Notation based on four-by-four time and space projection matrices enables solution from scratch of the isotropic static metric-tensor ansatz for the empty-space Einstein equation. This isotropic Schwarzschild solution's version of the Riemann tensor which contracts directly to the Ricci tensor is finite at the horizon despite the divergence there of the contravariant metric tensor and of the affine connection, but raising that tensor's third index produces a horizon-divergent version of the Riemann tensor as well; the horizon-finitude of the first-mentioned version of the Riemann tensor is nothing more than a fortuitous by-product of the Ricci tensor's being zero. Furthermore, certain curvature scalars calculated from the isotropic Schwarzschild solution become ill-defined at the horizon, which is a departure from the "no drama" horizon behavior of those scalars calculated from the "standard" Schwarzschild solution. That departure occurs because the Jacobian of the map of the "standard" Schwarzschild solution into the isotropic solution diverges at the horizon, which invalidates tensor-contraction theorems there. Gravitational horizons in empty-space models in fact merely reflect unphysical overstatement of the effective mass of the gravitational source: the internal gravitation of any extended source which can be inscribed in a sphere reduces the effective mass of that source below the value needed to produce a horizon in the empty space outside the sphere.