Regular black hole from a confined spin connection in Poincare gauge gravity

TL;DR

This paper proposes a new regular black hole solution within Poincare gauge gravity, where an asymptotically free spin connection leads to a trivial ultraviolet fixed point, addressing issues with RG-improved spacetimes in the presence of a cosmological constant.

Contribution

It introduces a novel regular black hole model in Poincare gauge gravity with an asymptotically free spin connection, ensuring a trivial UV fixed point for the cosmological constant.

Findings

A regular black hole solution consistent with asymptotic safety.

The spin connection's asymptotic freedom generates a trivial UV fixed point.

Addresses limitations of RG-improved spacetimes with cosmological constant.

Abstract

Within the asymptotic safety program, it is possible to construct renormalization group (RG) improved spacetimes by replacing the gravitational coupling $G$ by its running counterpart $G(k)$, and subsequently identifying the RG scale $k$ with a physical distance scale. This procedure has been used to construct a regular Schwarzschild geometry, but it fails in the presence of a cosmological constant. This can only be avoided if the dimensionless cosmological constant has a trivial ultraviolet fixed point, but so far no such scenario has been encountered in quantum general relativity (with or without matter). In this Letter we provide a possible solution to this problem. In Poincare gauge gravity an effective cosmological constant arises naturally, and if the non-Abelian Lorentz spin connection is asymptotically free, it generates a trivial ultraviolet fixed point for this cosmological constant. We thereby tentatively propose a nonsingular black hole consistent with the principles of asymptotic safety, embedded in Poincare gauge gravity.