A Derivation Of The Scalar Propagator In A Planar Model In Curved Space

TL;DR

This paper derives the scalar propagator in a curved 2+1 dimensional space using a modified Antonsen-Bormann method, extending the flat space result to a rotating black hole background.

Contribution

It introduces a novel derivation of the scalar propagator in curved space employing a modified Antonsen-Bormann approach, differing from traditional proper time methods.

Findings

Derived the scalar propagator in a rotating black hole background.

Extended flat space propagator results to curved spacetime.

Provided explicit formulas for the propagator in the given geometry.

Abstract

Given that the free massive scalar propagator in 2 + 1 dimensional Euclidean space is $D(x-y)=\frac{1}{4\pi \rho} 0.25cm e^{-m \rho} $ with $\rho^2=(x-y)^2$ we present the counterpart of $D(x-y)$ in curved space with a suitably modified version of the Antonsen - Bormann method instead of the familiar Schwinger - de Witt proper time approach, the metric being defined by the rotating solution of Deser et al. of the Einstein field equations associated with a single massless spinning particle located at the origin.