On Conformally Flat Stationary Axisymmetric Spacetimes

TL;DR

This paper identifies a new class of conformally flat stationary axisymmetric spacetimes beyond the static family, characterized by an arbitrary function linked to the matter content, with potential implications for black hole models on branes.

Contribution

It introduces a novel class of conformally flat stationary axisymmetric metrics, expanding the known solutions beyond static cases, with explicit dependence on matter distribution.

Findings

Existence of a new class of metrics in conformally flat stationary axisymmetric spacetimes.

Metrics depend on an arbitrary function determined by matter content.

Potential applications to black holes on two-branes in four dimensions.

Abstract

It is shown that within conformally flat stationary axisymmetric spacetimes, besides of the static family, there exists a new class of metrics, which is always stationary and axisymmetric. All these spacetimes, the static and the stationary ones, are endowed with an arbitrary function depending on the two non--Killingian coordinates. The explicit form of this function can be determined once the coupled matter, i.e., the energy--momentum tensor is given. One might hope possible extensions of this result to black holes on two--branes in four dimensions.