15,091 research outputs found
On the classification of stationary electro-vacuum black holes
We obtain a classification of stationary, --regular, non-degenerate and
analytic electro-vacuum space-times in terms of Weinstein solutions. In
particular, for connected horizons, we prove uniqueness of the Kerr-Newman
black holes
Elastic shocks in relativistic rigid rods and balls
We study the free boundary problem for the "hard phase" material introduced
by Christodoulou, both for rods in (1+1)-dimensional Minkowski spacetime and
for spherically symmetric balls in (3+1)-dimensional Minkowski spacetime.
Unlike Christodoulou, we do not consider a "soft phase", and so we regard this
material as an elastic medium, capable of both compression and stretching. We
prove that shocks must be null hypersurfaces, and derive the conditions to be
satisfied at a free boundary. We solve the equations of motion of the rods
explicitly, and we prove existence of solutions to the equations of motion of
the spherically symmetric balls for an arbitrarily long (but finite) time,
given initial conditions sufficiently close to those for the relaxed ball at
rest. In both cases we find that the solutions contain shocks if and only if
the pressure or its time derivative do not vanish at the free boundary
initially. These shocks interact with the free boundary, causing it to lose
regularity.Comment: 22 pages, 3 figures; v2: small changes, matches final published
version; v3: typos in the references fixe
Homogeneous cosmologies from the quasi-Maxwell formalism
We show how to use the quasi-Maxwell formalism to obtain solutions of
Einstein's field equations corresponding to homogeneous cosmologies - namely
Einstein's universe, Godel's universe and the Ozsvath-Farnsworth-Kerr class I
solutions - written in frames for which the associated observers are
stationary.Comment: 15 pages, references adde
A Geant4 based engineering tool for Fresnel lenses
Geant4 is a Monte Carlo radiation transport toolkit that is becoming a tool
of generalized application in areas such as high-energy physics, nuclear
physics, astroparticle physics, or medical physics. Geant4 provides an optical
physics process category, allowing the simulation of the production and
propagation of light. Its capabilities are well tailored for the simulation of
optics systems namely in cosmic-rays experiments based in the detection of
Cherenkov and fluorescence light. The use of Geant4 as an engineering tool for
the optics design and simulation of Fresnel lens systems is discussed through a
specific example.Comment: 4 pages, 6 figures, Proceedings of the 30th ICRC, International
Cosmic Ray Conference 2007, M\'erida, M\'exico, 3-11 July 200
Asymptotic expansions, -values and a new Quantum Modular Form
In 2010 Zagier introduced the notion of a quantum modular form. One of his
first examples was the "strange" function of Kontsevich. Here we produce
a new example of a quantum modular form by making use of some of Ramanujan's
mock theta functions. Using these functions and their transformation behaviour,
we also compute asymptotic expansions similar to expansions of .Comment: 7 page
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