# Black Hole Size: Calculating the Actual Size

• UrbanXrisis
In summary: There is no true "point of no return." However, any object that crosses the event horizon will cease to exist in the physical sense. In summary, a classical black hole is a point mass that is surrounded by a mathematical surface called the event horizon. The event horizon has a radius, usually known as the Schwarzschild radius: r_s = \frac{2 G M}{c^2} and anything that ventures inside the radius is committed to join the black hole. However, for BHs formed from the cores of "dead" stars, there is a minimum MASS that is required to be able to crunch the matter down to a singularity
UrbanXrisis
my physics teacher said that there is an actual size for the black hole and this size can be calculated. I thought a black hole is a point mass.

A classical black hole is a point mass, but that point is surrounded by a mathematical surface called the event horizon. The event horizon is the "point of no return," in the sense that anything that ventures inside the event horizon cannot come back out. The event horizon has a radius, usually known as the Schwarzschild radius:

$$r_s = \frac{2 G M}{c^2}$$

This is the figure most people use when describing the "size" of a black hole.

- Warren

UrbanXrisis said:
my physics teacher said that there is an actual size for the black hole and this size can be calculated. I thought a black hole is a point mass.
Warren's explanation is spot-on. Let me point out in common English the dichotomy that he laid out. In mathematical terms, the BH singularity is a dimensionless point. Pretty neat, isn't it, taking 3-D physical objects and embedding them in a dimensionless entity? In the physical model, the effects of a BH in our universe extend to the event horizon, which has a radius that can be calculated, and any object that ventures to that radius is committed to join the BH. The size of a BH varies infinitely between none and some depending on whether you are a mathemetician or a physicist.

I thought a black hole is a point mass.
That is classical mistake people make. BH has surface, ofcourse the problem can not be solved in SM. You need more fancy tools like quantum information theory!

---
Surf the web faster.

Marjan said:
That is classical mistake people make. BH has surface, ofcourse the problem can not be solved in SM. You need more fancy tools like quantum information theory!
Uh, what? You apparently don't know what you're talking about.

The classical black hole is modeled entirely by the general theory of relativity.

- Warren

chroot said:
The classical black hole is modeled entirely by the general theory of relativity.
Yes, but is BH modeled entirely by the GR enough to describe real BH? I know that SM isn't at all. We wouldn't need QG if GR would be enough!

---
Surf the web faster.

What I would like to know is if there is a min or max density a black hole can get. If so what happens next? Also, what happens if a black hold meets another one? If black holes truly do exists, then this would also be a possible scenario.

Marjan said:
Yes, but is BH modeled entirely by the GR enough to describe real BH? I know that SM isn't at all. We wouldn't need QG if GR would be enough!
Of course, but such complexity is not necessary to describe the event horizon. Please attempt to keep responses at a level appropriate for the original poster.

- Warren

mapper said:
What I would like to know is if there is a min or max density a black hole can get.
No.
Also, what happens if a black hold meets another one? If black holes truly do exists, then this would also be a possible scenario.
The two coalesce, and generate a lot of gravitational radiation. The merger of two black holes is actually a very well-studied scenario. The various gravitational-wave detectors (LIGO, etc.) are, in fact, looking for neutron star mergers or black hole mergers, since these are the most prolific generators of gravitational radiation in the universe.

- Warren

I would think that there is a min. =/

mapper said:
What I would like to know is if there is a min or max density a black hole can get.
chroot said:
No.
There'd be no max density according to general relativity, but there might be one according to quantum gravity, probably on the order of one Planck mass per Planck volume.

mapper said:
I would think that there is a min. =/

density = mass/volume
under GR, the black hole singularity has zero volume...not much you can do with that.

However, for BHs formed from the cores of "dead" stars, there is a minimum MASS that is required to be able to crunch the matter down to a singularity.

chroot said:
A classical black hole is a point mass, but that point is surrounded by a mathematical surface called the event horizon. The event horizon is the "point of no return," in the sense that anything that ventures inside the event horizon cannot come back out. The event horizon has a radius, usually known as the Schwarzschild radius:

$$r_s = \frac{2 G M}{c^2}$$

This is the figure most people use when describing the "size" of a black hole.

- Warren

I know nothing about QG, but some things can be said about Schwarzschild solution :

In fact the Schwarzschild metric has 2 singularities : r=r_s and r=0.

If r is smaller than r_s but greater than 0 the metric is not singular.

Curiously : when going inside this radius (let say just looking at the metric), then time becomes space, and the radial coordinate becomes time !

The other thing is that I think there is a coordinate system called Kruskal coordinates which are singular only at r=0.

Interprete this as : Schwarzschild radius is a singularity of coordinates, but not of space-time.

However, r=0 is singularity of symmetry...sthg like that.

Yes, kleinwolf, there are coordinate systems like the Finkelstein-Eddington coordinates which are only singular at the singularity, not at the event horizon.

- Warren

If I'm not mistaken while density is ill defined for a black hole itself, you can approach the problem from the other direction.

For example, a spherically symmetric object cannot exceed a certain density (with GR you really need to be looking at some sort of mass-pressure combination I imagine) or it will become a black hole. The maximum non-black hole density would corrospond to probably the most intuitive way to define a minimum black hole density, since every black hole candidate had that density at some point prior to becoming a black hole.

chroot said:
No.

The two coalesce, and generate a lot of gravitational radiation. The merger of two black holes is actually a very well-studied scenario. The various gravitational-wave detectors (LIGO, etc.) are, in fact, looking for neutron star mergers or black hole mergers, since these are the most prolific generators of gravitational radiation in the universe.

- Warren

Incidentally, while black holes may marry, they do not divorce.

chroot said:
Yes, kleinwolf, there are coordinate systems like the Finkelstein-Eddington coordinates which are only singular at the singularity, not at the event horizon.

- Warren

Consider a point mass at r=0, hence spherical symmetry.

a) Consider this is static, plug the standard spherical metric in Einstein's equ., solve it for the vacuum...get the Schwarzschild solution after a LONG calculation :

$$g_{00}(r)=1-\frac{2GM}{rc^2}$$

this corresponds to the squared time-dilatation factor.

b) I use the equivalence principle : gravitation is equiv. to an accelerating frame...of course the accel. depends on r (Newtonian potential) What is the time-dilation due to that change of frame squared ?

$$1-\frac{v^2}{c^2}$$ (*)

But what is the speed ?

1) It depends on r and I remark that it is just the classical speed :

$$\frac{1}{2}mv^2=\frac{GMm}{r}\Rightarrow v^2=\frac{2GM}{r}$$

Plug into (*)...you get the Schwarzschild coefficient...Is this a pure coincidence that works only in this case ?

Because if not, then I could say :

2) I Just compute the speed with the relativistic formula :

$$mc^2\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)=\frac{GMm}{r}$$

$$g1_{00}=1-\frac{v^2}{c^2}=\frac{1}{(1+\frac{GM}{rc^2})^2}$$

This has no singularity outer r=0...but look far away from r=0 leads to :

$$g1_{00}->1-\frac{2GM}{rc^2}+\frac{3G^2M^2}{r^2c^4}-...$$

The first approx. gives the Schwarzschild solution again...

Coincidence again ? Or is it somehow a physical calculation ?

Last edited:
That is meaningless. You are substituting identities.

You mean i do things of the type

F(a)=b and a=g(c) hence F(g(c))=b ?

## 1. What is a black hole and how does its size affect its properties?

A black hole is a region in space where the gravitational pull is so strong that even light cannot escape from it. The size of a black hole is directly related to its mass and density, which in turn affects its gravitational pull and other properties such as its event horizon and accretion disk.

## 2. How is the size of a black hole measured?

The size of a black hole is typically measured by its event horizon, which is the point of no return for anything that enters the black hole. The event horizon is usually measured in terms of its radius, known as the Schwarzschild radius, which is directly proportional to the mass of the black hole.

## 3. Can black holes have different sizes?

Yes, black holes can have different sizes depending on their mass. The more massive a black hole is, the larger its event horizon and therefore its size will be. However, all black holes have a singularity at their center, which is a point of infinite density and size.

## 4. How do scientists calculate the size of a black hole?

Scientists use various methods to calculate the size of a black hole, including using observations of its effects on surrounding matter and its gravitational lensing effects. They also use mathematical equations such as the Schwarzschild radius formula and the Virial theorem to estimate the size of a black hole.

## 5. Can the size of a black hole change over time?

Yes, the size of a black hole can change over time as it gains or loses mass. This can happen through the process of accretion, where a black hole absorbs surrounding matter, or through the emission of Hawking radiation, which causes a black hole to gradually lose mass and therefore decrease in size.

• Astronomy and Astrophysics
Replies
4
Views
360
• Astronomy and Astrophysics
Replies
11
Views
389
• Astronomy and Astrophysics
Replies
11
Views
300
• Astronomy and Astrophysics
Replies
4
Views
1K
• Astronomy and Astrophysics
Replies
1
Views
1K
• Astronomy and Astrophysics
Replies
9
Views
1K
• Astronomy and Astrophysics
Replies
5
Views
1K
• Astronomy and Astrophysics
Replies
6
Views
2K
• Astronomy and Astrophysics
Replies
7
Views
1K
• Astronomy and Astrophysics
Replies
5
Views
2K