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The Density of Matter in a Black Hole

-- | August 22, 2015

Question: A 10 solar mass object would have 10 solar masses enclosed in a radius of 30 km. The density of a spherical object scales as M/R3. Relative to the 10 solar mass black hole, how many times denser would a black hole the mass of the Earth be? How many times less dense would a black hole of 1 million solar masses be? — Paul

Answer: As my colleague Cole Miller points out in his description of the properties of black holes and neutron stars, unlike ordinary things (e.g., rocks), which have a size roughly proportional to the cube root of their mass, black holes have radii proportional to their mass. Taking the event horizon of a black hole as the definition of its outer boundary, the event horizon of a nonrotating black hole the mass of our Sun would have a radius of about 3 kilometers. This implies that the more massive the black hole is the denser it is, meaning that larger black holes are not very dense. For example, a one-billion solar mass black hole, which is the type of black hole that is thought to exist at the center of some galaxies (like ours), has an average density just twenty times the density of air.

Jeff Mangum

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