Multiwormholes and multi-black-holes in three dimensions

Abstract

We construct time-dependent multi-centre solutions to threedimensional general relativity with zero or negative cosmological constant. These solutions correspond to dynamical systems of freely falling black holes and conical singularities, with a multiply connected spacetime topology. Stationary multi-black-hole solutions are possible only in the extreme black hole case.

The gravitating model in 2 + 1 dimensions: black hole solutions

“…The resulting generalized Penrose diagram is similar to the diagram (Fig. 6) for the one-black hole spacetime, with multiple lines at 45 o standing for the multiple horizon components [26].…”

“…κν 2 a 2 = 4(1 − n)/n (n positive integer) for the first class of solutions, and κ < 0 for the black holes of the second class. However, besides the p black holes, additional conical singularities will in general be present at the (N − 1) zeroes z j of the function w ′ (z) [25] [26]. It is in principle possible to choose the parameters in (5.1) so that these conical singularities are absent, which is the case if the parameters are constrained by the 2(N − 1) relations n i=1 A i a q i = 0, (5.8)…”

“…We briefly discuss the dynamical evolution of such two-black hole systems generated from the different types of one-black holes encountered in this paper. In the case of the first-class black holes with n odd (n > 1; the case n = 1 is treated in [26]), the consideration of the generic timelike or null geodesic 3 leads to the following picture. A distant observer sees a single past horizon suddenly developing a conical singularity and bifurcating.…”

Multi-centered AdS3 solutions from Virasoro conformal blocks

“…[29]), that placing such strong restrictions on the monodromy group does not lead to a solution unless one introduces so-called spurious singularities in the differential equation (1.6). These are precisely the unphysical singularities found in [26][27][28].…”

“…Finally, in section 5, we will briefly comment on multi-centered solutions for which the metric is static rather than stationary, and give a new perspective on the observed phenomenon that such solutions always seem to have additional unphysical singularities [26][27][28]. We will show that a static ansatz restricts the monodromy group discussed above to be abelian.…”