Exact convoluted solutions in higher-dimensional Einstein-Maxwell theory

We construct two classes of exact solutions to six- and higher-dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and show a bolt structure on a single point in any dimensionality. Moreover, we find the exact nonstationary solutions to the Einstein-Maxwell theory with positive cosmological constant. We show that the cosmological solutions are expanding patches in asymptotically de Sitter spacetime.

Figure 1

The logarithmic plot of general solution (2.20) [$\log (H(r,0)-1)$ versus $\log (r)$].

Figure 2

The real and finite second solution for $H_1(r)$.

Figure 3

The $c$ function versus time for a $r$-constant slice on six-dimensional cosmological spacetime with the metric function (5.5).