The Initial-Value Problem of Spherically Symmetric Wyman Sector Nonsymmetric Gravitational Theory

TL;DR

This paper reformulates the spherically symmetric initial-value problem of the Wyman sector in Nonsymmetric Gravitational Theory for numerical analysis, providing analytic and numerical insights into its solvability.

Contribution

It introduces a numerical framework for the initial-value problem in NGT's Wyman sector and analyzes its well-posedness and solvability limits.

Findings

Identified parameter regions where the initial-value problem is solvable.

Confirmed analytic solvability limits through numerical solutions.

Provided a formulation suitable for numerical simulations of NGT.

Abstract

We cast the four-dimensional field equations of the Nonsymmetric Gravitational Theory (NGT) into a form appropriate for numerical study. In doing so, we have restricted ourselves to spherically symmetric spacetimes, and we have kept only the Wyman sector of the theory. We investigate the well-posedness of the initial-value problem of NGT for a particular data set consisting of a pulse in the antisymmetric field on an asymptotically flat space background. We include some analytic results on the solvability of the initial-value problem which allow us to place limits on the regions of the parameter space where the initial-value problem is solvable. These results are confirmed by numerically solving the constraints.