Planar warped spacetime
= Planar warped spacetime
{title2=$ds^2=A(z)^2(-dt^2+dx^2+dy^2)+dz^2$}
For positive smooth $A$, this <Lorentzian manifold> has flat $(t,x,y)$ slices scaled by $A(z)^2$. Translation in each slice coordinate gives a <Killing vector field>. An <orthonormal coframe> is $e^0=A\,dt$, $e^1=A\,dx$, $e^2=A\,dy$, $e^3=dz$. Its <Levi-Civita connection> and <Ricci tensor> are controlled by $a=A'/A$ and $q=A''/A=a'+a^2$.