Kaluza-Klein Bubble With Massive Scalar Field

TL;DR

This paper modifies a five-dimensional Kaluza-Klein bubble solution by adding a massive scalar field, resulting in a quantized gravitational mass that remedies previous violations of the equivalence principle.

Contribution

It introduces a massive scalar field into the Kaluza-Klein bubble, leading to a quantized mass and improved physical consistency in the classical setting.

Findings

Mass of the bubble is quantized as m_P / (4 √α).

Scalar field becomes short-range, fixing equivalence principle issues.

Mass quantization is an attractor for the field equations.

Abstract

A well-known soliton (bubble) solution of five-dimensional Kaluza-Klein General Relativity is modified by imposing mass on the scalar field. By forcing the scalar field to be short-range, the failure of the original bubble solution to satisfy the equivalence principle is remedied, and the bubble acquires gravitational mass.Most importantly, the mass is quantized, even in this classical setting, and has a value $m_P / (4 \sqrt{\alpha})$, where $m_P$ is the Planck mass,and $\alpha$ is the fine-structure constant. This result applies for any choice of scalar-field mass, as it is an attractor for the field equations.