Charged quantum Oppenheimer–Snyder model

Abstract

Abstract In the framework of loop quantum cosmology, particularly within the quantum Oppenheimer–Snyder model, the semiclassical Ashtekar–Pawlowski–Singh (APS) metric is associated with a static, spherically symmetric black hole that incorporates quantum effects derived from the APS metric. This quantum-corrected black hole can be interpreted as a modified Schwarzschild black hole, where the Schwarzschild metric function is adjusted by an additional term proportional to $$\frac{M^{2}}{r^{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi>r</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mfrac> </mml:math> , with r denoting the radial coordinate and M , the black hole mass. In this study, we show that such a quantum-mechanically modified black hole can arise in the context of nonlinear electrodynamics with either electric or magnetic charge. This charged, quantum-corrected solution is then matched to a dust ball of constant mass $$M_{APS}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>APS</mml:mi> </mml:mrow> </mml:msub> </mml:math> , governed by the APS metric, at a timelike thin-shell possessing nonzero mass m and electric charge Q or magnetic charge P . Analytically, it is demonstrated that the thin-shell oscillates around an equilibrium radius $$r=R_{eq}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>eq</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , which is expressed in terms of $$M_{APS}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>APS</mml:mi> </mml:mrow> </mml:msub> </mml:math> , m , and Q or P .

Topics & Concepts