Wormhole solutions in quantum spacetime

Abstract Polymer models have been used to describe non-singular quantum black holes, where the classical singularity is replaced by a transition from a black hole to a white hole. In a previous letter, in the context of a uni-parametric model with asymptotic flat exterior metric, we fixed the radius of the transition surface through the identification of its area with the area gap of loop quantum gravity. This revealed a dependence of the polymerisation parameter on the black hole mass, where the former increases as the latter decreases. It also enabled the extension of the model to Planck-scale black holes. We have identified the existence of limiting states with masses <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> and zero surface gravity, showing that Hawking evaporation asymptotically leads to remnant black holes of Planck size. In the present paper, we consider solutions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , again observing the presence of a minimal radius, but without formation of horizons. Unlike the previous mass range, only charged solutions are allowed in this case. We show that these non-singular solutions can be extended to static wormholes with a throat at the minimal radius, traversable by null geodesics and by test particles with high enough kinetic energy.