Resolving curvature singularities in holomorphic gravity

We formulate a 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 (Mantz and Prokopec in arXiv:0804.0213v1, 2008), 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. Our study of light bending and gravitational waves in weak holomorphic gravitational fields strongly suggests that holomorphic gravity reduces to general relativity at large distance scales.