Harrison metrics for the Schwarzschild black hole

TL;DR

This paper develops a method to generate Harrison metrics for Schwarzschild black holes using SL(2, R) symmetries, introducing a new metric and analyzing its conformal generators near the horizon.

Contribution

It presents a novel procedure to produce a family of Harrison metrics from SL(2, R) vector fields, including a new metric inspired by Kerr black hole geometry.

Findings

New Harrison metric for Schwarzschild black hole identified

Conformal generators analyzed via Killing equations near the horizon

Method applicable to generate metrics from symmetry vector fields

Abstract

Based on the hidden conformal symmetry, some authors have proposed a Harrison metric for the Schwarzschild black hole. We give a procedure which can generate a family of Harrison metrics starting from a general set of SL(2, R) vector fields. By analogy with the subtracted geometry of the Kerr black hole, we find a new Harrison metric for the Schwarzschild case. Its conformal generators are also investigated using the Killing equations in the near-horizon limit.