Extreme Kerr black hole microstates with horizon fluff

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of \(1.0 \times 10^{-21}\). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 {\sigma}. The source lies at a luminosity distance of \(410^{+160}_{-180}\) Mpc corresponding to a redshift \(z = 0.09^{+0.03}_{-0.04}\). In the source frame, the initial black hole masses are \(36^{+5}_{-4} M_\odot\) and \(29^{+4}_{-4} M_\odot\), and the final black hole mass is \(62^{+4}_{-4} M_\odot\), with \(3.0^{+0.5}_{-0.5} M_\odot c^2\) radiated in gravitational waves. All uncertainties define 90% credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

We consider a general, classical theory of gravity with arbitrary matter fields in \(n\) dimensions, arising from a diffeomorphism invariant Lagrangian, \(\bL\). We first show that \(\bL\) always can be written in a ``manifestly covariant" form. We then show that the symplectic potential current \((n-1)\)-form, \(\th\), and the symplectic current \((n-1)\)-form, \(\om\), for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current \((n-1)\)-form, \(\bJ\), and corresponding Noether charge \((n-2)\)-form, \(\bQ\). We derive a general ``decomposition formula" for \(\bQ\). Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, \(S_{dyn}\), of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of \(\bL\), \(\th\), and \(\bQ\). However, the issue of whether this dynamical entropy in general obeys a ``second law" of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.