Black Holes and Variable Infinities

[arrow564]

Hi all,
I have been thinking about black holes and the different sizes that they come in. With regular black holes and super massive and all of the in between black holes it begs a question. Can one infinity be bigger than the other? All black holes are said to have infinitely dense centers with infinite levels of mass. But Super Massive are, well, super massive and thus common sense would say that they are even more dense than regular black holes. But when you look at the research it still says that it is infinitely dense and has an infinite amount of mass.

I have read simple explanations that there are also an infinite amount of points between one inch and two inches on a ruler but an even bigger infinite number of points between one inch and one foot on that ruler.

Would all of these infinities simply imply that the numbers are indeed finite. But we don't have the means of getting precise readings, or does it go deeper than that?

Clear Skies!
Mo

 

[Nabeshin]

centers with infinite levels of mass

This is incorrect. While you can describe the singularity of the black hole as being infinitely dense (I myself do not like to go down this route but you may), its mass is indeed finite. So a solar mass black hole may have ~10^31kg of matter, while a supermassive hole will have upwards of 10^40 kg. The point is that the mass is finite, not infinite.

I have read simple explanations that there are also an infinite amount of points between one inch and two inches on a ruler but an even bigger infinite number of points between one inch and one foot on that ruler.

This is also incorrect. In this circumstance, both infinities are the same size. An example of two different sized infinities would be, say, the total number of integers and the total number of real numbers between 0 and 1 (the former set is the smaller). For more technicalities, look up countable and uncountable sets and some of the results derived by Cantor.

 

[Chronos]

There is a theoretical limit on how precisely you can define the position of a point known as the Planck length. A related rule limits maximum density - which is called the Planck density. I am partial to this particular limit when it comes to the density of black hole singularities, but, that is strictly a personal choice.