light sheets $L(B,B')$ in the neighbourhood of the (evolving) apparent horizon. We find no violations of the Bousso bound (for which $A(B')=0$), even though certain sufficient conditions for this bound do not hold. This result therefore shows that these conditions are not necessary.Comment: 10 pages, 5 figures; published version with typos correcte

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

How red is a quantum black hole?

Radiating black holes pose a number of puzzles for semiclassical and quantum gravity. These include the transplanckian problem -- the nearly infinite energies of Hawking particles created near the horizon, and the final state of evaporation. A definitive resolution of these questions likely requires robust inputs from quantum gravity. We argue that one such input is a quantum bound on curvature. We show how this leads to an upper limit on the redshift of a Hawking emitted particle, to a maximum temperature for a black hole, and to the prediction of a Planck scale remnant.Comment: 3 pages, essay for the Gravity Research Foundatio

A wearable headset for monitoring electromyography responses within spinal surgery

Purpose: This research examines an approach for enhancing the efficiency of spinal surgery utilising the technological capabilities and design functionalities of wearable headsets, in this case Google Glass. The aim was to improve the efficiency of the selective dorsal rhizotomy neurosurgical procedure initially through the use of Glass via an innovative approach to information design for an intraoperative monitoring display. Methods Utilising primary and secondary research methods the development of a new electromyography response display for a wearable headset was undertaken. Results: Testing proved that Glass was fit for purpose and that the new intraoperative monitor design provided an example platform for the innovative intraoperative monitoring display; however, alternative wearable headsets such as the Microsoft HoloLens could also be equally viable. Conclusion: The new display design combined with the appropriate wearable technology could greatly benefit the selective dorsal rhizotomy procedure

Overview and Features of Generic Security Protocols for Cloud Computing Environment

- In this research paper we are describing the several generic protocols use in Cloud computing environment. Now-a-days Cloud Computing has become very important in large and small enterprise so security has also become very important for Cloud Computing. Several technique use to protect the cloud. Techniques are implemented by protocols. This paper is based on overview of protocols that use in Cloud computing environment. The protocols of cloud computing can also use in different security system such as Cryptonet System, Mailing System and Authentication System

Quantum Hamiltonian for gravitational collapse

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.Comment: 17 pages, published version (minor changes