Homothetic Wyman Spacetimes

TL;DR

This paper investigates homothetic Wyman spacetimes, revealing their equivalence to a scalar field with a repulsive potential, and explores their dynamic behavior near critical collapse points through numerical integration.

Contribution

It introduces a homothetic symmetry in Wyman spacetimes and analyzes the resulting autonomous system's behavior near critical points.

Findings

System exhibits periodic collapse and dispersal near criticality

Homothetic symmetry simplifies the analysis of Wyman spacetimes

Numerical integration reveals complex dynamical behavior

Abstract

The time-dependent, spherically symmetric, Wyman sector of the Unified Field Theory is shown to be equivalent to a self-gravitating scalar field with a positive-definite, repulsive self-interaction potential. A homothetic symmetry is imposed on the fundamental tensor, and the resulting autonomous system is numerically integrated. Near the critical point (between the collapsing and non-collapsing spacetimes) the system displays an approximately periodic alternation between collapsing and dispersive epochs.