4,143 research outputs found
Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime
We discuss the relation between string quantization based on the Schild path
integral and the Nambu-Goto path integral. The equivalence between the two
approaches at the classical level is extended to the quantum level by a
saddle--point evaluation of the corresponding path integrals. A possible
relationship between M-Theory and the quantum mechanics of string loops is
pointed out. Then, within the framework of ``loop quantum mechanics'', we
confront the difficult question as to what exactly gives rise to the structure
of spacetime. We argue that the large scale properties of the string condensate
are responsible for the effective Riemannian geometry of classical spacetime.
On the other hand, near the Planck scale the condensate ``evaporates'', and
what is left behind is a ``vacuum'' characterized by an effective fractal
geometry.Comment: 19pag. ReVTeX, 1fig. Invited paper to appear in the special issue of
{\it Chaos, Solitons and Fractals} on ``Super strings, M,F,S,...Theory''
(M.S. El Naschie and C.Castro, ed
CARBayes: an R package for Bayesian spatial modeling with conditional autoregressive priors
Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping
Horizon wave-function for single localized particles: GUP and quantum black hole decay
A localised particle in Quantum Mechanics is described by a wave packet in
position space, regardless of its energy. However, from the point of view of
General Relativity, if the particle's energy density exceeds a certain
threshold, it should be a black hole. In order to combine these two pictures,
we introduce a horizon wave-function determined by the particle wave-function
in position space, which eventually yields the probability that the particle is
a black hole. The existence of a minimum mass for black holes naturally
follows, albeit not in the form of a sharp value around the Planck scale, but
rather like a vanishing probability that a particle much lighter than the
Planck mass be a black hole. We also show that our construction entails an
effective Generalised Uncertainty Principle (GUP), simply obtained by adding
the uncertainties coming from the two wave-functions associated to a particle.
Finally, the decay of microscopic (quantum) black holes is also described in
agreement with what the GUP predicts.Comment: 8 pages, 5 figures, extended version of arXiv:1305.3195 with new
results about the GUP and black hole decay, clarifications about black hole
decay adde
The Einstein-Vlasov sytem/Kinetic theory
The main purpose of this article is to guide the reader to theorems on global
properties of solutions to the Einstein-Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades where the main focus has
been on nonrelativistic- and special relativistic physics, e.g. to model the
dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In
1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
(e.g. fluid models). The first part of this paper gives an introduction to
kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is
introduced. We believe that a good understanding of kinetic theory in
non-curved spacetimes is fundamental in order to get a good comprehension of
kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity
(http://www.livingreviews.org
Gravitational waves, black holes and cosmic strings in cylindrical symmetry
Gravitational waves in cylindrically symmetric Einstein gravity are described
by an effective energy tensor with the same form as that of a massless Klein-
Gordon field, in terms of a gravitational potential generalizing the Newtonian
potential. Energy-momentum vectors for the gravitational waves and matter are
defined with respect to a canonical flow of time. The combined energy-momentum
is covariantly conserved, the corresponding charge being the modified Thorne
energy. Energy conservation is formulated as the first law expressing the
gradient of the energy as work and energy-supply terms, including the energy
flux of the gravitational waves. Projecting this equation along a trapping
horizon yields a first law of black-hole dynamics containing the expected term
involving area and surface gravity, where the dynamic surface gravity is
defined with respect to the canonical flow of time. A first law for dynamic
cosmic strings also follows. The Einstein equation is written as three wave
equations plus the first law, each with sources determined by the combined
energy tensor of the matter and gravitational waves.Comment: 10 pages, revtex. Published version with further detail
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