1,561 research outputs found
Energy extremality in the presence of a black hole
We derive the so-called first law of black hole mechanics for variations
about stationary black hole solutions to the Einstein--Maxwell equations in the
absence of sources. That is, we prove that where the black hole parameters and denote mass, surface gravity, horizon area, angular velocity of the
horizon, angular momentum, electric potential of the horizon and charge
respectively. The unvaried fields are those of a stationary, charged, rotating
black hole and the variation is to an arbitrary `nearby' black hole which is
not necessarily stationary. Our approach is 4-dimensional in spirit and uses
techniques involving Action variations and Noether operators. We show that the
above formula holds on any asymptotically flat spatial 3-slice which extends
from an arbitrary cross-section of the (future) horizon to spatial
infinity.(Thus, the existence of a bifurcation surface is irrelevant to our
demonstration. On the other hand, the derivation assumes without proof that the
horizon possesses at least one of the following two (related)properties: ()
it cannot be destroyed by arbitrarily small perturbations of the metric and
other fields which may be present, () the expansion of the null geodesic
generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil
Energy-momentum diffusion from spacetime discreteness
We study potentially observable consequences of spatiotemporal discreteness
for the motion of massive and massless particles. First we describe some simple
intrinsic models for the motion of a massive point particle in a fixed causal
set background. At large scales, the microscopic swerves induced by the
underlying atomicity manifest themselves as a Lorentz invariant diffusion in
energy-momentum governed by a single phenomenological parameter, and we derive
in full the corresponding diffusion equation. Inspired by the simplicity of the
result, we then derive the most general Lorentz invariant diffusion equation
for a massless particle, which turns out to contain two phenomenological
parameters describing, respectively, diffusion and drift in the particle's
energy. The particles do not leave the light cone however: their worldlines
continue to be null geodesics. Finally, we deduce bounds on the drift and
diffusion constants for photons from the blackbody nature of the spectrum of
the cosmic microwave background radiation.Comment: 13 pages, 4 figures, corrected minor typos and updated to match
published versio
The influence of boundaries on high pressure melting experiments
At low pressure, free surfaces play a crucial role in the melting transition.
Under pressure, the surface of the sample is acted upon by some pressure
transmitting medium. To examine the effect of this medium on melting, we
performed Monte Carlo simulations of a system of argon atoms in the form of a
slab with two boundaries. We examined two cases, one with a soft and the other
with a rigid medium at the boundaries. We found that in the presence of a rigid
medium, melting resembles the mechanical lattice instability found in a
surface-free solid. With a soft medium at the boundary, melting begins at the
surface and at a lower temperature. The relevance of these results to
experiment is discussed.Comment: 4 pages, 5 figure
A Causal Order for Spacetimes with Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves
We recast the tools of ``global causal analysis'' in accord with an approach
to the subject animated by two distinctive features: a thoroughgoing reliance
on order-theoretic concepts, and a utilization of the Vietoris topology for the
space of closed subsets of a compact set. We are led to work with a new causal
relation which we call , and in terms of it we formulate extended
definitions of concepts like causal curve and global hyperbolicity. In
particular we prove that, in a spacetime \M which is free of causal cycles,
one may define a causal curve simply as a compact connected subset of \M
which is linearly ordered by . Our definitions all make sense for
arbitrary metrics (and even for certain metrics which fail to be
invertible in places). Using this feature, we prove for a general metric,
the familiar theorem that the space of causal curves between any two compact
subsets of a globally hyperbolic spacetime is compact. We feel that our
approach, in addition to yielding a more general theorem, simplifies and
clarifies the reasoning involved. Our results have application in a recent
positive energy theorem, and may also prove useful in the study of topology
change. We have tried to make our treatment self-contained by including proofs
of all the facts we use which are not widely available in reference works on
topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by
R.S. Garcia. No change to chief results. 33 page
On critical collapse of gravitational waves
An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave packet. We find that near the threshold for black hole formation a curvature invariant with dimensions of length, scales as a power-law with the approximate exponent 0.38. In addition, the variation of the curvature in the critical limit is accompanied by increasing amount of echos, with nearly equal temporal and spatial periods. The scaling and the echoing patterns, and the corresponding constants are independent of the initial data and coordinate choices
Discreteness without symmetry breaking: a theorem
This paper concerns sprinklings into Minkowski space (Poisson processes). It
proves that there exists no equivariant measurable map from sprinklings to
spacetime directions (even locally). Therefore, if a discrete structure is
associated to a sprinkling in an intrinsic manner, then the structure will not
pick out a preferred frame, locally or globally. This implies that the
discreteness of a sprinkled causal set will not give rise to ``Lorentz
breaking'' effects like modified dispersion relations. Another consequence is
that there is no way to associate a finite-valency graph to a sprinkling
consistently with Lorentz invariance.Comment: 7 pages, laTe
Stable non-uniform black strings below the critical dimension
The higher-dimensional vacuum Einstein equation admits translationally
non-uniform black string solutions. It has been argued that infinitesimally
non-uniform black strings should be unstable in 13 or fewer dimensions and
otherwise stable. We construct numerically non-uniform black string solutions
in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using
local Penrose inequalities. Weakly non-uniform solutions behave as expected.
However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be
stable and can have greater horizon area than a uniform string of the same
mass. In 14 and 15 dimensions all non-uniform black strings appear to be
stable.Comment: 26 pages, 11 figures. V2: reference added, matches published versio
Payment Methods For Consumer-to-Consumer Online Transactions
Participants in online auctions use a variety of payment mechanisms, but checks and money orders still represent the most commonly used means of payment. Credit cards afford greater protection to buyers, but until recently payment by credit card was not even an option for person-to-person transactions. However, several online payment services have been established that enable individuals to make credit card payments to one another, generally with the payment service acting as an intermediary. These services are growing rapidly, mainly because of the speed and convenience that they offer. Yet relatively little attention has been paid to the risks and potential liabilities they involve for buyers and sellers. This Article compares online payment systems and similar intermediary services to traditional payment mechanisms in that context
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