Dynamical black rings with a positive cosmological constant

We construct dynamical black ring solutions in the five-dimensional Einstein-Maxwell system with a positive cosmological constant and investigate the geometrical structure. The solutions describe the physical process such that a thin black ring at early time shrinks and changes into a single black hole as time increases. We also discuss the multiblack rings and the coalescence of them.

Figure 1

Time evolution of the event horizon for a single black ring in $r_1–r_2$ plane. Coordinate values of the event horizon of each time slices are plotted. We set parameters $\lambda =1$, $m=1/2$, $a=1$.

Figure 2

Time evolution of the event horizon for concentric black rings in $r_1–r_2$ plane. Coordinate values of the event horizon of each time slices are plotted. We set parameters $\lambda =1$, $m_1=m_2=1/4$, $a_1=1$, $a_2=2$.

Figure 3

Time evolution of the event horizon for orthogonal black rings in $r_1–r_2$ plane. Coordinate values of the event horizon of each time slices are plotted. We set parameters $\lambda =1$, $m=n=1/4$, $a=b=1$.