Quantum black hole spectroscopy: probing the quantum nature of the black hole area using LIGO–Virgo ringdown detections
Danny Laghi, Gregorio Carullo, John Veitch, Walter Del Pozzo
Abstract
Abstract We present a thorough observational investigation of the heuristic quantised ringdown model presented by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). This model is based on the Bekenstein–Mukhanov conjecture, stating that the area of a black hole (BH) horizon is an integer multiple of the Planck area <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">P</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> multiplied by a phenomenological constant, α , which can be viewed as an additional BH intrinsic parameter. Our approach is based on a time-domain analysis of the gravitational wave (GW) signals produced by the ringdown phase of binary BH mergers detected by the LIGO and Virgo collaboration. Employing a full Bayesian formalism and taking into account the complete correlation structure among the BH parameters, we show that the value of α cannot be constrained using only GW150914, in contrast to what was suggested by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). We proceed to repeat the same analysis on the new GW events detected by the LIGO and Virgo Collaboration up to 1 October 2019, obtaining a combined-event measure equal to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>15</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>13.3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>20.5</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and a combined log odds ratio of 0.1 ± 0.6, implying that current data are not informative enough to favor or discard this model against general relativity. We then show that using a population of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">O</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> GW150914-like simulated events—detected by the current infrastructure of ground-based detectors at their design sensitivity—it is possible to confidently falsify the quantised model or prove its validity, in which case probing α at the few % level. Finally we classify the stealth biases that may show up in a population study.