A study of the properties of spatially dependent Newton-Cartan gravity under noninertial, nonrelativistic reference frames.
creator
Frank, Cameron A.
creator
Wickramasekara, Sujeev
Title
Spatial Dependence in Newton-Cartan Gravity in Nonintertial Reference Frames
supporting host
Grinnell College. Physics Department.
Index Date
2015
Approx. Date of Creation
2015-12-17
Publisher
Grinnell College
Type of Resource
text
Genre
research paper
Digital Origin
reformated digital
Digital Extent
21 pages
Media Type
application/pdf
description
We study the properties of spatially dependent Newton-Cartan gravity under noninertial, nonrelativistic reference frames. We define the transformation by an element of the set consisting of a rotation matrix which is a continuous function of x and t, a linear transformation function of x and t, and a constant time translation. The set of these transformation elements has the structure of an infinite dimensional semi-group. This semi-group is a generalization of the Galilean line group discussed in [1]. We prove the properties of this semi-group. We calculate the Ricci tensor for this Newtownian spacetime. We calculate the coefficients in the transformed autoparallel equation, and show all three terms, including the term quadratic in the velocity, are nonzero in the general case. We show how these terms simplify to the autoparallel terms from the previous paper[1] in the case of no spatial dependence.
Language
English
Topic
Space and time.
Topic
Gravity.
Topic
Modeling.
Keyword
Group structure.
Keyword
Newton-Cartan method
Keyword
Geometric modeling.
Classification
QC
Related Item
Digital Grinnell
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Undergraduate Student Symposium
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Student Scholarship
Related Item
Mentored Advanced Project
Identifier (local)
grinnell:13271
Access Condition
Copyright to this work is held by the author(s), in accordance with United States copyright law (USC 17). Readers of this work have certain rights as defined by the law, including but not limited to fair use (17 USC 107 et seq.).
