Final Mass and Spin of Merged Black Holes and the Golden Black Hole

Abstract

We present results on the mass and spin of the final black hole from mergers of equal mass, spinning black holes. The study extends over a broad range of initial orbital configurations, from direct plunges to quasi-circular inspirals to more energetic orbits (generalizations of Newtonian elliptical orbits). It provides a comprehensive search of those configurations that maximize the final spin of the remnant black hole. We estimate that the final spin can reach a maximum spin $a/M_h \approx 0.99\pm 0.01$ for extremal black hole mergers. In addition, we find that, as one increases the orbital angular momentum from small values, the mergers produce black holes with mass and spin parameters $\lbrace M_h/M, a/M_h \rbrace$ ~spiraling around the values $\lbrace \hat M_h/M, \hat a/M_h \rbrace$ of a {\it golden} black hole. Specifically, $(M_h-\hat M_h)/M \propto e^{\pm B\,\phi}\cos{\phi}$ and $(a-\hat a)/M_h \propto e^{\pm C\,\phi}\sin{\phi}$, with $\phi$ a monotonically growing function of the initial orbital angular momentum. We find that the values of the parameters for the \emph{golden} black hole are those of the final black hole obtained from the merger of a binary with the corresponding spinning black holes in a quasi-circular inspiral.