Cosmological production of noncommutative black holes

TL;DR

This paper explores the quantum creation of noncommutative black holes in a de Sitter universe, deriving new solutions, analyzing their properties, and assessing their production likelihood during cosmic inflation.

Contribution

It introduces a noncommutative geometry inspired Schwarzschild deSitter solution and analyzes black hole pair creation in this context, including stability and production rates during inflation.

Findings

New noncommutative black hole solutions with multiple horizons.

DeSitter space remains stable against black hole pair production today.

High production of Planck-sized black holes during inflation, but disfavoured at Planckian cosmological constants.

Abstract

We investigate the pair creation of noncommutative black holes in a background with positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild deSitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive mass spacetimes admit one cosmological horizon and two, one or no black hole horizons, while negative mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the non-singular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the deSitter background is quantum mechanically stable according to experience. However positive mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the universe, Planck size black holes production would have been largely disfavoured. We also find a potential instability for production of negative-mass solitons.