2,769 research outputs found
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
potential. The variable 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
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
Spherically symmetric scalar field collapse in any dimension
We describe a formalism and numerical approach for studying spherically
symmetric scalar field collapse for arbitrary spacetime dimension d and
cosmological constant Lambda. The presciption uses a double null formalism, and
is based on field redefinitions first used to simplify the field equations in
generic two-dimensional dilaton gravity. The formalism is used to construct
code in which d and Lambda are input parameters. The code reproduces known
results in d = 4 and d = 6 with Lambda = 0. We present new results for d = 5
with zero and negative Lambda.Comment: 16 pages, 6 figures, typos corrected, presentational changes, PRD in
pres
Constants of motion for vacuum general relativity
The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting
spacelike Killing vector fields, may be written as the equations of the
principal chiral model with certain `source' terms. Using this
formulation, we give a procedure for generating an infinite number of non-local
constants of motion for this sector of the Einstein equations. The constants of
motion arise as explicit functionals on the phase space of Einstein gravity,
and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D
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.
Flat slice Hamiltonian formalism for dynamical black holes
We give a Hamiltonian analysis of the asymptotically flat spherically
symmetric system of gravity coupled to a scalar field. This 1+1 dimensional
field theory may be viewed as the "standard model" for studying black hole
physics. Our analysis is adapted to the flat slice Painleve-Gullstrand
coordinates. We give a Hamiltonian action principle for this system, which
yields an asymptotic mass formula. We then perform a time gauge fixing that
gives a Hamiltonian as the integral of a local density. The Hamiltonian takes a
relatively simple form compared to earlier work in Schwarzschild gauge, and
therefore provides a setting amenable to full quantisation.Comment: 11 pages, refererences added, discussions clarified, version to
appear in PR
Quasi-static Normal Indentation of a Circular Disk Shaped Miniature Specimen by Rigid Hemispherical-headed Punches
The influence of diameter of rigid hemispherical-headed punches on a circular disk shaped miniature specimen of medium carbon steel has been investigated, in the small punch test. A 3-D finite-element model carried out the computation of the elastic-plastic solution ofdifferent hemispherical rigid punches. The three hemispherical-headed punches were designed and developed to conduct the miniature test. The small. punch test"was conducted on a circular shaped disk (l0.0 mm diameter, 0.5 mm thick), clamped around the periphery and deformed by central load applied by rigid hemispherical indenter. The ABAQUS finite-element software has been used to determine the load vs punch-displacement curves, von-Mises stresses, equivalent plastic strain, contact pressure, logarithmic stresses, load-till failure and full-field displacement in the model have been computed. The finite-element model was validated by comparing with the experimental data for load vs displacement curves. The effect of punch diameter on load vs displacement was observed experimentally as well as by finite-element method. The computational results compared reasonably well with the experimental results
Modified general relativity as a model for quantum gravitational collapse
We study a class of Hamiltonian deformations of the massless
Einstein-Klein-Gordon system in spherical symmetry for which the Dirac
constraint algebra closes. The system may be regarded as providing effective
equations for quantum gravitational collapse. Guided by the observation that
scalar field fluxes do not follow metric null directions due to the
deformation, we find that the equations take a simple form in characteristic
coordinates. We analyse these equations by a unique combination of numerical
methods and find that Choptuik's mass scaling law is modified by a mass gap as
well as jagged oscillations. Furthermore, the results are universal with
respect to different initial data profiles and robust under changes of the
deformation.Comment: 22 pages, 4 figure
Aerosol major ion record at Mount Washington
This study examined the seasonal cycles and regional-scale meteorological controls on the chemical properties of bulk aerosols collected from 1999 to 2004 at Mount Washington, the highest peak in the northeastern United States. The concentrations of NH4+ and SO42â peaked during summer months. The pattern for aerosol NO3â was more complicated with relatively high median concentrations characterizing spring and summer months, but with major elevated events occurring during fall, winter, and spring. The seasonal relationship between NH4+ and SO42â indicated that during warmer months a mixture of (NH4)2SO4 and NH4HSO4 was present, while it was mainly the latter in winter. More acidity and higher concentrations of the major species were generally associated with winds from the southwest and west sectors. The highest (â„95th percentile) concentrations of SO42â and NH4+ were associated with air mass transport from major upwind source regions in the Midwest and along the eastern seaboard. The ionic composition and seasonal cycle observed at Mount Washington were similar to those measured at other northeastern sites, but the range and average concentrations were much lower. These differences were exaggerated during wintertime. Included in this paper are several Eulerian case studies of SO2 conversion to SO42â during transit from Whiteface Mountain, New York, to Mount Washington. The calculations suggest a gas-phase SO2 oxidation rate of âŒ1â2% per hour and demonstrate the possibility of using these two sites to investigate the chemical evolution of air masses as they move from Midwestern source regions to northern New England
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