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 energeti
c 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 $a/M_h approx 0.99pm 0.01$ 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.
It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $ t=constant $ slice, which can
be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider {it booste
The horizon (the surface) of a black hole is a null surface, defined by those hypothetical outgoing light rays that just hover under the influence of the strong gravity at the surface. Because the light rays are orthogonal to the spatial 2-dimensiona
l surface at one instant of time, the surface of the black hole is the same for all observers (i.e. the same for all coordinate definitions of instant of time). This value is 4*(pi)* (2Gm/c^2)^2 for nonspinning black holes, with G= Newtons constant, c= speed of light, and m= mass of the black hole. The 3-dimensional spatial volume inside a black hole, in contrast, depends explicitly on the definition of time, and can even be time dependent, or zero. We give examples of the volume found inside a standard, nonspinning spherical black hole, for several different standard time-coordinate definitions. Elucidating these results for the volume provides a new pedagogical resource of facts already known in principle to the relativity community, but rarely worked out.
