Backreactions from loading the stable photon sphere in Weyl conformal gravity

TL;DR

This paper explores how loading null matter onto the stable photon sphere in Weyl conformal gravity affects the spacetime, revealing a new extremal horizon formation with unique geometric properties independent of cosmological curvature.

Contribution

It demonstrates that loading matter on the stable photon sphere in Weyl conformal gravity can produce an extremal horizon with AdS$_2\times$S$^2$ geometry, a novel phenomenon not seen in standard metrics.

Findings

Loading null matter on the stable photon sphere leaves its area unchanged.

A critical threshold loading produces an extremal horizon with AdS$_2\times$S$^2$ geometry.

Jump in radial pressure occurs unless the shell radius matches photon sphere radii.

Abstract

We investigate the accumulation of null matter at the stable photon sphere in the Mannheim-Kazanas metric, the analogue to the Schwarzschild solution in Weyl's conformal theory of gravity. In our toy problem in which we consider an infinitely-thin shell, we find that a jump in radial pressure ${T^r}_r$ is induced across the shell unless the shell has a radius of either the unstable or stable photon sphere radii. We then find that upon loading the stable photon sphere, its area remains invariant. Furthermore, at a critical threshold loading limit for this zero-width null matter shell, we are able to produce a metric containing an extremal horizon with an AdS$_2\times$S$^2$ geometry completely independent of the cosmological curvature. This hitherto unencountered and therefore unexpected result is a phenomenon unseen in standard nonconformal second-order metrics with nonzero cosmological constants.