7,505 research outputs found
Exact Fermi coordinates for a class of spacetimes
We find exact Fermi coordinates for timelike geodesic observers for a class
of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the
constant density interior Schwarzschild spacetime with positive, zero, and
negative cosmological constant, and the Einstein static universe. Maximal
charts for Fermi coordinates are discussed.Comment: 15 page
On The Use Of Writing Assignments In Intermediate Microeconomic Theory
A typical writing assignment in upper level required courses is a term paper. However many economics majors, particularly those in business schools, need to develop skill at writing shorter pieces. In this paper I describe numerous examples of shorter writing assignments that I have incorporated into an Intermediate Microeconomic Theory course. The assignments include such activities as comparison of competing theories; non-traditional applications of theory; book reviews; and explorations of the nuances of the standard consumer choice model. In addition to describing the details of the various assignments, the paper presents both student and instructor assessment of them
Mean curvature flow and quasilocal mass for two-surfaces in Hamiltonian General Relativity
A family of quasilocal mass definitions that includes as special cases the
Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike
2-surfaces in spacetime. The definitions involve an integral of powers of the
norm of the spacetime mean curvature vector of the 2-surface, whose properties
are connected with apparent horizons. In particular, for any spacelike
2-surface, the direction of mean curvature is orthogonal (dual in the normal
space) to a unique normal direction in which the 2-surface has vanishing
expansion in spacetime. The quasilocal mass definitions are obtained by an
analysis of boundary terms arising in the gravitational ADM Hamiltonian on
hypersurfaces with a spacelike 2-surface boundary, using a geometric time-flow
chosen proportional to the dualized mean curvature vector field at the boundary
surface. A similar analysis is made choosing a geometric rotational flow given
in terms of the twist covector of the dual pair of mean curvature vector
fields, which leads to a family of quasilocal angular momentum definitions
involving the squared norm of the twist. The large sphere limit of these
definitions is shown to yield the ADM mass and angular momentum in
asymptotically flat spacetimes, while at apparent horizons a quasilocal version
of the Gibbons-Penrose inequality is derived. Finally, some results concerning
positivity are proved for the quasilocal masses, motivated by consideration of
spacelike mean curvature flow of 2-surfaces in spacetime.Comment: Revised version, includes an analysis of null flows with applications
to mass and angular momentum for apparent horizon
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Pricing in Day-Ahead Electricity Markets with Near-Optimal Unit Commitment
This paper revisits some peculiar pricing properties of near-optimal unit commitment solutions. Previous work has found that prices can behave erratically even as unit commitment solutions approach the optimal solution, resulting in potentially large wealth transfers due to suboptimality of the solution. Our analysis considers how recently proposed pricing models affect this behavior. Results demonstrate a previously unknown property of one of these pricing models, called approximate Convex Hull Pricing (aCHP), that eliminates erratic price behavior, and therefore limits wealth transfers with respect to the optimal unit commitment solution. The absence of wealth transfers may imply fewer strategic bidding incentives, which could enhance market efficiency
Limit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A
general limit curve theorem is formulated which includes the case of converging
curves with endpoints and the case in which the limit points assigned since the
beginning are one, two or at most denumerable. Some applications are
considered. It is proved that in chronological spacetimes, strong causality is
either everywhere verified or everywhere violated on maximizing lightlike
segments with open domain. As a consequence, if in a chronological spacetime
two distinct lightlike lines intersect each other then strong causality holds
at their points. Finally, it is proved that two distinct components of the
chronology violating set have disjoint closures or there is a lightlike line
passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio
Magnification relations for Kerr lensing and testing Cosmic Censorship
A Kerr black hole with mass parameter m and angular momentum parameter a
acting as a gravitational lens gives rise to two images in the weak field
limit. We study the corresponding magnification relations, namely the signed
and absolute magnification sums and the centroid up to post-Newtonian order. We
show that there are post-Newtonian corrections to the total absolute
magnification and centroid proportional to a/m, which is in contrast to the
spherically symmetric case where such corrections vanish. Hence we also propose
a new set of lensing observables for the two images involving these
corrections, which should allow measuring a/m with gravitational lensing. In
fact, the resolution capabilities needed to observe this for the Galactic black
hole should in principle be accessible to current and near-future
instrumentation. Since a/m >1 indicates a naked singularity, a most interesting
application would be a test of the Cosmic Censorship conjecture. The technique
used to derive the image properties is based on the degeneracy of the Kerr lens
and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple
physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in
Phys. Rev.
Measures of gravitational entropy I. Self-similar spacetimes
We examine the possibility that the gravitational contribution to the entropy
of a system can be identified with some measure of the Weyl curvature. In this
paper we consider homothetically self-similar spacetimes. These are believed to
play an important role in describing the asymptotic properties of more general
models. By exploiting their symmetry properties we are able to impose
significant restrictions on measures of the Weyl curvature which could reflect
the gravitational entropy of a system. In particular, we are able to show, by
way of a more general relation, that the most widely used "dimensionless"
scalar is \textit{not} a candidate for this measure along homothetic
trajectories.Comment: revtex, minor clarifications, to appear in Physical Review
Causes of Prolonged Waiting Time in Public Health Facilities among Health Care Seekers in Calabar Municipal Council of Cross River State, Nigeria
The purpose of this study was to investigate the causes of prolonged waiting time in public health care facilities among health care seekers in Calabar Municipal Council of Cross River State, Nigeria. To carry out this investigation, two hypotheses were formulated to guide the study. Survey research design was adopted for this study. A sample of one hundred and eighteen (118) respondents was selected. The selection was done through cluster sampling technique. The questionnaire was the main instrument used for data collection. It was constructed by the researchers with assistance of some measurement experts that gave it face and content validity. The Chi-square (X2) inferential statistics set at 0.05 was used to test the hypothesis. The result shows that there is significant contribution of poor record keeping and inadequate health personnel to the prolonged waiting time in public health care facilities among health care seekers. Based on these findings, some recommendations and suggestions for further studies were made. Keywords: Prolong waiting time; Public health facilities, Health care seekers. Poor record keeping; inadequate health personnel
The sectional curvature remains positive when taking quotients by certain nonfree actions
We study some cases when the sectional curvature remains positive under the
taking of quotients by certain nonfree isometric actions of Lie groups. We
consider the actions of the groups and such that the quotient space
can be endowed with a smooth structure using the fibrations
and . We prove that the quotient space
carries a metric of positive sectional curvature, provided that the original
metric has positive sectional curvature on all 2-planes orthogonal to the
orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam
Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms
We give a spinorial characterization of isometrically immersed surfaces of
arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For
Lorentzian surfaces, this generalizes a recent work of the first author in
to other Lorentzian space forms. We also characterize
immersions of Riemannian surfaces in these spaces. From this we can deduce
analogous results for timelike immersions of Lorentzian surfaces in space forms
of corresponding signature, as well as for spacelike and timelike immersions of
surfaces of signature (0,2), hence achieving a complete spinorial description
for this class of pseudo-Riemannian immersions.Comment: 9 page
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