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(1) The density of water increases as one approaches the bottom of the sea.

(2) The density of neutron stars also increases from crust to core.

Black holes with greater mass have a larger radius and I have read the density of a SMBH might be similar to air at the Event Horizon. Would there be any dependable ratio between mass and density in Black Holes?

AND is the density of the interior isotropic?

IF NOT...

Is there any evidence to suggest that a Black Hole would increase in density in a similar way to cases (1) and (2) mentioned above?

Qmechanic
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    Your question doesn't make much sense. The density of a black hole is not well defined. https://physics.stackexchange.com/q/26515/ – ProfRob Feb 04 '20 at 22:39
  • Everywhere except the singularity, the local energy density inside and outside a stable Schwarzschild black hole is zero (because such a black hole is a vacuum solution of Einstein’s field equations), and at the singularity the energy density has no meaningful value. Other people are talking about average densities, which has basically nothing to do with the interior state of the hole. – G. Smith Feb 05 '20 at 05:06

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