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The gravitational field of a body with rotational symmetry in Einstein's theory of gravitation

Citation

Zhou, Peiyuan (1928) The gravitational field of a body with rotational symmetry in Einstein's theory of gravitation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06282004-092506

Abstract

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Einstein's set of field equations in vaccuo [...] is reduced to such a form that simple problems like the sphere (Schwarzschild's solution), the infinite plane and the infinite cylinder can be solved. The fundamental quadratic differential forms for the latter two cases are respectively [...] where [...] is the surface density of matter on the plane, [...] the linear density of matter on the cylinder, p=const.; (p,z,[...]) the cylindrical coordinates; [...] an indeterminate constant and the velocity of light is unity. Setting [...] = the Newtonian potential [plus] const., we can get the solution of the general gravitational problem for a body whose mass is distributed symmetrically about an axis provided we can solve [...]. The gravitational field of an oblate spheroidal homoeoid is characterized by [...] where [...], M = mass of the homoeoid whose equation is [...] and [...] are related to the cylindrical coordinates (p,z,[...]) by [...]. Analogous expressions for a prolate spheroidal homoeoid are obtainable. The oblateness of the homoeoid causes a slight increase in the advance of the perihelion of a planet's orbit derived from Schwarzschild's solution.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bell, Eric Temple
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1928
Record Number:CaltechETD:etd-06282004-092506
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06282004-092506
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2747
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:29 Jun 2004
Last Modified:26 Dec 2012 02:54

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