Does the Schwarzschild metric prove that around the earth, 99.9999% of the warping of spacetime is temporal? In several posts on Quora, here Howard Landman writes that the Schwarzschild metric shows/proves that around a smaller body, like the Earth or the Sun, 99.9999% of the warping of spacetime is time, and only 0.0001% is the warping of space.  And that space warping only reaches 50% at a black hole or neutron star.  First, is this interpretation of the SM correct?
I created a spreadsheet based on the SM, and the graphs agree with Landman that the time component crosses into negative numbers at the Schwarzschild radius. And the space component curves in the opposite direction, increasing.
How do I interpret this result to understand what Landman is saying?  And why is this never discussed, anywhere as far as I can see.  Or have I just missed something obvious?
 A: What Landman writes is just nonsense. The components of the metric are not measures of curvature. Measures of curvature involve second derivatives of the metric's components. Spacetime is locally flat, so we can always choose local coordinates such that the components of the metric are the same as in flat spacetime.
There is no such thing as purely temporal curvature. The components of the Riemann curvature tensor vanish if you use only a timelike axis for all four indices.
A: The question is: how GR explains that we (and all objects) are under an acceleration of $g$ at the surface of the earth?
The argument of the link is that for small velocities compared to the light speeds and $r_s \lll r$, the time dilation is basically a function of $r$. But it doesn't answer the question above. It only notes that now there is a time dilation. As there is not such a thing in Minkowski spacetime for objects at rest in its frame, it concludes that time dilation is the "cause" of gravity.
In order to get an answer, we can write the geodesic equation for the coordinate $r$. After eliminating the null terms, using the Schwarzshild equation:
$$\frac{\partial^2 r}{\partial \tau^2} + \Gamma^1_{00} \frac{\partial t}{\partial \tau}\frac{\partial t}{\partial \tau} + \Gamma^1_{11} \frac{\partial r}{\partial \tau}\frac{\partial r}{\partial \tau} + \Gamma^1_{22} \frac{\partial \theta}{\partial \tau}\frac{\partial \theta}{\partial \tau} + \Gamma^1_{33} \frac{\partial \phi}{\partial \tau}\frac{\partial \phi}{\partial \tau} = 0$$
Now we use the argument of small velocities: $dr, d\theta, d\phi \lll dt$, so only 2 terms matter:
$$\frac{\partial^2 r}{\partial \tau^2} + \Gamma^1_{00} \frac{\partial t}{\partial \tau}\frac{\partial t}{\partial \tau} \approx 0$$
Using Schwarzshild metric:
$$\Gamma^1_{00} = \frac{2GM}{r^2}\frac{1-\frac{2GM}{r}}{2}$$
From the Schwarzshild equation, where $dr, d\theta, d\phi \lll dt$:
$$d\tau^2 \approx \left(1-\frac{2GM}{r}\right)dt^2$$
Leading to the desired $g$ acceleration:
$$\frac{\partial^2 r}{\partial \tau^2} \approx -\frac{GM}{r^2}$$
