GW150914 verifies the black hole area theorem that the surface area of black holes should always increase over time How would you relate such area to the black hole mass At what statistical significan

The black hole area theorem states that the surface area of a black hole can never decrease over time. This is directly related to the black hole mass through the equation for the event horizon radius, which is proportional to the square root of the black hole mass. Therefore, as the mass of a black hole increases, so does its event horizon radius and surface area.

GW150914 provided strong evidence for the black hole area theorem, as the merger of two black holes resulted in the formation of a new, larger black hole with a surface area that was greater than the sum of the surface areas of the two original black holes. This increase in surface area is consistent with the black hole area theorem and provides strong support for the idea that the surface area of black holes always increases over time.

The statistical significance of this verification can be quantified through various methods, such as Bayesian model selection or hypothesis testing. In the case of GW150914, the detection of gravitational waves from the black hole merger was highly significant, with a false alarm probability of less than one in 203,000 years. This provides strong confidence in the observation and supports the verification of the black hole area theorem.