Non Metric Mass

TL;DR

This paper explores the effects of non-metricity in generalized geometries on wave equations in general relativity, revealing new conditions and properties when metric compatibility is relaxed.

Contribution

It introduces a modified wave equation incorporating non-metricity and analyzes its implications and properties in generalized geometric frameworks.

Findings

Wave equation acquires a non-zero M term with non-metricity.

Derived conditions relating non-metricity to wave propagation.

Analyzed properties of the M function in non-metric geometries.

Abstract

In general relativity g_ab;c=0 implies that the wave equation (\Box^2-M)g_ab=0 always has M=0. If the underlying geometry is generalized to include non-metricity this incurs M \neq 0, and the above wave equation can be rewritten as M(x)+\td{\na}_a Q_.^a+(\ep+\fr{d}{2}-2)Q_a Q_.^a=0, where \ep=0, 1, 2, or 3, d is the dimension of the spacetime, and Q is the object of non-metricity. The consequences of this equation and the properties of M are investigated.