The Penrose inequality for perturbations of the Schwarzschild initial data

TL;DR

This paper proves that the Penrose inequality holds for conformally flat perturbations of Schwarzschild initial data with small axially symmetric curvature, identifying conditions for equality.

Contribution

It demonstrates the Penrose inequality's validity under specific perturbations of Schwarzschild data and characterizes cases of equality.

Findings

Penrose inequality holds for small axially symmetric perturbations

Equality occurs only for special Schwarzschild sections

Results extend understanding of initial data perturbations

Abstract

We show that in the conformally flat case the Penrose inequality is satisfied for the Schwarzschild initial data with a small addition of the axially symmetric traceless exterior curvature. In this class the inequality is saturated only for data related to special sections of the Schwarzschild spacetime.