What is the size of a black hole?

[Deepak Kapur]

1. I repeat, 'what is the size of a black hole'.



2. Is there anything denser/smaller than a black hole?

 

[nicksauce]

1. A black hole of mass M has radius R = 2GM/c^2

2. This question seems to assume that all black holes have the same size, which is false. At a given mass, a black hole would be the smallest, densest thing of that mass.

 

[jnorman]

hmmm - from the wiki entry on this topic, they reference sean carroll:
"At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[38] For a non-rotating black hole this region takes the shape of a single point and for a rotating black hole it is smeared out to form a ring shape lying in the plane of rotation.[39] In both cases the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[40] The singular region can thus be thought of as having infinite density."

the NCSA website states:
"By definition a black hole is a region where matter collapses to infinite density..." implying zero volume.

the NASA website states:
"the center of a black hole spacetime has infinite curvature and matter is crushed to infinite density under the pull of infinite gravity. At a singularity, space and time cease to exist as we know them. The laws of physics as we know them break down at a singularity, so it's not really possible to envision something with infinite density and zero volume."

and:
"The star eventually collapses to the point of zero volume and infinite density, creating what is known as a " singularity ""

and penrose's paper (http://www.ias.ac.in/jarch/jaa/17/213-231.pdf) clearly states that a singularity (differentiating between singularity and schwarzchild radius) has infinite density, zero volume.

 

[nicksauce]

All good points.

First we have to define what we mean by a black hole. Usually people define this to mean everything inside the event horizon, i.e., the ball 0 r < Rs, where Rs is the Schwarzschild radius.

Second, it is true that the density profile of the black hole will be zero everywhere except the singulariy (r=0) where the desntiy is infinite. However, it still seems sensible to talk about the average density of the black hole as M / (4/3 * pi * Rs^3).

 

[Medium9]

I wonder if there could exist an object with non-zero volume (or non-infinite density) that has a schwarzschild radius. Something of the order of a quark star. Would that be possible?
And if so, would it be distinguishable from a BH formed by a singularity?

 

[silentbob14]

2. A singularity at the moment of the big bang was smaller than any of the black hole singularities.

 

[Deepak Kapur]

2. A singularity at the moment of the big bang was smaller than any of the black hole singularities.

How is it possible when the volume is zero in either case?

 

[silentbob14]

I think it's not zero, more like so close to zero that it's negligible. Though I'm not sure about this.

 

[silentbob14]

Back to this topic, black holes indeed have a zero volume in classical physics, however in quantum mechanics, they have a volume which is not 0.
Here's some more about it:
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/040527a.html

 

[Nabeshin]

All astrophysical black holes have some spin anyways, which means their singularities are actually rings.

Also, until anyone actually invents a viable theory of quantum gravity, I think we should hold off on speculating about what this theory might say about a singularity.

 

[silentbob14]

This thread got me thinking. Shouldn't an object, which has a mass have a volume (bigger than zero)?

 

[S. Hardt]

Shouldn't an object, which has a mass have a volume (bigger than zero)?

I found these 2 Quotes giving a good answer and I tried to explain it by looking for a similar problem.

2. Is there anything denser/smaller than a black hole?

This question seems to assume that all black holes have the same size, which is false. At a given mass, a black hole would be the smallest, densest thing of that mass.

If the density can still increase with the same mass, the Volume has to be more than zero but can approach it.

I would relate this "phenomena" with a heater that can heat water to 100 Celsius.
To get 100 Celsius a heater is needed that can add more energy than just for 100 Celsius.
If you look counter wise at the absolute 0 point,
you can never get colder, and that means you will never reach it exactly.
I think it is the same with the Volume of a black hole...but I am only a student interested in this so I hope it is all right

 

[Medium9]

I would actually relate it to the limit of some mathematical function that tends to zero. It'll never reach it, but get infinitely close. Something along the way of 1/x. That is, as long as there is room for speculation in this field, which I strongly hope will change within my lifetime!

 

[S. Hardt]

If you want to write it as an equation you can write it as

Volume = Mass/Density

Volume the Space created by the energy of an atom(/particle?)

If it is possible to set up an equation with Density in relation to an energy used to form space for a single particle, you can rewrite this and get a really answer. The whole problem of this is that you can not easily determine this energy factor.
...but this goes into another sector.I hope there is room for speculation...

 

[Nabeshin]

I think you guys are mistakenly trying to apply a) common sense and b) simple mathematics/physics to a situation which is neither common nor simple.

For example, volume as measured by who? In relativity, different observers will see different volumes. Time as measured by who? Different observers measure different times... Just because intuition tells you something with mass must have nonzero size has no bearing on whether or not this is actually the case. Take an electron. No volume, yet a distinct mass, charge, spin.

From classical GR we know the following: Any matter inside the event horizon is doomed to fall inward and inward until it finally impacts the singularity. Therefore we conclude all matter is doomed to end up at a single point. As far as how long this takes for which observers, that's an incredibly trickier question. I can state, however, that for any particle falling through the event horizon, it will reach the singularity in a finite (and very short!) proper time. Of course, no one OUTSIDE the horizon could ever hope to observe any of this (and indeed, sees objects as taking an infinite amount of time to cross the horizon), so is it really of any consequence?

 

[S. Hardt]

Thank you Nabeshin,
You are right it was the attempt to explain this phenomena by common sense and simple mathematics, and there is also no consequence.

I think I got some facts wrong and should study more before I contribute to a topic specific like this. Anyway I found another answer to one of my questions in what you wrote, and another somewhere in this Forum, too.

 

[AUK 1138]

1. A black hole of mass M has radius R = 2GM/c^2

this is the size of the Schwarzschild radius, not the size of the black hole. by your definition, the black hole is a rather large object. when in reality, a black hole operates more like a point particle, ie a singularity.

 

[Frame Dragger]

this is the size of the Schwarzschild radius, not the size of the black hole. by your definition, the black hole is a rather large object. when in reality, a black hole operates more like a point particle, ie a singularity.

No, a singularity behaves that way, a Black Hole is the whole (PUN!) shebang: Event horizon, Ergoregion and singularity.

 

[ViewsofMars]

1. I repeat, 'what is the size of a black hole'.

Hello Deepak Kapur (OP), I think that The National Radio Astronomy Observatory should be of help to you in your search. It is a 'facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.' that means it's "A" ok!

What is a black hole?
A black hole is a concentration of matter so dense that not even light can escape its gravitational pull.

What is a supermassive black hole?
Black holes come in many sizes. Astronomers believe that a “supermassive” black hole, with a mass of about 4 million Suns, lies at the center of the Milky Way galaxy. NRAO telescopes offer the best prospect for actually imaging such a supermassive black hole.

More generally, a supermassive black hole has a mass of several hundred thousand to more than ten billion solar masses. The central region of virtually every galaxy is thought to contain an object of this type. The primary evidence for supermassive black holes comes from optical and radio observations which show a sharp rise in the velocities of stars or gas clouds orbiting the centers of galaxies. High orbital velocities mean that something massive is creating a powerful gravitational field that is accelerating the stars. Additionally, X-ray observations indicate that a large amount of energy is produced in the centers of many galaxies, presumably by material falling into the accretion disk that surrounds the central black hole.

How do supermassive black holes form?
One theory is that an individual star-like black hole forms and swallows up enormous amounts of matter over the course of millions of years to produce a supermassive black hole. Another possibility is that a cluster of star-like black holes forms and eventually merges into a single, supermassive black hole. Or, a single large gas cloud could collapse to form a supermassive black hole.

Recent research suggests that galaxies and their central black holes do not grow steadily, but in fits and starts. In the beginning of a growth cycle, the galaxy and its central black hole accumulate matter. The energy generated by the jets that accompany the growth of the supermassive black hole eventually brings the in-fall of matter and the growth of the galaxy to a halt. The activity around the central black hole then ceases because of the lack of a steady supply of matter, and the jets disappear. Millions of years later the hot gas around the galaxy cools and resumes falling into the galaxy, initiating a new season of growth.

[Read on . . .]
http://www.nrao.edu/index.php/learn/science/blackholes

 

[Frame Dragger]

Hello Deepak Kapur (OP), I think that The National Radio Astronomy Observatory should be of help to you in your search. It is a 'facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.' that means it's "A" ok!

You do realize that has nothing to do with what he asked, or the course of the discussion? Nicksauce answered this question in the second post, which then led to

How is it possible when the volume is zero in either case?

and finally Nabeshin put it to rest. Don't take this the wrong way, but how is a puff-piece from NRAO clarifying this? A supermassive BH is still conforming to its Schwarzschild Radius, and then related phenomenon such as the Event Horizon, and Ergoregion (and accretion disc if you like) would be the "rest". I think Nabeshin already took us past the approximation offered in that article.

Perhaps I'm missing some element you are trying to communicate?

 

[Chronos]

The formula for deriving the diameter of the event horizon has already been given. The diameter of the singularity approaches zero irrespective of mass, albeit I think it is finite.

 

[ViewsofMars]

Since we on the topic of a black hole(s), I like to share the lastest information.

Nature 464, 380-383 (18 March 2010)
Dust-free quasars in the early Universe
Linhua Jiang1, Xiaohui Fan1,2, W. N. Brandt3, Chris L. Carilli4, Eiichi Egami1, Dean C. Hines5, Jaron D. Kurk2,6, Gordon T. Richards7, Yue Shen8, Michael A. Strauss9, Marianne Vestergaard1,10 & Fabian Walter2
[...]
The most distant quasars known, at redshifts z ≈ 6, generally have properties indistinguishable from those of lower-redshift quasars in the rest-frame ultraviolet/optical and X-ray bands. This puzzling result suggests that these distant quasars are evolved objects even though the Universe was only seven per cent of its current age at these redshifts. Recently one z ≈ 6 quasar was shown not to have any detectable emission from hot dust4, but it was unclear whether that indicated different hot-dust properties at high redshift or if it is simply an outlier. Here we report the discovery of a second quasar without hot-dust emission in a sample of 21 z ≈ 6 quasars. Such apparently hot-dust-free quasars have no counterparts at low redshift. Moreover, we demonstrate that the hot-dust abundance in the 21 quasars builds up in tandem with the growth of the central black hole, whereas at low redshift it is almost independent of the black hole mass. Thus z ≈ 6 quasars are indeed at an early evolutionary stage, with rapid mass accretion and dust formation. The two hot-dust-free quasars are likely to be first-generation quasars born in dust-free environments and are too young to have formed a detectable amount of hot dust around them.
[Read on . . .]
http://www.nature.com/nature/journal/v464/n7287/full/nature08877.html

The following two articles give added information relating to the Nature article. (Nature is a peer-reviewed journal.)

1. University of Arizona astronomers discover most primitive supermassive black holes known
http://www.eurekalert.org/pub_releases/2010-03/uoa-uoa031810.php

2. UA Astronomers Discover Most Primitive Supermassive Holes Known
"Astronomers have come across what appear to be two of the earliest and most primitive supermassive black holes known. The discovery will provide a better understanding of the roots of our universe, and how the very first black holes, galaxies and stars all came to be."
By Jet Propulsion Laboratory/University Communications March
17, 2010
[Read on . . .]
http://uanews.org/node/30721