Lee-Wick Black Holes

TL;DR

This paper explores black hole solutions in a higher derivative Lee-Wick gravity theory, revealing the existence of singularity-free black holes with horizons and stable remnants after evaporation.

Contribution

It introduces approximate static vacuum solutions in Lee-Wick gravity, showing the formation of regular black holes with critical mass and extremal states.

Findings

Existence of singularity-free black holes for masses above a critical value

Black holes develop an outer horizon and an inner Cauchy horizon

Black hole evaporation results in a zero-temperature remnant

Abstract

We derive and study an approximate static vacuum solution generated by a point-like source in a higher derivative gravitational theory with a pair of complex conjugate ghosts. The gravitational theory is local and characterized by a high derivative operator compatible with Lee-Wick unitarity. In particular, the tree-level two-point function only shows a pair of complex conjugate poles besides the massless spin two graviton. We show that singularity-free black holes exist when the mass of the source $M$ exceeds a critical value $M_{\rm crit}$. For $M > M_{\rm crit}$ the spacetime structure is characterized by an outer event horizon and an inner Cauchy horizon, while for $M = M_{\rm crit}$ we have an extremal black hole with vanishing Hawking temperature. The evaporation process leads to a remnant that approaches the zero-temperature extremal black hole state in an infinite amount of time.