2,029 research outputs found
Sea state bias in altimeter sea level estimates determined by combining wave model and satellite data
This study documents a method for increasing the precision of satellite-derived sea level measurements. Results are achieved using an enhanced three-dimensional (3-D) sea state bias (SSB) correction model derived from both Jason-1 altimeter ocean observations (i.e., sea state and wind) and estimates of mean wave period from a numerical ocean wave model, NOAA’s WAVEWATCH III. A multiyear evaluation of Jason-1 data indicates sea surface height variance reduction of 1.26 (±0.2) cm2 in comparison to the commonly applied two-parameter SSB model. The improvement is similar for two separate variance reduction metrics and for separate annual data sets spanning 2002–2004. Spatial evaluation of improvement shows skill increase at all latitudes. Results indicate the new model can reduce the total Jason-1 and Jason-2 altimeter range error budgets by 7.5%. In addition to the 2-D (two-dimensional) and 3-D model differences in correcting the range for wavefield variability, mean model regional differences also occur across the globe and indicate a possible 1–2 cm gradient across ocean basins linked to the zonal variation in wave period (short fetch and period in the west, swells and long period in the east). Overall success of this model provides first evidence that operational wave modeling can support improved ocean altimetry. Future efforts will attempt to work within the limits of wave modeling capabilities to maximize their benefit to Jason-1 and Jason-2 SSB correction methods
Gravitational energy
Observers at rest in a stationary spacetime flat at infinity can measure
small amounts of rest-mass+internal energies+kinetic energies+pressure energy
in a small volume of fluid attached to a local inertial frame. The sum of these
small amounts is the total "matter energy" for those observers. The total
mass-energy minus the matter energy is the binding gravitational energy.
Misner, Thorne and Wheeler evaluated the gravitational energy of a
spherically symmetric static spacetime. Here we show how to calculate
gravitational energy in any static and stationary spacetime for isolated
sources with a set of observers at rest.
The result of MTW is recovered and we find that electromagnetic and
gravitational 3-covariant energy densities in conformastatic spacetimes are of
opposite signs. Various examples suggest that gravitational energy is negative
in spacetimes with special symmetries or when the energy-momentum tensor
satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra
Planck Fluctuations, Measurement Uncertainties and the Holographic Principle
Starting from a critical analysis of recently reported surprisingly large
uncertainties in length and position measurements deduced within the framework
of quantum gravity, we embark on an investigation both of the correlation
structure of Planck scale fluctuations and the role the holographic hypothesis
is possibly playing in this context. While we prove the logical independence of
the fluctuation results and the holographic hypothesis (in contrast to some
recent statements in that direction) we show that by combining these two topics
one can draw quite strong and interesting conclusions about the fluctuation
structure and the microscopic dynamics on the Planck scale. We further argue
that these findings point to a possibly new and generalized form of quantum
statistical mechanics of strongly (anti)correlated systems of degrees of
freedom in this fundamental regime.Comment: 19 pages, Latex, no figures, some new references, to appear
ModPhysLett
On the stable configuration of ultra-relativistic material spheres. The solution for the extremely hot gas
During the last stage of collapse of a compact object into the horizon of
events, the potential energy of its surface layer decreases to a negative value
below all limits. The energy-conservation law requires an appearance of a
positive-valued energy to balance the decrease. We derive the internal-state
properties of the ideal gas situated in an extremely strong, ultra-relativistic
gravitational field and suggest to apply our result to a compact object with
the radius which is slightly larger than or equal to the Schwarzschild's
gravitational radius. On the surface of the object, we find that the extreme
attractivity of the gravity is accompanied with an extremely high internal,
heat energy. This internal energy implies a correspondingly high pressure, the
gradient of which has such a behavior that it can compete with the gravity. In
a more detail, we find the equation of state in the case when the magnitude of
the potential-type energy of constituting gas particles is much larger than
their rest energy. This equation appears to be identical with the
general-relativity condition of the equilibrium between the gravity and
pressure gradient. The consequences of the identity are discussed.Comment: 12 pages (no figure, no table) Changes in 3-rd version: added an
estimate of neutrino cooling and relative time-scale of the final stage of
URMS collaps
Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
The Planck spectrum of thermal scalar radiation is derived suggestively
within classical physics by the use of an accelerating coordinate frame. The
derivation has an analogue in Boltzmann's derivation of the Maxwell velocity
distribution for thermal particle velocities by considering the thermal
equilibrium of noninteracting particles in a uniform gravitational field. For
the case of radiation, the gravitational field is provided by the acceleration
of a Rindler frame through Minkowski spacetime. Classical zero-point radiation
and relativistic physics enter in an essential way in the derivation which is
based upon the behavior of free radiation fields and the assumption that the
field correlation functions contain but a single correlation time in thermal
equilibrium. The work has connections with the thermal effects of acceleration
found in relativistic quantum field theory.Comment: 23 page
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
Collapsing Spheres Satisfying An "Euclidean Condition"
We study the general properties of fluid spheres satisfying the heuristic
assumption that their areas and proper radius are equal (the Euclidean
condition). Dissipative and non-dissipative models are considered. In the
latter case, all models are necessarily geodesic and a subclass of the
Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions
are non-geodesic and are characterized by the fact that all non-gravitational
forces acting on any fluid element produces a radial three-acceleration
independent on its inertial mass.Comment: 1o pages, Latex. Title changed and text shortened to fit the version
to appear in Gen.Rel.Grav
Black hole evaporation in a heat bath as a nonequilibrium process and its final fate
When a black hole evaporates, there arises a net energy flow from black hole
into its outside environment (heat bath). The existence of energy flow means
that the thermodynamic state of the whole system, which consists of the black
hole and the heat bath, is in a nonequilibrium state. Therefore, in order to
study the detail of evaporation process, the nonequilibrium effects of the
energy flow should be taken into account. Using the nonequilibrium
thermodynamics which has been formulated recently, this paper shows the
following: (1) Time scale of black hole evaporation in a heat bath becomes
shorter than that of the evaporation in an empty space (a situation without
heat bath), because a nonequilibrium effect of temperature difference between
the black hole and heat bath appears as a strong energy extraction from the
black hole by the heat bath. (2) Consequently a huge energy burst (stronger
than that of the evaporation in an empty space) arises at the end of
semi-classical stage of evaporation. (3) It is suggested that a remnant of
Planck size remains after the quantum stage of evaporation in order to
guarantee the increase of total entropy of the whole system
Huygens' Principle for the Klein-Gordon equation in the de Sitter spacetime
In this article we prove that the Klein-Gordon equation in the de Sitter
spacetime obeys the Huygens' principle only if the physical mass of the
scalar field and the dimension of the spatial variable are tied by
the equation . Moreover, we define the incomplete Huygens'
principle, which is the Huygens' principle restricted to the vanishing second
initial datum, and then reveal that the massless scalar field in the de Sitter
spacetime obeys the incomplete Huygens' principle and does not obey the
Huygens' principle, for the dimensions , only. Thus, in the de Sitter
spacetime the existence of two different scalar fields (in fact, with m=0 and
), which obey incomplete Huygens' principle, is equivalent to
the condition (in fact, the spatial dimension of the physical world). For
these two values of the mass are the endpoints of the so-called in
quantum field theory the Higuchi bound. The value of the
physical mass allows us also to obtain complete asymptotic expansion of the
solution for the large time. Keywords: Huygens' Principle; Klein-Gordon
Equation; de Sitter spacetime; Higuchi Boun
Statistical mechanical theory of an oscillating isolated system. The relaxation to equilibrium
In this contribution we show that a suitably defined nonequilibrium entropy
of an N-body isolated system is not a constant of the motion in general and its
variation is bounded, the bounds determined by the thermodynamic entropy, i.e.,
the equilibrium entropy. We define the nonequilibrium entropy as a convex
functional of the set of n-particle reduced distribution functions
(n=0,......., N) generalizing the Gibbs fine-grained entropy formula.
Additionally, as a consequence of our microscopic analysis we find that this
nonequilibrium entropy behaves as a free entropic oscillator. In the approach
to the equilibrium regime we find relaxation equations of the Fokker-Planck
type, particularly for the one-particle distribution function
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