# Black hole equations

Hello, I would first just like to introduce myself I'm Adrian and I am a grade 11 student so this type of stuff is way out of my league in terms of mathematical complexity.. but are there equations that define a black hole (What is happening to particles when they enter the event horizon.. etc).

Thank you for your answers and just tell me if the question I am asking doesn't make sense I will try to reword it. :)

## Answers and Replies

Hey Adrian....
yes there are equations and your question makes perfect sense.

There are a lot of aspects to black holes....how they form, do they 'create' galaxies, how do they disappear, when do they disappear, which stars and matter formd black holes, how do they affect space and time around them, how do they affect nearby planets,stars,space dust, what do you see when you fall into one, what is on the other side,etc,etc....

As a general guide, the mathematics associated with black holes [BH] is quite complicated.
No one view gives all the insights associated with black holes. Associated with BH are a SINGULARITY at the center and a surrounding HORIZON. That's what the math says. In fact there are several different horizons. So use the descriptions of experts who have studied the math in detail. Nothing inside the horizon is visible to us...the horizon blocks our measurement access from the outside.

What makes descriptions confusing is that some math and insights are global [only valid from a distance] and others are local [what you see as you fall into a black hole]. Also, it turns out free falling observers [those freely falling with gravity, both near and far] see different things than those who are 'stationary'; a stationary observer is one who accelerates,say outside the horizon, via rocket power.

After you have read some general background that interests you, such as the links below and those suggested by others, if you want to learn more, search BLACK HOLES in these forums....there are VERY detailed discussions you can read...that's how I learned a lot of the details.

You can even just read posts in those threads from just a few people, like PAllen, PeterDonis, Chronos and Zapper to name a few.....their descriptions have proven insightful...accurate.
That way you can get through more discussions faster.

There are some video illustrations of black holes colliding here:
http://www.black-holes.org/explore2.html

Try seaching for the three exact solutions of Einstein's equations:
[The mathematics is so complex, these are the only exact solutions that have been found.]

a non spinning, non charged black hole
http://en.wikipedia.org/wiki/Schwarzschild_radius

Reissner-Nordström black hole if the angular momentum is zero

a Kerr-Newman black hole if it has both angular momentum and electric charge.

and here are some reliable sources with good descriptions

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

http://www.jimhaldenwang.com/black_hole.htm

also, I can't find the link, but Steve Carlip has some good descriptions

For some alternative ideas, including those from string theory and quantum mechanics,check out black hole complementarity...very little math, lots of insightful descriptions:

http://en.wikipedia.org/wiki/Black_hole_complementarity

Susskind has a really cool book THE BLACK HOLE WAR which you can buy cheap online which describes his ideas and how he and t'Hooft eventually convinced Stephen Hawking their views were correct. The book shows how the development of such ideas takes special persistence, the efforts of many and following your own beliefs despite criticism from others.

WannabeNewton
Science Advisor
Try seaching for the three exact solutions of Einstein's equations:
[The mathematics is so complex, these are the only exact solutions that have been found.]

It's quite possible that I'm misunderstanding what you're saying but these are certainly not the only known exact solutions to Einstein's equations.

Hey Adrian....
yes there are equations and your question makes perfect sense.

There are a lot of aspects to black holes....how they form, do they 'create' galaxies, how do they disappear, when do they disappear, which stars and matter formd black holes, how do they affect space and time around them, how do they affect nearby planets,stars,space dust, what do you see when you fall into one, what is on the other side,etc,etc....

As a general guide, the mathematics associated with black holes [BH] is quite complicated.
No one view gives all the insights associated with black holes. Associated with BH are a SINGULARITY at the center and a surrounding HORIZON. That's what the math says. In fact there are several different horizons. So use the descriptions of experts who have studied the math in detail. Nothing inside the horizon is visible to us...the horizon blocks our measurement access from the outside.

What makes descriptions confusing is that some math and insights are global [only valid from a distance] and others are local [what you see as you fall into a black hole]. Also, it turns out free falling observers [those freely falling with gravity, both near and far] see different things than those who are 'stationary'; a stationary observer is one who accelerates,say outside the horizon, via rocket power.

After you have read some general background that interests you, such as the links below and those suggested by others, if you want to learn more, search BLACK HOLES in these forums....there are VERY detailed discussions you can read...that's how I learned a lot of the details.

You can even just read posts in those threads from just a few people, like PAllen, PeterDonis, Chronos and Zapper to name a few.....their descriptions have proven insightful...accurate.
That way you can get through more discussions faster.

There are some video illustrations of black holes colliding here:
http://www.black-holes.org/explore2.html

Try seaching for the three exact solutions of Einstein's equations:
[The mathematics is so complex, these are the only exact solutions that have been found.]

a non spinning, non charged black hole
http://en.wikipedia.org/wiki/Schwarzschild_radius

Reissner-Nordström black hole if the angular momentum is zero

a Kerr-Newman black hole if it has both angular momentum and electric charge.

and here are some reliable sources with good descriptions

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

http://www.jimhaldenwang.com/black_hole.htm

also, I can't find the link, but Steve Carlip has some good descriptions

For some alternative ideas, including those from string theory and quantum mechanics,check out black hole complementarity...very little math, lots of insightful descriptions:

http://en.wikipedia.org/wiki/Black_hole_complementarity

Susskind has a really cool book THE BLACK HOLE WAR which you can buy cheap online which describes his ideas and how he and t'Hooft eventually convinced Stephen Hawking their views were correct. The book shows how the development of such ideas takes special persistence, the efforts of many and following your own beliefs despite criticism from others.

THANKS! Also last question do white holes exist and if they do and they are the reverse of a black hole couldn't we do the inverse of our black hole equations to get what happens in a white hole?

bapowell
Science Advisor
THANKS! Also last question do white holes exist and if they do and they are the reverse of a black hole couldn't we do the inverse of our black hole equations to get what happens in a white hole?
White holes are part of the full black hole solution! For example, the Schwazschild spacetime is the spherically symmetric solution describing a static, non-rotating, charge-free black hole. As you may know, there are singularities associated with this solution -- 2, actually. One corresponds to r=0 -- the very center of the black hole, and one occurs at r = 2GM (units of c=1) -- the event horizon. The former singularity is fundamental, i.e. it is really part of the geometry. The second, however , is not -- it's the result of a poor choice of coordinates. In coordinate systems which possess the coordinate singularity, the solution includes interior and exterior black hole regions. But, it's possible to find a coordinate system that avoids these coordinate singularities, called the Kruskal extension. When Kruskal coordinates are used, the solution "doubles" -- in addition to the interior/exterior black hole, one all of a sudden finds interior/exterior white hole regions "attached" to the black hole (see the diagram here: http://en.wikipedia.org/wiki/White_hole.)

There's much more to be said about this interesting solution, but I must run for now. But to answer your question, the black hole and white hold should be recognized as two parts of a full spherically symmetric solution of Einstein Equations. It is, however, unlikely that white holes exist. One simple reason is that the presence of the collapsing body replaces the white hole in the diagram.

Last edited:
Bill_K
Science Advisor
This article says there are four exact solutions.....

http://en.wikipedia.org/wiki/Rotating_black_hole#Types_of_black_holes

regardless, these seem to be the ones most often discussed.
It says there are four BLACK HOLE solutions. Actually there is only one black hole solution: three of the four listed are special cases of the Kerr-Newman solution.