By E. Poisson

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**Extra info for A Relativist's Toolkit - The Math of Black Hole Mechanics**

**Example text**

4 Slight flattening of the Earth results in a difference between the radius measured to the poles vs. that to a point on the equator. 0033. Given that the Earth is spinning, the centrifugal accelerations are greatest at the equator and vanish at the poles. mass nearer the poles. This counters some of the center-directed gravitational force, and therefore reduces the pressure at the base of a column of rock at low latitudes. Over geologic time this results in a slow ﬂow of mass toward the equator until the system is in hydrostatic balance.

As another example, we also live in the atmospheric boundary layer, the base of the atmosphere where one of several properties changing rapidly is the wind velocity. It is zero at the ground surface and changes rapidly within the bottom kilometer, even in the bottom few meters. The other edge of a boundary layer is often arbitrary. In the case of the lithosphere, we chose to take the bottom boundary of the lithosphere to be where the mantle has reached a temperature of about 1200 C. This choice is based upon laboratory experiments that show that mantle materials above this temperature deform suﬃciently rapidly to behave as ﬂuids on geological timescales.

The slight flattening of this sphere is attributed to the fact that it is spinning, which accounts for a bulge that is of the order of 20 km. This is roughly the magnitude of the roughness of the Earth’s surface, as measured by the full range of its topography. Neither the bulge nor the roughness is significant when seen from the Moon – the Earth looks very round and very smooth. The histogram of the Earth’s surface topography is bimodal. This reflects the two distinct compositions and thicknesses of crustal material: thin, dense oceanic crust and thick lower density continental crust.