A proof of holographic complexity conjecture: wormhole between horizon and singularity

TL;DR

This paper provides evidence supporting holographic complexity conjectures by analyzing a black hole's geometry with a wormhole connecting the horizon and singularity, suggesting the information paradox is a paradox of perception.

Contribution

It offers a novel geometric analysis of black holes that supports the complexity-volume and complexity-action conjectures, linking black hole structure to holographic complexity.

Findings

Black hole geometry resembles Gabriel's horn.

Supports complexity-volume and complexity-action conjectures.

Suggests the information paradox is a perceptual paradox.

Abstract

This letter provides evidence of complexity-volume and complexity-action conjectures by examining the structure of a black hole, which comprises a horizon linked to the singularity through a wormhole. In this situation, the shape of the black hole's geometry resembles that of Gabriel's horn. In essence, our results indicate that the information paradox is merely the painter's paradox.