Physics & Astronomy ETDs

Publication Date

7-11-1977

Abstract

A formalism for the manipulation of tensors in both real and complex spacetimes is introduced, which utilizes the irreducible representations of the Lorentz group to substantially simplify certain general relativistic calculations. The notation is completely covariant and is most effective for massless field calculations. Results emerge which eliminate the majority of the algebraic burden of the traditional Newman­Penrose formalism and, simultaneously, allow the reader to understand both the physical and geometrical meanings of each step of the derivations. The technique developed is well suited for perturbation analyses. Consequently, the perturbed wave equations for massless fields are examined. The notation has led to the successful decoupling and separation of the radiative components of perturbing scalar, neutrino, electromagnetic, and gravitational fields in an arbitrary vacuum type D background. These include the uncharged accelerating cases of Kinnersley and Walker. This generalizes the results of Teukolsky and others in non-accelerating backgrounds. The separation was accomplished in the coordinates of Plebanski and Demianski. In addition, the work of other authors regarding the use of the radiative solutions to evaluate other helicity components from the first-order perturbed field equations can be similarly generalized. For complex spacetimes, initial results from the application of the formalism to perturbed wave equations for type I (plane) hyper­Heavenly metrics are presented. The left-degenerated portion is perturbed for the gravitational case. The first of the five equations inherently decouples, and the second is coupled only to the first. For the remaining three the situation becomes progressively worse due to perturbed tetradial partial derivatives and perturbed connections. However, it is proposed that the decoupling could be completed for all five if the spacetime behaves in a specific manner. The necessary calculations to establish this speculation are not yet complete.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

James Daniel Finley III

Second Committee Member

Christopher Pratt Leavitt

Third Committee Member

Stanly Lee Steinberg

Fourth Committee Member

David Solomon King

Language

English

Document Type

Dissertation

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