4 ms·

Technically, the radius of a black hole is uniquely determined by its mass, so one can construct a unit system where mass and radius use the same unit of measur

Technically, the radius of a black hole is uniquely determined by its mass, so one can construct a unit system where mass and radius use the same unit of measure...

tjradcliffe 12y ago
I want to see that: "How many solar masses is it from Paris to London again?" (115... it's actually a kind of convenient unit, quite close to half an English league and just a bit larger than a Roman league.) Or: "Man! I stepped on the scales today and I've put on another ten million Planck lengths!"
- jen729w 12y ago
  Randall has us covered, as always. http://xkcd.com/687/ http://xkcd.com/687/ and "You can even plug it into Wolfram|Alpha, and it’ll tell you that 20 MPG is about 0.1 square millimeters (roughly the area of two pixels on a computer screen)." https://what-if.xkcd.com/11/ https://what-if.xkcd.com/11/
hamoid 12y ago
That unit system might allow comparing black holes to other black holes. But our sun does not have the same density as a black hole, or? The nature article [1] does not compare it to the size of our sun, but to its mass. [1] http://www.nature.com/nature/journal/v518/n7540/full/nature14241.html http://www.nature.com/nature/journal/v518/n7540/full/nature1...
- Retric 12y ago
  Actually, black holes density decreases linearly as their mass increases. So, there could easily be a black hole with a density of the sun with supper massive black holes having a density near that of water. (Where density = mass / volume inside event horizon). Because Gravity ~= Mass/distance ^ 2 but volume is 4/3 pi * r ^ 3
- semaphoreP 12y ago
  Actually, you can use this unit system (called Geometrized units [1]) for anything, but it is especially convenient for describing black holes and general relativity in general. As a rule of thumb, in the geometrized units, 1 solar mass = ~1.5 km = ~5 microseconds. They have the same units so you can use them interchangeably (Our sun weights 5 microseconds). I'm just being pedantic here obviously.. [1] http://en.wikipedia.org/wiki/Geometrized_unit_system http://en.wikipedia.org/wiki/Geometrized_unit_system
dredmorbius 12y ago
Wording nit: entirely determined, not uniquely determined. The former says that mass => size. The latter says that a black hole's mass-size relationship is necessarily unique. Which I don't believe you intended.

Technically, the radius of a black hole is uniquely determined by its mass, so one can construct a unit system where mass and radius use the same unit of measure...

tjradcliffe 12y ago

I want to see that: "How many solar masses is it from Paris to London again?" (115... it's actually a kind of convenient unit, quite close to half an English league and just a bit larger than a Roman league.) Or: "Man! I stepped on the scales today and I've put on another ten million Planck lengths!"

jen729w 12y ago
Randall has us covered, as always. http://xkcd.com/687/ http://xkcd.com/687/ and "You can even plug it into Wolfram|Alpha, and it’ll tell you that 20 MPG is about 0.1 square millimeters (roughly the area of two pixels on a computer screen)." https://what-if.xkcd.com/11/ https://what-if.xkcd.com/11/

hamoid 12y ago

That unit system might allow comparing black holes to other black holes. But our sun does not have the same density as a black hole, or? The nature article [1] does not compare it to the size of our sun, but to its mass. [1] http://www.nature.com/nature/journal/v518/n7540/full/nature14241.html http://www.nature.com/nature/journal/v518/n7540/full/nature1...

Retric 12y ago
Actually, black holes density decreases linearly as their mass increases. So, there could easily be a black hole with a density of the sun with supper massive black holes having a density near that of water. (Where density = mass / volume inside event horizon). Because Gravity ~= Mass/distance ^ 2 but volume is 4/3 pi * r ^ 3
semaphoreP 12y ago
Actually, you can use this unit system (called Geometrized units [1]) for anything, but it is especially convenient for describing black holes and general relativity in general. As a rule of thumb, in the geometrized units, 1 solar mass = ~1.5 km = ~5 microseconds. They have the same units so you can use them interchangeably (Our sun weights 5 microseconds). I'm just being pedantic here obviously.. [1] http://en.wikipedia.org/wiki/Geometrized_unit_system http://en.wikipedia.org/wiki/Geometrized_unit_system

dredmorbius 12y ago

Wording nit: entirely determined, not uniquely determined. The former says that mass => size. The latter says that a black hole's mass-size relationship is necessarily unique. Which I don't believe you intended.