# A Penrose-Type Inequality with Angular Momentum and Charge for Axisymmetric Initial Data

## TL;DR

This paper establishes a lower bound for the ADM mass in axisymmetric Einstein-Maxwell initial data, linking it to angular momentum, charge, and horizon area, and proves conditions for equality with Kerr-Newman solutions.

## Contribution

It introduces a Penrose-type inequality incorporating angular momentum and charge for axisymmetric initial data, extending previous results and providing a rigidity condition for Kerr-Newman spacetime.

## Key findings

- Derived a mass inequality involving angular momentum, charge, and horizon area.
- Proved the inequality reduces to the Kerr-Newman case under certain conditions.
- Established a rigidity statement characterizing Kerr-Newman data as the equality case.

## Abstract

A lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the horizon, the given data agree to a certain extent with the associated model Kerr-Newman data, then the inequality reduces to the conjectured Penrose inequality with angular momentum and charge. In addition, a rigidity statement is also proven whereby equality is achieved if and only if the data set arises from the canonical slice of a Kerr-Newman spacetime.