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**Technology, Science & Alt Science / Low Density Black Holes**

« **on:**February 04, 2015, 08:33:37 PM »

Today I learned that a black hole can theoretically be less dense than air.

True radius is proportional to the cubed root of mass. Mass increases by a factor of 8 while the radius doubles in order to maintain density.

However, Schwarzschild radius grows proportional to mass!

This means for any arbitrary non-zero density there exists a mass such that the Schwarzschild radius is equal to the physical radius: a black hole.

Edit: apparently the wiki article on Schwarzschild Radius talks about the same thing but says it better:

"If you assume that the Schwarzschild radius is the outer edge of the black hole (note that this assumption is in contrast to the typical assumption that a black hole is a singularity, and therefore has zero radial extent). Under this assumption, the average density of a supermassive black hole can be less than the density of water.

The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density.[7] In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at normal density (in this example, 103 kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million (1.36 × 108) M☉, its physical radius would be smaller than its Schwarzschild radius, and thus it would form a supermassive black hole."

True radius is proportional to the cubed root of mass. Mass increases by a factor of 8 while the radius doubles in order to maintain density.

However, Schwarzschild radius grows proportional to mass!

This means for any arbitrary non-zero density there exists a mass such that the Schwarzschild radius is equal to the physical radius: a black hole.

Edit: apparently the wiki article on Schwarzschild Radius talks about the same thing but says it better:

"If you assume that the Schwarzschild radius is the outer edge of the black hole (note that this assumption is in contrast to the typical assumption that a black hole is a singularity, and therefore has zero radial extent). Under this assumption, the average density of a supermassive black hole can be less than the density of water.

The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density.[7] In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at normal density (in this example, 103 kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million (1.36 × 108) M☉, its physical radius would be smaller than its Schwarzschild radius, and thus it would form a supermassive black hole."