156 research outputs found
The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum
We show that the pathology which afflicts the Hartle-Hawking vacuum on the
Kerr black hole space-time can be regarded as due to rigid rotation of the
state with the horizon in the sense that when the region outside the
speed-of-light surface is removed by introducing a mirror, there is a state
with the defining features of the Hartle-Hawking vacuum. In addition, we show
that when the field is in this state, the expectation value of the
energy-momentum stress tensor measured by an observer close to the horizon and
rigidly rotating with it corresponds to that of a thermal distribution at the
Hawking temperature rigidly rotating with the horizon.Comment: 17 pages, 7 figure
A Radiation Scalar for Numerical Relativity
This letter describes a scalar curvature invariant for general relativity
with a certain, distinctive feature. While many such invariants exist, this one
vanishes in regions of space-time which can be said unambiguously to contain no
gravitational radiation. In more general regions which incontrovertibly support
non-trivial radiation fields, it can be used to extract local,
coordinate-independent information partially characterizing that radiation.
While a clear, physical interpretation is possible only in such radiation
zones, a simple algorithm can be given to extend the definition smoothly to
generic regions of space-time.Comment: 4 pages, 1 EPS figur
Redshifts and Killing Vectors
Courses in introductory special and general relativity have increasingly
become part of the curriculum for upper-level undergraduate physics majors and
master's degree candidates. One of the topics rarely discussed is symmetry,
particularly in the theory of general relativity. The principal tool for its
study is the Killing vector. We provide an elementary introduction to the
concept of a Killing vector field, its properties, and as an example of its
utility apply these ideas to the rigorous determination of gravitational and
cosmological redshifts.Comment: 16 Latex pages, 6 postscript figures, submitted to Am. J. Phy
Metric of a tidally perturbed spinning black hole
We explicitly construct the metric of a Kerr black hole that is tidally
perturbed by the external universe in the slow-motion approximation. This
approximation assumes that the external universe changes slowly relative to the
rotation rate of the hole, thus allowing the parameterization of the
Newman-Penrose scalar by time-dependent electric and magnetic tidal
tensors. This approximation, however, does not constrain how big the spin of
the background hole can be and, in principle, the perturbed metric can model
rapidly spinning holes. We first generate a potential by acting with a
differential operator on . From this potential we arrive at the metric
perturbation by use of the Chrzanowski procedure in the ingoing radiation
gauge. We provide explicit analytic formulae for this metric perturbation in
spherical Kerr-Schild coordinates, where the perturbation is finite at the
horizon. This perturbation is parametrized by the mass and Kerr spin parameter
of the background hole together with the electric and magnetic tidal tensors
that describe the time evolution of the perturbation produced by the external
universe. In order to take the metric accurate far away from the hole, these
tidal tensors should be determined by asymptotically matching this metric to
another one valid far from the hole. The tidally perturbed metric constructed
here could be useful in initial data constructions to describe the metric near
the horizons of a binary system of spinning holes. This perturbed metric could
also be used to construct waveforms and study the absorption of mass and
angular momentum by a Kerr black hole when external processes generate
gravitational radiation.Comment: 17 pages, 3 figures. Final PRD version, minor typos, etc corrected.
v3: corrected typo in Eq. (35) and (57
Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars
We study the general relativistic orbital equation and using a
straightforward perturbation method and a mathematical device first introduced
by d'Alembert, we work out approximate expressions of a bound planetary orbit
in the form of trigonometrical polynomials and the first three terms of the
power series development of the perihelion advance. The results are applied to
a more precise determination of the total mass of the double pulsar J0737-3039.Comment: 8 pages. Accepted for publication in "Astrophysics & Space Science
Ion trap simulations of quantum fields in an expanding universe
We propose an experiment in which the phonon excitation of ion(s) in a trap, with a trap frequency exponentially modulated at rate kappa, exhibits a thermal spectrum with an Unruh temperature given by k(B)T=h kappa. We discuss the similarities of this experiment to the response of detectors in a de Sitter universe and the usual Unruh effect for uniformly accelerated detectors. We demonstrate a new Unruh effect for detectors that respond to antinormally ordered moments using the ion's first blue sideband transition
Constraint rule-based programming of norms for electronic institutions
Peer reviewedPostprin
The Sun's position in the sky
We express the position of the Sun in the sky as a function of time and the
observer's geographic coordinates. Our method is based on applying rotation
matrices to vectors describing points on the celestial sphere. We also derive
direct expressions, as functions of date of the year and geographic latitude,
for the duration of daylight, the maximum and minimum altitudes of the Sun, and
the cardinal directions to sunrise and sunset. We discuss how to account for
the eccentricity of the earth's orbit, the precessions of the equinoxes and the
perihelion, the size of the solar disk, and atmospheric refraction. We
illustrate these results by computing the dates of "Manhattanhenge" (when
sunset aligns with the east-west streets on the main traffic grid for
Manhattan, in New York City), by plotting the altitude of the Sun over
representative cities as a function of time, and by showing plots ("analemmas")
for the position of the Sun in the sky at a given hour of the day.Comment: 19 pages, 16 figures. v3: Replaced to match published version and to
re-package Mathematica notebook as an ancillary fil
Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation
The periodic and step-like solutions of the double-Sine-Gordon equation are
investigated, with different initial conditions and for various values of the
potential parameter . We plot energy and force diagrams, as functions
of the inter-soliton distance for such solutions. This allows us to consider
our system as an interacting many-body system in 1+1 dimension. We therefore
plot state diagrams (pressure vs. average density) for step-like as well as
periodic solutions. Step-like solutions are shown to behave similarly to their
counterparts in the Sine-Gordon system. However, periodic solutions show a
fundamentally different behavior as the parameter is increased. We
show that two distinct phases of periodic solutions exist which exhibit
manifestly different behavior. Response functions for these phases are shown to
behave differently, joining at an apparent phase transition point.Comment: 17pages, 15 figure
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