Dynamic $C$ metrics in gauged supergravities

We construct an exact time-dependent charged dilaton $C$ metric in four-dimensional $\mathcal{N}=4$ gauged supergravity. The scalar field drives the time evolution by transferring energy to the black holes, thereby causing their masses to increase and their acceleration to decrease. The values of the electric/magnetic and scalar charges determine three regions of potential time evolution. This solution holographically describes a strongly coupled three-dimensional conformal field theory on the background of an evolving black hole. We also find new static charged dilaton $C$ metrics, which arise in four-dimensional Einstein-Maxwell-dilaton theories whose scalar potential can be expressed in terms of a superpotential.

Figure 1

Three types of time evolution of the effective mass $m(u)$.

Figure 2

The effective mass $m(u)$ for $m(0)=1$ and $m(\infty )=2$, 3 and 4.