Resolving Curvature Singularities in Holomorphic Gravity

TL;DR

This paper introduces a holomorphic theory of gravity that modifies classical singularities like black holes and the Big Bang, suggesting they may not be encountered by observers, and explores its properties and relation to general relativity.

Contribution

It formulates a holomorphic gravity model that alters singular solutions of general relativity and investigates its implications and similarities to Hermitian gravity.

Findings

Observers do not encounter singularities in holomorphic black holes.

The model reduces to general relativity at large distances.

Holomorphic gravity does not respect reciprocity symmetry.

Abstract

We formulate holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity. Likewise, typical observers do not experience Big Bang singularity. Unlike Hermitian gravity \cite{MantzHermitianGravity}, Holomorphic gravity does not respect the reciprocity symmetry and thus it is mainly a toy model for a gravity theory formulated on complex space-times. Yet it is a model that deserves a closer investigation since in many aspects it resembles Hermitian gravity and yet calculations are simpler. We have indications that holomorphic gravity reduces to the laws of general relativity correctly at large distance scales.