## Abstract

The black hole area theorem implies that when two black holes merge, the area of the final black hole should be greater than the sum of the areas of the two original black holes. We examine how this prediction can be tested with gravitational-wave observations of binary black holes. By separately fitting the early inspiral and final ringdown stages, we calculate the posterior distributions for the masses and spins of the two initial and the final black holes. This yields posterior distributions for the change in the area and thus a statistical test of the validity of the area increase law. We illustrate this method with a GW150914-like binary black hole waveform calculated using numerical relativity, and detector sensitivities representative of both the first observing run and the design configuration of Advanced LIGO. We obtain a ∼74.6% probability that the simulated signal is consistent with the area theorem with current sensitivity, improving to ∼99.9% when Advanced LIGO reaches design sensitivity. An important ingredient in our test is a method of estimating when the postmerger signal is well fit by a damped sinusoid ringdown waveform.

Original language | English |
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Article number | 124069 |

Journal | Physical Review D |

Volume | 97 |

Issue number | 12 |

DOIs | |

State | Published - 15 Jun 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018 American Physical Society.

### Funding

We thank Juan Caldern-Bustillo, Thomas Dent, Ben Farr, Will Farr, Domenico Giulini, David Keitel, Sebastian Khan, Andrew Lundgren, Frank Ohme and Reinhard Prix for interesting discussions. This research has made use of data, software and/or web tools obtained from the LIGO Open Science Center , a service of LIGO Laboratory and the LIGO Scientific Collaboration. LIGO is funded by the U.S. National Science Foundation. Virgo is funded by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale della Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by Polish and Hungarian institutes. O.F.-B. acknowledges the NSF for financial support from Grant No. PHY-1607520.

Funders | Funder number |
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Norsk Sykepleierforbund | PHY-1607520 |

National Science Foundation |