Search for echoes on the edge of quantum black holes

Abstract I perform a template-based search for stimulated emission of Hawking radiation (or Boltzmann echoes) by combining the gravitational wave data from 47 binary black hole merger events observed by the LIGO-Virgo-KAGRA collaboration. With a Bayesian inference approach, I found no statistically significant evidence for this signal in either of the 3 Gravitational Wave Transient Catalogs GWTC-1, GWTC-2 and GWTC-3. While the data does not provide definitive evidence against the presence of Boltzmann echoes, the Bayesian evidence for most events falls within the range of 0.3–1.6, with the hypothesis of a common (non-vanishing) echo amplitude for all mergers being weakly disfavored at 2:5 odds. The only exception is GW190521, the most massive and confidently detected event ever observed, which shows a positive evidence of 9.2 for stimulated Hawking radiation. The ‘look-elsewhere’ effect for this outlier event is assessed by applying two distinct methods to add simulated signals in real data, before and after the event, giving false (true) positive detection probabilities for higher Bayes factors of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mn>1.5</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mn>4.4</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2.0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>35</mml:mn> <mml:mo>±</mml:mo> <mml:mn>7</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>35</mml:mn> <mml:mo>±</mml:mo> <mml:mn>15</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> ). An optimal combination of posteriors yields an upper limit of A &lt; 0.4 (at 90% confidence level) for a universal echo amplitude, whereas <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> was predicted in the canonical model. To ensure the robustness of the results, I have employed an additional method to combine the events hierarchically. This approach involves using a target Gaussian distribution and extracting the parameters from multiple uncertain observations, which may be affected by selection biases.