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No relativity required here. Escape velocity is given classically by
v_esc = (2 g R)^(1/2)
For an escape velocity equal to the speed of light with g = 37,000 g_earth
we would find R = 120 million km (the size of a red giant) and
M = 42 million solar masses. A white dwarf has (I think) a radius closer
to that of Earth so the escape velocity would be "only"
37000^(1/2) x 11.2 km/s = 2.2 x 10^6 m/s, less than 1/100 the speed of
light.