Interior of a Charged Distorted Black Hole

TL;DR

This paper investigates the interior structure of charged, distorted black holes, analyzing horizon properties, curvature, and free-fall dynamics, revealing a duality between horizons and conditions for Cauchy horizon regularity.

Contribution

It provides a detailed analysis of the inner geometry and horizon properties of charged distorted black holes, including a duality relation and conditions for horizon regularity.

Findings

Cauchy horizon remains regular under certain distortions.

Existence of a duality between outer and inner horizon properties.

Derived relations between curvature invariants and horizon surface curvature.

Abstract

We study interior of a charged, non-rotating distorted black hole. We consider static and axisymmetric black holes, and focus on a special case when an electrically charged distorted solution is obtained by the Harrison-Ernst transformation from an uncharged one. We demonstrate that the Cauchy horizon of such black hole remains regular, provided the distortion is regular at the event horizon. The shape and the inner geometry of both the outer and inner (Cauchy) horizons are studied. We demonstrate that there exists a duality between the properties of the horizons. Proper time of a free fall of a test particle moving in the interior of the distorted black hole along the symmetry axis is calculated. We also study the property of the curvature in the inner domain between the horizons. Simple relations between the 4D curvature invariants and the Gaussian curvature of the outer and inner horizon surfaces are found.