Born-Infeld Determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

TL;DR

This paper presents an exact vacuum solution in Born-Infeld determinantal gravity in 3D that removes conical singularities and closed timelike curves, resulting in a regular, non-singular rotating spacetime with finite curvature invariants.

Contribution

It introduces a novel 3D vacuum solution in Born-Infeld gravity that eliminates conical singularities and closed timelike curves, enhancing the understanding of regular spacetimes in modified gravity.

Findings

The solution is a rotating, non-singular vacuum spacetime.

Curvature invariants vanish at asymptotic limits, indicating no divergences.

The spacetime ends at a minimal circle unreachable by particles, avoiding singularities.

Abstract

In the context of Born-Infeld \emph{determinantal} gravity formulated in a n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional \emph{vacuum} circular symmetric solution without cosmological constant consisting in a rotating spacetime with non singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.