1,209 research outputs found
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A time-dependent coordinate transformation of a constant coeffcient hyperbolic equation which results in a variable coeffcient problem is considered. By using the energy method, we derive well-posed boundary conditions for the continuous problem. It is shown that the number of boundary conditions depend on the coordinate transformation. By using Summation-by-Parts (SBP) operators for the space discretization and weak boundary conditions, an energy stable finite dieffrence scheme is obtained. We also show how to construct a time-dependent penalty formulation that automatically imposes the right number of boundary conditions. Numerical calculations corroborate the stability and accuracy of the approximations
Berättelser rörande göromälen vid Bergs-Skolan år 1837 = An account of the activities of the Swedish School of Mines in year 1827
Horizon Mass Theorem
A new theorem for black holes is found. It is called the horizon mass
theorem. The horizon mass is the mass which cannot escape from the horizon of a
black hole. For all black holes: neutral, charged or rotating, the horizon mass
is always twice the irreducible mass observed at infinity. Previous theorems on
black holes are: 1. the singularity theorem, 2. the area theorem, 3. the
uniqueness theorem, 4. the positive energy theorem. The horizon mass theorem is
possibly the last general theorem for classical black holes. It is crucial for
understanding Hawking radiation and for investigating processes occurring near
the horizon.Comment: A new theorem for black holes is establishe
See a Black Hole on a Shoestring
The modes of vibration of hanging and partially supported strings provide
useful analogies to scalar fields travelling through spacetimes that admit
conformally flat spatial sections. This wide class of spacetimes includes
static, spherically symmetric spacetimes. The modes of a spacetime where the
scale factor depends as a power-law on one of the coordinates provide a useful
starting point and yield a new classification of these spacetimes on the basis
of the shape of the string analogue. The family of corresponding strings follow
a family of curves related to the cycloid, denoted here as hypercycloids (for
reasons that will become apparent). Like the spacetimes that they emulate these
strings exhibit horizons, typically at their bottommost points where the string
tension vanishes; therefore, hanging strings may provide a new avenue for the
exploration of the quantum mechanics of horizons.Comment: 5 pages, 1 figure, extensive changes to refect version accepted to
PR
Electrically charged fluids with pressure in Newtonian gravitation and general relativity in d spacetime dimensions: theorems and results for Weyl type systems
Previous theorems concerning Weyl type systems, including Majumdar-Papapetrou
systems, are generalized in two ways, namely, we take these theorems into d
spacetime dimensions (), and we also consider the very
interesting Weyl-Guilfoyle systems, i.e., general relativistic charged fluids
with nonzero pressure. In particular within Newton-Coulomb theory of charged
gravitating fluids, a theorem by Bonnor (1980) in three-dimensional space is
generalized to arbitrary space dimensions. Then, we prove a new
theorem for charged gravitating fluid systems in which we find the condition
that the charge density and the matter density should obey. Within general
relativity coupled to charged dust fluids, a theorem by De and Raychaudhuri
(1968) in four-dimensional spacetimes in rendered into arbitrary
dimensions. Then a theorem, new in and dimensions, for
Weyl-Guilfoyle systems, is stated and proved, in which we find the condition
that the charge density, the matter density, the pressure, and the
electromagnetic energy density should obey. This theorem comprises, as
particular cases, a theorem by Gautreau and Hoffman (1973) and results in four
dimensions by Guilfoyle (1999). Upon connection of an interior charged solution
to an exterior Tangherlini solution (i.e., a Reissner-Nordstr\"om solution in
d-dimensions), one is able to give a general definition for gravitational mass
for this kind of relativistic systems and find a mass relation with the several
quantities of the interior solution. It is also shown that for sources of
finite extent the mass is identical to the Tolman mass.Comment: 27 page
A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology
Recent developments in string theory suggest that there might exist extra
spatial dimensions, which are not small nor compact. The framework of most
brane cosmological models is that in which the matter fields are confined on a
brane-world embedded in five dimensions (the bulk). Motivated by this we
reexamine the classification of the second order symmetric tensors in 5--D, and
prove two theorems which collect together some basic results on the algebraic
structure of these tensors in 5-dimensional space-times. We also briefly
indicate how one can obtain, by induction, the classification of symmetric
two-tensors (and the corresponding canonical forms) on n-dimensional spaces
from the classification on 4-dimensional spaces. This is important in the
context of 11--D supergravity and 10--D superstrings.Comment: 12 pages, to appear in Mod. Phys. Lett. A (2003) in the present for
Report of IAU Commission 30 on Radial Velocities (2006-2009)
Brief summaries are given on the following subjects: Radial velocities and
exoplanets (Toward Earth-mass planets; Retired A stars and their planets;
Current status and prospects); Toward higher radial velocity precision; Radial
velocities and asteroseismology; Radial velocities in Galactic and
extragalactic clusters; Radial velocities for field giants; Galactic structure
-- Large surveys (The Geneva-Copenhagen Survey; Sloan Digital Sky Survey;
RAVE); Working groups (WG on radial velocity standards; WG on stellar radial
velocity bibliography; WG on the catalogue of orbital elements of spectroscopic
binaries [SB9]).Comment: 11 pages, to appear in the IAU Transactions Vol. XXVIIA, Reports on
Astronomy 2006-2009, ed. Karel van der Hucht. Editor: G. Torre
Geometry and quantum delocalization of interstitial oxygen in silicon
The problem of the geometry of interstitial oxygen in silicon is settled by
proper consideration of the quantum delocalization of the oxygen atom around
the bond-center position. The calculated infrared absorption spectrum accounts
for the 517 and 1136 cm bands in their position, character, and isotope
shifts. The asymmetric lineshape of the 517 cm peak is also well
reproduced. A new, non-infrared-active, symmetric-stretching mode is found at
596 cm. First-principles calculations are presented supporting the
nontrivial quantum delocalization of the oxygen atom.Comment: uuencoded, compressed postscript file for the whole. 4 pages (figures
included), accepted in PR
Black string and velocity frame dragging
We investigate velocity frame dragging with the boosted Schwarzschild black
string solution and the boosted Kaluza-Klein bubble solution, in which a
translational symmetry along the boosted -coordinate is implemented. The
velocity frame dragging effect can be nullified by the motion of an observer
using the boost symmetry along the coordinate if it is not compact.
However, in spacetime with the compact coordinate, we show that the effect
cannot be removed since the compactification breaks the global Lorentz boost
symmetry. As a result, the comoving velocity is dependent on and the
momentum parameter along the coordinate becomes an observer independent
characteristic quantity of the black string and bubble solutions. The dragging
induces a spherical ergo-region around the black string.Comment: 8 pages, no figure, some correction
Warped product approach to universe with non-smooth scale factor
In the framework of Lorentzian warped products, we study the
Friedmann-Robertson-Walker cosmological model to investigate non-smooth
curvatures associated with multiple discontinuities involved in the evolution
of the universe. In particular we analyze non-smooth features of the spatially
flat Friedmann-Robertson-Walker universe by introducing double discontinuities
occurred at the radiation-matter and matter-lambda phase transitions in
astrophysical phenomenology.Comment: 10 page
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