Classical Kalb-Ramond field theory in curved spacetimes

TL;DR

This paper develops the classical Kalb-Ramond field theory in curved spacetimes, analyzing solutions with static sources and exploring the possibility of polarization effects similar to dielectric polarization in Maxwell theory.

Contribution

It extends the classical Kalb-Ramond theory to curved spacetimes and investigates polarization phenomena, paralleling Maxwell electrodynamics.

Findings

Solutions of Kalb-Ramond in various curved spacetimes analyzed

Potential polarization effects in curved spacetimes discussed

Comparison with dielectric polarization in Maxwell theory

Abstract

We propose to develop the Kalb-Ramond theory in four-dimensional spacetime at the level of a classical field theory by following the same formal development steps as in Maxwell theory of standard electrodynamics. Solutions of Kalb-Ramond theory in the presence of static sources in various curved spacetimes are then analyzed. A question that we address here is that of a possible Kalb-Ramond polarization in curved spacetimes, like one can encounter a dielectric polarization in ordinary Maxwell electrodynamics in certain types of spacetimes.