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Non–Relativistic Spacetimes with Cosmological Constant
, 1999
"... Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non–relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein’s equations with a cosmological constant, reduce in the non– ..."
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Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non–relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein’s equations with a cosmological constant, reduce in the non–relativistic
The nonlinear Schrödinger equation and the conformal properties of nonrelativistic spacetime
, 2009
"... The cubic nonlinear Schrödinger equation where the coefficient of the nonlinear term is a function F(t,x) only passes the Painlevé test of Weiss, Tabor, and Carnevale only for F = (a+bt) −1, where a and b are constants. This is explained by transforming the timedependent system into the constantc ..."
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coefficient NLS by means of a timedependent nonlinear transformation, related to the conformal properties of nonrelativistic spacetime. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background. The recent upsurge of interest in nonrelativistic conformal
c © World Scientific Publishing Company Finsler metrics and relativistic spacetimes
, 2014
"... ar ..."
Virtual Time and Global States of Distributed Systems
 PARALLEL AND DISTRIBUTED ALGORITHMS
, 1988
"... A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a consiste ..."
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Cited by 741 (6 self)
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orderedand form a lattice. By using timestamps and a simple clock update mechanism the structure of causality is represented in an isomorphic way. The new model of time has a close analogy to Minkowski's relativistic spacetime and leads among others to an interesting characterization of the global
The variablecoefficient nonlinear Schrödinger equation and the conformal properties of nonrelativistic spacetime
, 2009
"... The cubic nonlinear Schrödinger equation where the coefficient of the nonlinear term can be a function F(t,x), is shown to pass the Painlevé test of Weiss, Tabor, and Carnevale only for F = (a+bt) −1, where a and b are constants. This is explained by transforming the timedependent system into the ..."
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into the constantcoefficient NLS by means of a timedependent nonlinear transformation, related to the conformal properties of nonrelativistic spacetime. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background. 1
The Geometry of Relativistic Spacetime: from Euclid's Geometry to Minkowski's Spacetime
"... "...the word relativitypostulate for the requirement of the invariance under the group Gc seems to me very feeble. Since the postulate comes to mean that only the fourdimensional world in space and time is given by phenomena, but that the projection in space and in time may still be undertake ..."
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"...the word relativitypostulate for the requirement of the invariance under the group Gc seems to me very feeble. Since the postulate comes to mean that only the fourdimensional world in space and time is given by phenomena, but that the projection in space and in time may still be undertaken with a certain degree of freedom, I prefer to call it the postulate of the absolute world (or brie
y the worldpostulate)."
A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime
 ApJS
, 2004
"... We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, agileboltztran, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in selfconsistent simulations of stellar co ..."
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Cited by 13 (2 self)
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We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, agileboltztran, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in selfconsistent simulations of stellar
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 566 (11 self)
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We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
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