We generalize the Friedmann--Lema^{i}tre--Robertson--Walker (FLRW) line element by promoting the scale factor to a function of space and time, $ds^2=-c^2dt^2+R^2(t,bx),delta_{ij}dx^idx^j/(1+kr^2/4)^2$, and ask whether such a geometry can account for the large voids observed in the galaxy distribution. Writing $R/(1+kr^2/4)equiv e^{alpha(t,bx)}$, we derive the complete Einstein tensor without approximation and decompose it, relative to the comoving observers $u^a=delta^a_0$, into an energy density, an isotropic pressure, an energy flux and an anisotropic stress. The comoving congruence is geodesic, shear-free and irrotational; its Weyl tensor is purely electric and equal to $4pi G$ times the anisotropic stress. We prove that the source is a perfect fluid only if the metric is FLRW, so that any void requires an imperfect effective fluid. The Hamiltonian constraint becomes a Lichnerowicz equation for $e^{alpha/2}$, which allows any observed void density profile to be reconstructed exactly as a domain of negative spatial curvature; for a void of radius $30,Mpch$ and central contrast $-0.85$ the conformal factor is depressed by only $4.8times10^{-6}$, while the local curvature parameter reaches $Omega_k^{m loc}=0.27$. We study three closures. A static spatial factor makes the inhomogeneity behave as a $w=-1/3$ ``curvature fluid'' whose contrast grows as $a$ at all times; a pressureless closure gives acoustic oscillations with $c_s=c/sqrt3$; and a growth-matched closure reproduces $Lambda$CDM growth by construction. In all cases the absence of a lapse perturbation halves gravitational lensing relative to general relativity at fixed density, giving $E_G=Omega_m/(2f)$. We complement the theory with a statistical analysis of $3times10^5$-galaxy mock catalogues in a $(1,h^{-3},mathrm{Gpc}^3)$ volume: power spectra, Landy--Szalay correlation functions, counts-in-cells moments, void probability functions, genus statistics and some $3,500$ voids per catalogue. We find that $95%$ of void centres lie in regions of negative smoothed spatial curvature, and that the static-factor model is distinguished from $Lambda$CDM by its void size function at $z=0$ with Kolmogorov--Smirnov $psim10^{-86}$. An exact Lema^{i}tre--Tolman--Bondi void evolved from the same initial profile shows that the static model is valid only while $|delta|ll1$: for a linear contrast of $-2$ the exact central contrast is $-0.72$, and the LTB void expands $30%$ faster than the background. Redshift-space power-spectrum and void--galaxy quadrupoles of the mocks vanish for the static model and change sign for the growth-matched one. A fit to eight $fsigma_8$ and five $E_G$ measurements disfavors the two closures by $Deltachi^2=72$ and $21$ relative to $Lambda$CDM. Restoring a spatially varying lapse, $ds^2=-N^2dt^2+R^2dbx^2$, admits perfect fluids, recovers $Lambda$CDM dynamics with no gravitational slip, and keeps the Lichnerowicz description of voids. The spatially varying scale factor is thus the correct description of the spatial geometry of voids, while their dynamics requires the lapse.