Are Larger Black Holes Less Dense Than Smaller Ones?

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Discussion Overview

The discussion revolves around the density of black holes in relation to their mass and size, particularly questioning whether larger black holes are less dense than smaller ones. Participants explore theoretical aspects of black hole density, including the implications of singularities and event horizons.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that both black holes and singularities have infinite densities, though this may depend on how density is defined.
  • One participant suggests that the density of a black hole can be calculated as its mass divided by the volume within its event horizon, which would not necessarily be infinite.
  • Another participant mentions that larger black holes may have lower densities, questioning the validity of this claim and seeking an explanation.
  • A participant elaborates that if the mass of a black hole is concentrated in a singularity, the volume of the black hole increases with mass, leading to a decrease in density as the size of the event horizon grows.
  • It is noted that the surface area of the event horizon increases proportionately to the mass of the black hole, which may contribute to the understanding of density in this context.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between black hole size and density, with some supporting the idea that larger black holes are less dense while others question this notion. The discussion remains unresolved regarding the implications of density in relation to black holes and singularities.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about density, the definitions of volume and mass in the context of black holes, and the complexities of black hole geometry that are not fully addressed.

Will Langas
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What has a higher density? Black Holes or Singularities?

I looked online and all I saw was that they both have infinite densities.
 
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The density of a black hole would be computed as its mass over its volume - the volume within the event horizon. So that would be far from infinite.

A black hole with zero angular momentum should have an embedded singularity where almost all of the black hole's mass will be accumulated. I'm not sure if makes sense to talk about its volume at all, but if it has one perhaps it is zero. Of course, if it is zero, that would give it "infinite density".
 
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I heard that a black hole can have a extremely low density. Also I heard that the bigger the black hole the lower the density. This does not make much sense to me, is it true? And if so can someone explain why?
 
Hoophy said:
I heard that a black hole can have a extremely low density. Also I heard that the bigger the black hole the lower the density. This does not make much sense to me, is it true? And if so can someone explain why?
As I said in the previous post the "size of a black hole" is generally taken to be the diameter of its event horizon. The actual geometry of the black hole is pretty involved - but as a simplification, imagine that all of the mass of the black hole is concentrated in a singularity, a point, at the center. The size of the event horizon is the sphere around that point where light cannot escape. If you double the mass at the center, the distance to the event horizon increases so the total volume of the black hole increases. That total volume will more than double. So, heavier black holes are less dense because they can enclose more empty space.

Interestingly, it is the surface area of the black hole (the event horizon) that increases proportionately to the mass.
 
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