= Bertotti-Robinson spacetime
{c}
{title2=$\widetilde{\mathrm{AdS}}_2(m)\times S^2(m)$}
The simply connected Bertotti-Robinson geometry is the product of the <universal cover> of <two-dimensional anti-de Sitter spacetime> and a <two-sphere> with equal <radius> $m>0$. In <metric signature> $(-,+,+,+)$,
$$
g=m^2\sec^2X(-dT^2+dX^2)+m^2d\Omega_2^2,\qquad T\in\mathbb R,\quad |X|<\pi/2.
$$
Its radial <Penrose diagram> is an infinite <conformal strip of two-dimensional anti-de Sitter spacetime>. The <metric tensor> $-\lambda^2dt^2+m^2\lambda^{-2}d\lambda^2+m^2d\Omega_2^2$ is a patch of it, with $\lambda=m(\sin T-\sin X)/\cos X$. Its <Killing vector field> $\partial_t$ extends across alternating <degenerate Killing horizons> $\lambda=0$. Both factors are <geodesically complete>, giving a <maximal analytic extension> of this patch without periodic time identification.
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