3,116 research outputs found
The geometry of low-rank Kalman filters
An important property of the Kalman filter is that the underlying Riccati
flow is a contraction for the natural metric of the cone of symmetric positive
definite matrices. The present paper studies the geometry of a low-rank version
of the Kalman filter. The underlying Riccati flow evolves on the manifold of
fixed rank symmetric positive semidefinite matrices. Contraction properties of
the low-rank flow are studied by means of a suitable metric recently introduced
by the authors.Comment: Final version published in Matrix Information Geometry, pp53-68,
Springer Verlag, 201
Light-cone averaging in cosmology: formalism and applications
We present a general gauge invariant formalism for defining cosmological
averages that are relevant for observations based on light-like signals. Such
averages involve either null hypersurfaces corresponding to a family of past
light-cones or compact surfaces given by their intersection with timelike
hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of
these light-cone averages are given. After introducing some adapted "geodesic
light-cone" coordinates, we give explicit expressions for averaging the
redshift to luminosity-distance relation and the so-called "redshift drift" in
a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected.
Version accepted for publication in JCA
The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some familiar stationary axisymmetric spacetimes
The tools developed in a preceding article for interpreting spacetime
geometry in terms of all possible space-plus-time splitting approaches are
applied to circular orbits in some familiar stationary axisymmetric spacetimes.
This helps give a more intuitive picture of their rotational features including
spin precession effects, and puts related work of Abramowicz, de Felice, and
others on circular orbits in black hole spacetimes into a more general context.Comment: 59 pages latex 2.09, uses ijmpd.sty macros, pictex, epsf.sty for 10
eps figures; typographical corrections made compared to published versio
Black Hole Evaporation in an Expanding Universe
We calculate the quantum radiation power of black holes which are asymptotic
to the Einstein-de Sitter universe at spatial and null infinities. We consider
two limiting mass accretion scenarios, no accretion and significant accretion.
We find that the radiation power strongly depends on not only the asymptotic
condition but also the mass accretion scenario. For the no accretion case, we
consider the Einstein-Straus solution, where a black hole of constant mass
resides in the dust Friedmann universe. We find negative cosmological
correction besides the expected redshift factor. This is given in terms of the
cubic root of ratio in size of the black hole to the cosmological horizon, so
that it is currently of order but could have been significant at the formation epoch of
primordial black holes. Due to the cosmological effects, this black hole has
not settled down to an equilibrium state. This cosmological correction may be
interpreted in an analogy with the radiation from a moving mirror in a flat
spacetime. For the significant accretion case, we consider the Sultana-Dyer
solution, where a black hole tends to increase its mass in proportion to the
cosmological scale factor. In this model, we find that the radiation power is
apparently the same as the Hawking radiation from the Schwarzschild black hole
of which mass is that of the growing mass at each moment. Hence, the energy
loss rate decreases and tends to vanish as time proceeds. Consequently, the
energy loss due to evaporation is insignificant compared to huge mass accretion
onto the black hole. Based on this model, we propose a definition of
quasi-equilibrium temperature for general conformal stationary black holes.Comment: Accepted for publication in Class.Quant.Grav., 18 pages and 3 figure
Quasi-periodic Oscillations in the X-ray Light Curves from Relativistic Tori
We use a relativistic ray-tracing code to analyze the X-ray emission from a
pressure-supported oscillating relativistic torus around a black hole. We show
that a strong correlation exists between the {\it intrinsic} frequencies of the
torus normal modes and the {\it extrinsic} frequencies seen in the observed
light curve power spectrum. This correlation demonstrates the feasibility of
the oscillating-torus model to explain the multiple peaks seen in black hole
high-frequency quasi-periodic oscillations. Using an optically thin,
monochromatic emission model, we also determine how a relativistically
broadened emission line and the amplitude of the X-ray modulations are
dependent on the observer's inclination angle and on the torus oscillation
amplitudes. Observations of these features can provide important information
about the torus as well as the black hole.Comment: 4 pages, 3 figures, submitted to ApJ
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