Polymer Schwarzschild black hole: An effective metric

Understand

We consider the modified Einstein equations obtained in the framework of effective spherically symmetric polymer models inspired by Loop Quantum Gravity.

• When one takes into account the anomaly free point-wise holonomy quantum corrections, the modification of Einstein equations is parametrized by a function $f(x)$ of one phase space variable.
• We solve explicitly these equations for a static interior black hole geometry and find the effective metric describing the trapped region, inside the black hole, for any $f(x)$.
• This general resolution allows to take into account a standard ambiguity inherent to the polymer regularization: namely the choice of the spin $j$ labelling the SU$(2)$-representation of the holonomy corrections.