Towards nonsingular rotating compact object in ghost-free infinite derivative gravity

TL;DR

This paper explores how ghost-free infinite derivative gravity can eliminate the ring singularity in rotating compact objects, potentially leading to nonsingular solutions without horizons, unlike classical Kerr black holes.

Contribution

It demonstrates that non-locality in IDG can smear out singularities in rotating metrics and shows Kerr metric does not solve the full non-linear equations of IDG.

Findings

Ring singularity can be resolved in IDG by smearing delta sources.

Kerr metric does not satisfy the full non-linear IDG equations.

No horizons form in the linear regime for smeared ring sources.

Abstract

The vacuum solution of Einstein's theory of general relativity provides a rotating metric with a ring singularity, which is covered by the inner and outer horizons, and an ergo region. In this paper, we will discuss how ghost-free, quadratic curvature, Infinite Derivative Gravity (IDG) may resolve the ring singularity. In IDG the non-locality of the gravitational interaction can smear out the delta-Dirac source distribution by making the metric potential finite everywhere including at $r=0$. We show that the same feature also holds for a rotating metric. We can resolve the ring singularity such that no horizons are formed in the linear regime by smearing out a delta-source distribution on a ring. We will also show that the Kerr-metric does not solve the full non-linear equations of motion of ghost-free quadratic curvature IDG.