In general relativity there is a correction for the gravitational acceleration of a free falling body found in newtonian mechanics. instead of a = gm/r^2 we have
a= gm/√ 1-2gm/c^2xr = gm x r^-3/2(r−rs(m))^-1 ,where r≥rs(m): = 2gm/c^2
where rs is the schwarzschild radius, a =acceleration, m =mass of gravitating body, r =distance to the mass, c =speed of light (299,792,458 m /sec) and g =gravitational constant (6.674 × 10−11 n·kg−2·m). supposing we fell into a back hole with an initial mass of m = 2 × 1030 kg (one solar mass). what would be the approximate percentage change in our acceleration if we fell one hundred meters from a distance of 2rs during which the black hole increases its mass by 1%?
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