Matter without matter: Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

We consider Einstein-Gauss-Bonnet gravity in $n(\ge 6)$-dimensional Kaluza-Klein spacetime ${\mathcal{M}}^4\times {\mathcal{K}}^{n-4}$, where ${\mathcal{K}}^{n-4}$ is the Einstein space with negative curvature. In the case where ${\mathcal{K}}^{n-4}$ is the space of negative constant curvature, we have recently obtained a new static black-hole solution [Phys. Rev. D 74, 021501(R) (2006)] which is a pure gravitational creation including Maxwell field in four-dimensional vacuum spacetime. The solution has been generalized to make it radially radiate null radiation representing gravitational creation of charged null dust. The same class of solutions though exists in spacetime ${\mathcal{M}}^d\times {\mathcal{K}}^{n-d}$ for $d=3,4$, however the gravitational creation of the Maxwell field is achieved only for $d=4$. Also, the Gauss-Bonnet effect could be brought down to ${\mathcal{M}}^d$ only for $d=4$. Further some new exact solutions are obtained including its analogue in Taub-NUT spacetime on ${\mathcal{M}}^4$ for $d=4$.

Figure 1

A schematic diagram of the black-hole formation from the AdS spacetime without any matter field. Here the AdS spacetime for $v<0$ is joined to the static black-hole spacetime (3.2) for $v>v_f$ by way of the Vaidya-like spacetime (3.13). We set $\Theta =0$, $M(v)=m_{0}v$ and $q(v)=-1$, where $m_0$ is a positive constant. A singularity is formed at $v=r=0$ and develops.