On a General Class of Wormhole Geometries

TL;DR

This paper introduces a broad class of spherically symmetric wormhole solutions supported by an anisotropic matter source, emphasizing matter manipulation over geometric construction, and explores their potential to connect multiple universes.

Contribution

It presents a new, flexible framework for wormhole geometries using arbitrary functions and matter fields, allowing positive mass and minimized energy condition violations.

Findings

Multiple explicit wormhole solutions are constructed.

The solutions can connect finite or infinite universes.

Positive stellar mass is achievable with minimal energy violations.

Abstract

A general class of solutions is obtained which describe a spherically symmetric wormhole system. The presence of arbitrary functions allows one to describe infinitely many wormhole systems of this type. The source of the stress-energy supporting the structure consists of an anisotropic brown dwarf ``star'' which smoothly joins the vacuum and may possess an arbitrary cosmological constant. It is demonstrated how this set of solutions allows for a non-zero energy density and therefore allows positive stellar mass as well as how violations of energy conditions may be minimized. Unlike examples considered thus far, emphasis here is placed on construction by manipulating the matter field as opposed to the metric. This scheme is generally more physical than the purely geometric method. Finally, explicit examples are constructed including an example which demonstrates how multiple closed universes may be connected by such wormholes. The number of connected universes may be finite or infinite.