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\begin_layout Title
A Computational Elucidation of Curved Spacetime
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\begin_layout Author
Bryan Newbold
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Advisor: Prof.
 Gerald J.
 Sussman, EECS
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I propose to implement a geometric formulation of curved space time in a
 functional computer programming language, and to explore the space of simulatio
ns and manipulations made possible by such a formulation.
 A primary motivation is to state the foundations of General Relativity
 in a non-ambiguous manner.
 
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This work follows several attempts to formulate curved spacetime on computers
 for the purpose of numerical calculations and algebraic manipulation.
 Most of these packages are specially designed for the tasks of tensor analysis
 and/or efficient numerical calculation, as is appropriate for use in calculatio
ns.
 A crucial difference of this proposed work will be to carefully build up
 the geometric and analytical tools in a general purpose functional programing
 language (mit-scheme).
 As a learning and reference tool, this will allow users to explore the
 inner workings and structure of the system, which I believe is essential
 to understanding the system as a whole.
 
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The frame field representation will be used to emphasize the geometric propertie
s of curved space time, as opposed to the more traditional coordinate heavy
 tensor analysis approach.
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The resulting work will include a full implementation with source code and
 documentation, as well as example problems and qualitative comparisons
 with existing packages and software systems.
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Functional Differential Geometry, G.
 Sussman and J.
 Wisdom (2005)
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Structure and Interpretation of Classical Mechanics, G.
 Sussman and J.
 Wisdom (2001)
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"Algebraic Computing in General Relativity", Ray d'Inverno (from General
 Relativity, G.
 Hall and J.
 Pulham)
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"The Use of Algebraic Computing in General Relativity", H.
 I.
 Cohen, A.
 Leringe and Y.
 Sundblad 
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