Can Two Black Holes Merge Without Breaking Thermodynamic Laws?

[Quantum1332]

Ok, so i sit around losing myself within my thoughts, which usually brings forth questions. What if a 2 black holes came with in close distance? I know in the Theory of Relativity, it says that the energy would be greater than all the stars in the visible universe, but...still?

 

[marcus]

Ok, so i sit around losing myself within my thoughts, which usually brings forth questions. What if a 2 black holes came with in close distance? I know in the Theory of Relativity, it says that the energy would be greater than all the stars in the visible universe, but...still?

Hi Quantum1332, how would you like to open this question in the Gen Relativity forum (or "special and general" whatever)?

Animated movies have been made of black hole merger and also of neutron star merger. the computer animation shows the spiraling in closer and closer and the release of energy

these mergers of dense objects spiraling into each other has been studied a lot, analytically and with computer sim

If you start your thread in the right place you are more likely to get helpful response. and links to more info.

what you are asking comes under the heading of classical 1915 Gen Rel.

topics here are for example more like quantum gravity and unification of spacetime geometry with matter------theories still under construction by professional theorists

good luck getting some responses in the right forum!

 

[Thrice]

http://www.mathpages.com/rr/s7-02/7-02.htm

You might like that.

 

[AlphaNumeric]

I know in the Theory of Relativity, it says that the energy would be greater than all the stars in the visible universe, but...still?

I don't think GR says there's that much energy, because it would output more energy than the total mass of the black holes!

The two black holes would spiral into one another, their event horizons merge and form one larger black hole. During this process a lot of gravitational radiation would be thrown out. One result related to the 'Second Law of Black Hole Mechanics' is that the event horizon of the new big black hole would be greater than or equal to the sum of the two event horizons of the original black holes.

With a bit of Googling you can find various computer animations of black holes spiraling into one another and the radiation given off :)

 

[pervect]

Given two black holes of masses m1 and m2, we can use the fact that the total area of the event horizon always increases to provide a strict upper limit as to the amount of energy that can be radiated.

The area of the event horizon is proportional to the square of the mass, therefore m3, the mass of the black hole formed by the merger is greater than or equal to $\sqrt{m1^2 + m2^2}$.

(This is an approximation that ignores rotational stored energy).

The maximum amount of energy avaliable for radiation is thus the difference between the sum of the masses of the initial black holes minus the mass of the final blackk hole. This is

$$m1 + m2 - \sqrt{m1^2 + m2^2}$$

For example, if two solar mass black holes merged, .59 solar masses could be released in the form of energy. This is a lot of energy, and it would be released very quickly, so it would definitely be a spetacular event.

Much of the released energy would probably be in the form of gravitational waves, though I'm sure there would be other emissions as well.

People are trying to do numerical simulations of the highly complicated details, for instanace see the news reports such as

http://news.bbc.co.uk/2/hi/science/nature/4923396.stm

 

[AlphaNumeric]

For example, if two solar mass black holes merged, .59 solar masses could be released in the form of energy.

Sweet Jiminy on a stick! 0.59 solar masses!?

It's in the form of gravitational radiation though isn't it? It's not quite the same as a supernova which would flash fry nearby objects (spectical wise). Though thinking about it, that much gravity flux would probably tear apart nearby objects.

 

[TheTechNoir]

Sweet Jiminy on a stick! 0.59 solar masses!?

It's in the form of gravitational radiation though isn't it? It's not quite the same as a supernova which would flash fry nearby objects (spectical wise). Though thinking about it, that much gravity flux would probably tear apart nearby objects.

I believe you're correct. Though gravitational waves doesn't sound as threatening as a near light-speed down pour of gamma rays or any of the other harmful effects of a near by supernova, sufficiently intense/near by gravitational waves would cause extreme stretching and contracting of spatial dimensions causing serious problems for any inhabitants.

 

[JesseM]

I believe you're correct. Though gravitational waves doesn't sound as threatening as a near light-speed down pour of gamma rays or any of the other harmful effects of a near by supernova, sufficiently intense/near by gravitational waves would cause extreme stretching and contracting of spatial dimensions causing serious problems for any inhabitants.

Just FYI, the last post on this thread before yours is from 2006, and the poster you're responding to hasn't posted anything since 2007...when searching old threads, best to check the dates before replying (if the subject of black hole collisions interests you it'd probably be better to just start a new thread)

 

[TheTechNoir]

Wow, oops sorry thanks for the heads up. It was actually one of the links in the similar/related threads section at the bottom, I just assumed they were also active threads but should've had in mind to look at the date.

 

[yuiop]

Given two black holes of masses m1 and m2, we can use the fact that the total area of the event horizon always increases to provide a strict upper limit as to the amount of energy that can be radiated.

I was wondering how strict this upper limit is?

The idea that the total event horizon area should increase comes from the notion that the area represents the entropy of the black hole and entropy should always increase according to the laws of thermodynamics. However, what the laws of thermodynamics really say is that the entropy of the universe (or closed system) as a whole should always increase and this allows a local reduction in entropy and as long as there is a compensating greater increase in entropy elsewhere in the system. For the black hole merger the radiation of energy in any form (gravitational or otherwise) affects the entropy "elsewhere" so to me it seems uncertain with the given information exactly how much radiation is released during the merger. An example of breaking the thermodynamic "law" that the area of the event horizon should always increase is Hawking radiation which reduces the size of the black hole, but this is "allowed" because the release of radiation represents a increase in entropy elsewhere.

 

[bcrowell]

I was wondering how strict this upper limit is?
[...] For the black hole merger the radiation of energy in any form (gravitational or otherwise) affects the entropy "elsewhere" so to me it seems uncertain with the given information exactly how much radiation is released during the merger. An example of breaking the thermodynamic "law" that the area of the event horizon should always increase is Hawking radiation which reduces the size of the black hole, but this is "allowed" because the release of radiation represents a increase in entropy elsewhere.

This is the Hawking area theorem, which is Proposition 9.2.7 on p. 318 of Hawking and Ellis. There are some technical conditions, which I don't know enough to decode, but he appears to be claiming that it's an exact result in classical GR, not an approximation that neglects radiation.

Note that the area theorem came first, and only later did people form a hypothesis that black hole area should be counted toward the entropy in some generalized version of the second law of thermodynamics. So the statement about increasing area doesn't come from an uncertain attempt to apply the second law of thermodynamics; it's the other way around.

[EDIT] It depends on an energy condition, but I'm not clear on which energy condition it is from the way he states it. I think it may be the WEC.