Un-graviton corrections to the Schwarzschild black hole

TL;DR

This paper develops an effective action incorporating un-gravity effects into Einstein's equations, leading to a corrected Schwarzschild solution and revealing a fractal-like event horizon structure in the un-gravity regime.

Contribution

It introduces a novel effective action approach to include un-gravity effects in black hole solutions, confirming the un-gravity corrected Schwarzschild metric and uncovering a fractal horizon structure.

Findings

Un-gravity effects modify the Schwarzschild geometry.

The event horizon exhibits fractal properties with dimension twice the un-gravity scale.

The approach confirms previous un-gravity corrections to black hole metrics.

Abstract

We introduce an effective action smoothly extending the standard Einstein-Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original ``guess'' of the form of the Un-Schwarzschild metric. Instead of working in the weak field approximation and ``dressing'' the Newtonian potential with un-gravitons, we solve the ``effective Einstein equations'' including all order un-gravity effects. An unexpected ``bonus'' of accounting un-gravity effects is the fractalisation of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension d_U.