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

Related Item

Undergraduate Student Symposium

Related Item

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.).