Evidence for Planck luminosity bound in quantum gravity

Abstract Recently, we introduced a non-perturbative quantization of impulsive gravitational null initial data. In this note, we investigate an immediate physical implication of the model. One of the quantum numbers is the total luminosity carried to infinity. We show that a transition happens when the luminosity reaches the Planck power <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">P</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . Below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">P</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous. A physical state that lies in the continuous spectrum consists of a superposition of kinematical states in which the shear is unbounded from above. We argue that such states are unphysical because they contain caustics that are in conflict with the falloff conditions at asymptotic infinity.