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newtonian-derivation-cdt-v2.bib
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newtonian-derivation-cdt-v2.bib
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0_4NXMN8KT 0_77J2USAA 0_7ASDST9I 0_H6TI3CIK 0_K2T3QRM9 0_PSBHXPCT 0_S6RZGX9C 0_UQUPGTXE
@article{chou1931thegravitational,
title = {The {G}ravitational {F}ield of a {B}ody with {R}otational {S}ymmetry in {E}instein's {T}heory of {G}ravitation},
volume = {53},
issn = {0002-9327},
url = {http://www.jstor.org/stable/2370784},
doi = {10.2307/2370784},
number = {2},
journal = {American Journal of Mathematics},
author = {Chou, P. Y.},
month = apr,
year = {1931},
note = {{ArticleType:} research-article / Full publication date: Apr., 1931 / Copyright {\textcopyright} 1931 The Johns Hopkins University Press},
pages = {289--308}
}
@article{curzon1924,
title = {Cylindrical {S}olutions of {E}instein's {G}ravitational {E}quations},
volume = {s2--23},
journal = {Proceedings of the London Mathematical Society},
author = {Curzon, H. E. J.},
year = {1925},
pages = {477--480}
}
@article{katz1967derivation,
title = {Derivation of {N}ewton's {L}aw of {G}ravitation from {G}eneral {R}elativity},
volume = {9},
lccn = {0000},
abstract = {A static situation of two objects held apart by a strut is considered within the framework of general relativity, and the gravitational attraction between the objects is inferred from the stress in the strut. In the Newtonian limit -- the objects are well separated and the field weak everywhere except in their immediate vicinity -- Newton's law of gravitation is reproduced. This check goes well beyond verifications of the Newtonian limit based on considerations of "test particles", since arbitrarily strong self-fields are not excluded for either object. It is also an explicit verification of the equality of active and passive gravitational masses.},
number = {7},
journal = {Journal of Mathematical Physics},
author = {Katz, Amnon},
month = sep,
year = {1967},
pages = {983--985}
}
@article{ambjorn2008thenonperturbative,
title = {The Nonperturbative Quantum de Sitter Universe},
lccn = {0000},
url = {http://arxiv.org/abs/0807.4481},
doi = {doi:10.1103/PhysRevD.78.063544},
abstract = {The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of Causal Dynamical Triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and how the effective action determining its dynamics can be reconstructed uniquely from Monte Carlo data. We also provide evidence that it may be possible to penetrate to the {sub-Planckian} regime, where the Planck length is large compared to the lattice spacing of the underlying regularization of geometry.},
journal = {0807.4481},
author = {Ambjorn, J. and Goerlich, A. and Jurkiewicz, J. and Loll, R.},
month = jul,
year = {2008},
note = {{Phys.Rev.D78:063544},2008},
keywords = {Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Theory}
}
@book{cormen2001introduction,
edition = {2nd},
title = {Introduction to Algorithms, Second Edition},
isbn = {0262032937},
publisher = {The {MIT} Press},
author = {Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford},
month = sep,
year = {2001}
}
@article{trzesniewski2011analysis,
title = {Analysis of the {S}emiclassical {S}olution of {CDT}},
lccn = {0000},
url = {http://arxiv.org/abs/1102.4643},
abstract = {Causal dynamical triangulations {(CDT)} constitute a background independent, nonperturbative approach to quantum gravity, in which the gravitational path integral is approximated by the weighted sum over causally well-behaving simplicial manifolds i.e. causal triangulations. This thesis is an analysis of the data from the Monte Carlo computer simulations of {CDT} in 3+1 dimensions. It is confirmed here that there exist the semiclassical limit of {CDT} for so-called (4,1) (or equivalent (1,4)) simplices, being a discrete version of the mini-superspace model. Next, the form of the corresponding discrete action is investigated. Furthermore, it is demonstrated that the effective, semiclassical solution works also after the inclusion of remaining (3,2) and (2,3) simplices, treated collectively. A specific form of the resulting extended discrete action is examined and a transition from the broader framework to the former narrower one is shown.},
journal = {{arXiv:1102.4643}},
author = {Trzesniewski, T.},
month = feb,
year = {2011},
keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Lattice, High Energy Physics - Theory}
}
@article{loll1998discrete,
title = {Discrete approaches to quantum gravity in four dimensions},
url = {http://arxiv.org/abs/gr-qc/9805049},
abstract = {The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.},
journal = {{arXiv:gr-qc/9805049}},
author = {Loll, R.},
month = may,
year = {1998},
note = {{LivingRev.Rel.1:13},1998},
keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Theory, Read}
}
@article{letelier1997superposition,
title = {Superposition of Weyl solutions: The equilibrium forces},
shorttitle = {Superposition of Weyl solutions},
url = {http://arxiv.org/abs/gr-qc/9710122},
doi = {10.1088/0264-9381/15/2/015},
abstract = {Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detail},
journal = {{arXiv:gr-qc/9710122}},
author = {Letelier, Patricio. S and Oliveira, Samuel R},
month = oct,
year = {1997},
note = {{Class.Quant.Grav.} 15 (1998) 421-433},
keywords = {General Relativity and Quantum Cosmology}
}
@book{carroll2003spacetime,
title = {Spacetime and Geometry: An Introduction to General Relativity},
isbn = {0805387323},
shorttitle = {Spacetime and Geometry},
publisher = {Benjamin Cummings},
author = {Carroll, Sean},
month = sep,
year = {2003}
}
@article{weisstein1,
author = {Weisstein, Eric W.},
title = {Simplicial {C}omplex},
url = {http://mathworld.wolfram.com/SimplicialComplex.html},
journal = {MathWorld - A Wolfram Web Resource}
}
@article{kommu2011,
title = {A {V}alidation of {C}ausal {D}ynamical {T}riangulations},
url = {http://arxiv.org/abs/1110.6875},
abstract = {The Causal Dynamical Triangulation {(CDT)} approach to quantum gravity is a lattice approximation to the gravitational path integral. Developed by Ambj{\textbackslash}o{}rn, Jurkiewicz and Loll, it has yielded some important results, notably the emergence of classical spacetime and short scale dimensional reduction. However, virtually all the results reported so far have been based on a single computer code. In this paper we present the first completely independent verification of the {CDT} algorithm, and report the successful reproduction of the emergence of classical spacetime and smooth reduction in the spectral dimension of the 2+1 and 3+1 dimensional spacetimes.},
journal = {{arXiv:1110.6875}},
author = {Kommu, Rajesh},
month = oct,
year = {2011},
keywords = {General Relativity and Quantum Cosmology, High Energy Physics - Theory, To Read}
}
@article{knuth_literate_1984,
title = {Literate {P}rogramming},
volume = {27},
url = {http://comjnl.oxfordjournals.org/content/27/2/97.abstract},
doi = {10.1093/comjnl/27.2.97},
abstract = {The author and his associates have been experimenting for the past several years with a programming language and documentation system called {WEB.} This paper presents {WEB} by example, and discusses why the new system appears to be an improvement over previous ones.},
number = {2},
journal = {The Computer Journal},
author = {Knuth, D. E.},
month = jan,
year = {1984},
pages = {97 --111}
}
@book{rathore_clojure_2011,
edition = {1},
title = {Clojure in Action},
isbn = {1935182595},
publisher = {Manning Publications},
author = {Rathore, Amit},
month = nov,
year = {2011}
}
@book{synge_relativity,
title = {Relativity: the general theory},
shorttitle = {Relativity},
publisher = {{North-Holland} Pub. Co.},
author = {Synge, John Lighton},
year = {1960},
keywords = {General relativity {(Physics)}, Relativity {(Physics)}, Science / Relativity}
}
@article{araujo_static_1995,
title = {Static axisymmetric approach for the head-on collision of two black holes},
volume = {52},
url = {http://link.aps.org/doi/10.1103/PhysRevD.52.816},
doi = {10.1103/PhysRevD.52.816},
abstract = {This paper presents a semianalytical approach to the interaction of two (originally) spherically symmetric black holes through a head-on collision process. It is shown that an expression for the rate of emission of gravitational radiation can be derived from the so-called Weyl potential. The total output of gravitational wave energy released is then calculated and the results are compared to recent numerical investigations of this problem.},
number = {2},
journal = {Physical Review D},
author = {Araújo, M. E. and Oliveira, S. R.},
month = jul,
year = {1995},
pages = {816--820}
}
@article{weisstein_gauss-bonnet,
author = {Weisstein, Eric},
title = {{Gauss-Bonnet} Formula},
url = {http://mathworld.wolfram.com/Gauss-BonnetFormula.html},
journal = {MathWorld - A Wolfram Web Resource}
}
@misc{first_fundamental-form,
title = {First fundamental form},
copyright = {Creative Commons {Attribution-ShareAlike} License},
url = {http://en.wikipedia.org/w/index.php?title=First_fundamental_form&oldid=479957456},
abstract = {In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which is induced canonically from the dot product of R3. It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consistent with the ambient space. The first fundamental form is denoted by the Roman numeral I,},
journal = {Wikipedia, the free encyclopedia},
publisher = {Wikimedia Foundation, Inc.},
author = {{{Wikipedia} contributors}},
month = mar,
year = {2012},
note = {Page Version {ID:} 479957456}
}
@article{schleifer_condition_1985,
title = {Condition of elementary flatness and the two-particle Curzon solution},
volume = {112},
issn = {0375-9601},
url = {http://www.sciencedirect.com/science/article/pii/0375960185905031},
doi = {10.1016/0375-9601(85)90503-1},
abstract = {The condition of elementary flatness — used in demonstrating the existence of a strut (along r = 0) in the two-particle Curzon solution of the Einstein field equations — is given a rigorous foundation. We show, by using the {Gauss-Bonnet} theorem, that if elementary flatness is violated then the spacetime including r = 0 is not a lorentzian manifold.},
number = {5},
journal = {Physics Letters A},
author = {Schleifer, Nathan},
month = oct,
year = {1985},
pages = {204--207}
}
@article{ambjorn_semiclassical,
title = {Semiclassical Universe from First Principles},
volume = {607},
lccn = {0059},
url = {http://arxiv.org/abs/hep-th/0411152},
abstract = {Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor.},
number = {2005},
urldate = {2009-03-16},
journal = {Physics Letters B},
author = {{J. Ambjorn} and {J. Jurkiewicz} and {R. Loll}},
keywords = {Causal Dynamical Triangulations, Read},
pages = {205--213},
annote = {Read 6th},
file = {[hep-th/0411152] Semiclassical Universe from First Principles:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/TC2AM4T6/0411152.html:text/html;0411152v1.pdf:/Users/getchell/Library/Application Support/Zotero/Profiles/2wundcq4.default/zotero/storage/IXTTMJU5/0411152v1.pdf:application/pdf}
}