New class of exact solutions in Einstein-Maxwell-dilaton theory

We find new solutions to the five-dimensional Einstein-Maxwell-dilaton theory with cosmological constant where the dilaton field couples to the electromagnetic field as well as to the cosmological term with two different coupling constants. The five-dimensional spacetime is nonstationary and is a conformally regular spacetime, everywhere. Both the dilaton field and the electromagnetic field depend on time and two spatial directions. The cosmological constant takes a positive, negative, or zero value, depending on the value of the coupling constant. We study the physical properties of the spacetime, and we show that the solutions are unique in five dimensions and that they cannot be uplifted to higher-dimensional Einstein-Maxwell theory or Einstein gravity in the presence of the cosmological constant. Moreover, we construct new solutions to the theory in which both coupling constants are equal.

Figure 1

The metric function $H(r,\theta )$ as a function of $r$ and $x=\cos \theta$, where we set $h=2,g_{+}=5,g_{-}=3,a=1$.

Figure 2

The $r$-component of electric field as function of $r$ and $x=\cos \theta$ for three time slices, $t=1$ (upper surface), $t=10$ (middle surface), and $t=100$ (lower surface), where we set $h=2$, $g_{+}=5$, $g_{-}=3$, $a=1$, $\xi =2$, $\zeta =4$.

Figure 3

The $\theta$-component of the electric field as a function of $r$ and $x=\cos \theta$ for three time slices, $t=1$ (upper surface), $t=10$ (middle surface), and $t=100$ (lower surface), where we set $h=2$, $g_{+}=5$, $g_{-}=3$, $a=1$, $\xi =2$, $\zeta =4$.

Figure 4

The dilaton field $\varphi (t,r,\theta )$ as a function of $r$ and $x=\cos \theta$ for three time slices, $t=1$ (upper surface), $t=10$ (middle surface), and $t=100$ (lower surface), where we set $h=2$, $g_{+}=5$, $g_{-}=3$, $a=1$, $\xi =2$, $\zeta =4$.

Figure 5

The metric function $H(t,r,\theta )$ as a function of $r$ and $x=\cos \theta$ for three time slices, $t=1$ (upper surface), $t=2$ (middle surface), and $t=5$ (lower surface), where we set $h=2,k_{+}=5,k_{-}=3,a=1,\mu =1,\nu =2$.

Figure 6

The dilaton $\varphi (t,r,\theta )$ as a function of $r$ and $x=\cos \theta$ for two time slices, $t=1$ (upper surface) and $t=2$ (lower surface), where we set $h=2,k_{+}=5,k_{-}=3,a=1,\mu =1,\nu =2$.

Figure 7

The $r$-component of the electric field as a function of $r$ and $x=\cos \theta$ for two time slices, $t=1$ (lower surface), $t=2$ (upper surface), where we set $h=2,k_{+}=5,k_{-}=3,a=1,\mu =1,\nu =2$.

Figure 8

The $\theta$-component of the electric field as a function of $r$ and $x=\cos \theta$ for one time slice, $t=1$, where we set $h=2,k_{+}=5,k_{-}=3,a=1,\mu =1,\nu =2$.

Figure 9

The metric function $H(t,r,\theta )$ as a function of $r$ and $x=\cos \theta$ for two time slices, $t=1$ (upper surface) and $t=2$ (lower surface), where we set $\epsilon =+1,h=2,a_{+}=5,a_{-}=3,\mathrm{\Lambda }=3$.

Figure 10

The metric function $H(t,r,\theta )$ as a function of $r$ and $x=\cos \theta$ for two time slices, $t=1$ (lower surface) and $t=2$ (upper surface), where we set $\epsilon =-1,h=2,a_{+}=5,a_{-}=3,\mathrm{\Lambda }=3$.

Figure 11

The $r$-component of the electric field as a function of $r$ and $x=\cos \theta$ for $t=1$, where we set $h=2,a_{+}=5,a_{-}=3,\mathrm{\Lambda }=3$.

Figure 12

The $\theta$-component of the electric field as a function of $r$ and $x=\cos \theta$ for $t=1$, where we set $h=2,a_{+}=5,a_{-}=3,\mathrm{\Lambda }=3$.