Testing the Black-Hole Area Law with GW150914

We present observational confirmation of Hawking’s black-hole area theorem based on data from GW150914, finding agreement with the prediction with 97% (95%) probability when we model the ringdown including (excluding) overtones of the quadrupolar mode. We obtain this result from a new time-domain analysis of the pre- and postmerger data. We also confirm that the inspiral and ringdown portions of the signal are consistent with the same remnant mass and spin, in agreement with general relativity.

Figure 1

GW150914 reconstruction. Hanford waveforms drawn randomly from the posterior of the premerger (blue) and postmerger (orange) analyses, compared to a draw from the full inspiral-merger-ringdown analysis (black). The bottom panel shows the corresponding whitened residuals obtained by subtracting the maximum a posteriori (MAP) piecewise waveforms from the data. The detector data are sampled at 2048 Hz, and the time origin corresponds to the truncation time ($t=1126259462.423\mathrm{s}\mathrm{GPS}$).

Figure 2

Fractional change in the horizon area before and after the GW150914 merger, $\mathrm{\Delta }\mathcal{A}/{\mathcal{A}}_0=({\mathcal{A}}_f-{\mathcal{A}}_0)/{\mathcal{A}}_0$. We infer the premerger area ${\mathcal{A}}_0$ from the inspiral alone (Fig. 1). We infer the postmerger area ${\mathcal{A}}_f$ from the remnant mass and spin as estimated from an analysis of the ringdown using the fundamental mode and one overtone at the peak (green), as well as solely the fundamental mode 3 ms after the peak (orange). For the former (latter), we measure $\mathrm{\Delta }\mathcal{A}/{\mathcal{A}}_0=0.52_{-0.47}^{+0.71}(0.60_{-0.60}^{+0.82})$ at 90% credibility and find agreement with Hawking’s area theorem with 97% (95%) probability.

Figure 3

Measurements of $\mathrm{\Delta }\mathcal{A}/{\mathcal{A}}_0$ (ordinate) obtained by truncating the inspiral at different times before the peak (abscissa), and with respect to two ringdown measurements (color). Bars show the symmetric 90% credible interval around the median, itself indicated by a marker. The rightmost points correspond to the distributions in Fig. 2. All measurements support the area theorem, with probabilities within $88\%-97\%$.

Figure 4

Redshifted remnant BH mass $m_f$ (abscissa) and dimensionless spin ${\chi }_f$ (ordinate), as inferred from different segments of the GW150914 data. One measurement is based on the prepeak inspiral data alone (dashed blue); two others focus on the postpeak ringdown data, using either the fundamental mode plus an overtone at the peak (solid green) or just the fundamental 3 ms after the peak (dash-dotted orange); one final measurement relies on the full inspiral-merger-ringdown signal (dotted black). Contours enclose 90% of the probability mass, while the top and right panels show the $m_f$ and ${\chi }_f$ marginals respectively. All measurements agree.