473 research outputs found
Optical scalars in spherical spacetimes
Consider a spherically symmetric spacelike slice through a spherically
symmetric spacetime. One can derive a universal bound for the optical scalars
on any such slice. The only requirement is that the matter sources satisfy the
dominant energy condition and that the slice be asymptotically flat and regular
at the origin. This bound can be used to derive new conditions for the
formation of apparent horizons. The bounds hold even when the matter has a
distribution on a shell or blows up at the origin so as to give a conical
singularity
Trapped surfaces in spherical expanding open universes
Consider spherically symmetric initial data for a cosmology which, in the
large, approximates an open Friedmann-Lema{\^\i}tre
universe. Further assume that the data is chosen so that the trace of the
extrinsic curvature is a constant and that the matter field is at rest at this
instant of time. One expects that no trapped surfaces appear in the data if no
significant clump of excess matter is to be found. This letter confirms this
belief by displaying a necessary condition for the existence of trapped
surfaces.This necessary condition, simply stated, says that a relatively large
amount of excess matter must be concentrated in a small volume for trapped
surfaces to appear.Comment: 8 pages, Late
Geometry of Keplerian disk systems and bounds on masses of their components
We investigate accreting disk systems with polytropic gas in Keplerian
motion. Numerical data and partial analytic results show that the
self-gravitation of the disk speeds up its rotation -- its rotational frequency
is larger than that given by the well known strictly Keplerian formula that
takes into account the central mass only. Thus determination of central mass in
systems with massive disks requires great care -- the strictly Keplerian
formula yields only an upper bound. The effect of self-gravity depends on
geometric aspects of disk configurations. Disk systems with a small (circa
) ratio of the innermost radius to the outermost disk radius have the
central mass close to the upper limit, but if this ratio is of the order of
unity then the central mass can be smaller by many orders of magnitude from
this bound.Comment: 20 pages, 10 figure
A Semiparametric Intraday GARCH Model
We propose a multiplicative component model for intraday volatility. The model consists of a seasonality factor, as well as a semiparametric and parametric component. The former captures the well-documented intraday seasonality of volatility, while the latter two account for the impact of the state of the limit order book, utilizing an additive structure, and fluctuations around this state by means of a unit GARCH specification. The model is estimated by a simple and easy-to-implement approach, consisting of across-day-averaging, smooth-backfitting and QML steps. We derive the asymptotic properties of the three component estimators. Further, our empirical application based on high-frequency data for NASDAQ equities investigates non-linearities in the relationship between the limit order book and subsequent return volatility and underlines the usefulness of including order book variables for out-of-sample forecasting performance
Schwarzschild horizon and the gravitational redshift formula
The gravitational redshift formula is usually derived in the geometric optics
approximation. In this note we consider an exact formulation of the problem in
the Schwarzschild space-time, with the intention to clarify under what
conditions this redshift law is valid. It is shown that in the case of shocks
the radial component of the Poynting vector can scale according to the redshift
formula, under a suitable condition. If that condition is not satisfied, then
the effect of the backscattering can lead to significant modifications. The
obtained results imply that the energy flux of the short wavelength radiation
obeys the standard gravitational redshift formula while the energy flux of long
waves can scale differently, with redshifts being dependent on the frequency.Comment: Revtex, 5 p. Rewritten Sec. II, minor changes in Secs III - VII. To
appear in the Classical and Quantum Gravit
Trapped surfaces in nonspherical open universes
We continue our investigation of formation of trapped surfaces in strongly curved geometries which do not contain gravitational waves. The expansion of open, flat universes does not change substantially the results obtained hitherto in the case of asymptotically and conformally flat space-time. The necessary and sufficient conditions for the formation of trapped surfaces are given, which explicitly demonstrate that the quicker universes are expanding, the more matter is required to develop a trapped surface
Three-dimensional shapelets and an automated classification scheme for dark matter haloes
We extend the two-dimensional Cartesian shapelet formalism to d-dimensions.
Concentrating on the three-dimensional case, we derive shapelet-based equations
for the mass, centroid, root-mean-square radius, and components of the
quadrupole moment and moment of inertia tensors. Using cosmological N-body
simulations as an application domain, we show that three-dimensional shapelets
can be used to replicate the complex sub-structure of dark matter halos and
demonstrate the basis of an automated classification scheme for halo shapes. We
investigate the shapelet decomposition process from an algorithmic viewpoint,
and consider opportunities for accelerating the computation of shapelet-based
representations using graphics processing units (GPUs).Comment: 19 pages, 11 figures, accepted for publication in MNRA
The Constraints in Spherically Symmetric General Relativity II --- Identifying the Configuration Space: A Moment of Time Symmetry
We continue our investigation of the configuration space of general
relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian
constraint when the spatial geometry is momentarily static (MS). We show that
MS configurations satisfy both the positive quasi-local mass (QLM) theorem and
its converse. We derive an analytical expression for the spatial metric in the
neighborhood of a generic singularity. The corresponding curvature singularity
shows up in the traceless component of the Ricci tensor. We show that if the
energy density of matter is monotonically decreasing, the geometry cannot be
singular. A supermetric on the configuration space which distinguishes between
singular geometries and non-singular ones is constructed explicitly. Global
necessary and sufficient criteria for the formation of trapped surfaces and
singularities are framed in terms of inequalities which relate appropriate
measures of the material energy content on a given support to a measure of its
volume. The strength of these inequalities is gauged by exploiting the exactly
solvable piece-wise constant density star as a template.Comment: 50 pages, Plain Tex, 1 figure available from the authors
The Jang equation, apparent horizons, and the Penrose inequality
The Jang equation in the spherically symmetric case reduces to a first order
equation. This permits an easy analysis of the role apparent horizons play in
the (non)existence of solutions. We demonstrate that the proposed derivation of
the Penrose inequality based on the Jang equation cannot work in the
spherically symmetric case. Thus it is fruitless to apply this method, as it
stands, to the general case. We show also that those analytic criteria for the
formation of horizons that are based on the use of the Jang equation are of
limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte
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