Particle-like platonic solutions in scalar gravity

TL;DR

This paper constructs new globally regular solutions with discrete symmetries in scalar gravity, specifically focusing on cubic symmetric solutions related to Yang-Mills-dilaton theory, and explores their relation to Einstein-Yang-Mills solutions.

Contribution

It introduces the first two solutions of the cubic N=4 sequence with discrete symmetries in scalar gravity, expanding the understanding of such solutions and their connection to known black hole solutions.

Findings

Presented the first two cubic N=4 solutions with discrete symmetry.

Suggested the sequence converges to an extremal Reissner-Nordstrom solution with magnetic charge 4.

Demonstrated solutions are exact or approximate in scalar and Einstein-Yang-Mills theories.

Abstract

We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein-Yang-Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map of degree N=4. We present the first two solutions of the cubic N=4 sequence, and expect this sequence to converge to an extremal Reissner-Nordstrom solution with magnetic charge P=4.