[1/5/2] Multi black holes

Case that the space-time asymptotically approaches to the de Sitter universe at the infinity.

According to the paper ``Cosmological multi-black-hole solutions, Physical Review D, Vol.47, pp.5370-5375 (1993)'', the following interesting metric:

ds^2 = -(1/F^2)dt^2+(F*G)^2(dx^2+dy^2+dz^2),
　F = 1+Σ(Mi/Ri)/G,
　G = exp(H*t),
　Ri = sqrt((x-xi)^2+(y-yi)^2+(z-zi)^2)

approaches to the de Sitter universe at the infinity and has n (> 0) charged black holes, where H is the Hubble constant, Mi and (xi, yi, zi), respectively, are the mass and the position of an i-th black hole (0 < i <= n). Because the attraction by the gravity and the repulsion by the charge are balanced, all the black holes are stable at any given positions in the de Sitter universe. The interesting points are
(1) We can put black holes of any masses at any positions in the de Sitter universe.
(2) When the Hubble constant is negative, the universe is contracting with some speed. If there are two black holes in this kind of contracting universe, we can watch a collision of the black holes, though it is a bit different from the usual sense of the collision of black holes.

[1/5/2/1] Double black holes
[1/5/2/2] Collision of black holes
[1/5/2/3] Lined up black holes: This metric can put arbitrary number of black holes at arbitrary positions.

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