Why does the horizon area of a black hole never decrease?

In summary: If the area were decreased, then something would have to violate the second law of black hole mechanics- either the entropy would increase (due to the release of energy in the form of Hawking radiation), or the black hole would no longer be a classical BH (due to the emission of particles outside of the event horizon). Putting it all together, we can see that decreasing the area of the event horizon doesn't violate any conventional notions of physics.
  • #1
M. next
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Hawking said that the horizon area of a black hole never decreases and illustrated that in his Hawking Are Theorem:

dA/dt ≥ 0

Does anyone know why is it like that. Why doesn't the area decrease?
 
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  • #2
M. next said:
Hawking said that the horizon area of a black hole never decreases and illustrated that in his Hawking Are Theorem:

dA/dt ≥ 0

Does anyone know why is it like that. Why doesn't the area decrease?


According to the Second Law of BH Thermodynamics, in any classical process, the area of the event horizon does not decrease

[itex]dA\geq 0[/itex]

nor does the black hole's entropy, [itex]S_{bh}[/itex] (the BH's event horizon area can remain stable in classical mechanics but will increase 1) if mass is added or 2) if spin or charge are reduced). The second law of black hole mechanics can, however, be violated if the quantum effect is taken into account, namely that the area of the event horizon can be reduced via Hawking radiation.


BH thermodynamics-

http://www.fysik.su.se/~narit/bh.pdf [Broken] pages 9-13

http://edoc.ub.uni-muenchen.de/6024/1/Deeg_Dorothea.pdf pages 11-13
 
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  • #3
Thank you a lot for your reply. I now know why does it increase. You are saying if mass is added or if spin or charge is reduced. How was it known? If this is difficult to answer, then I ask why doesn't it decrease? What will happen if you took the other option IF THE AREA DECREASED what will happen? Will this violate something conventional or what do you say?
 
  • #4
M. next said:
What will happen if you took the other option IF THE AREA DECREASED what will happen? Will this violate something conventional or what do you say?

Hawking proved the area theorem for a classical black hole (i.e., one in which no quantum effects like Hawking radiation are operating) by a geometric argument which requires considerable groundwork to understand. But the gist of it is that the horizon is made up of outgoing light rays that just barely fail to escape to infinity, and the area of the horizon, roughly speaking, counts the "number" of such light rays that make up the horizon, assuming that they don't converge. Since nothing can escape from a classical black hole, the number of the light rays can't decrease; and Hawking's geometric argument showed that they can't converge. Putting those two things together establishes that the horizon area can't decrease.
 
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  • #5
Thank you very much for putting this in a simple way!
 
  • #6
stevebd1 said:
the BH's event horizon area can remain stable in classical mechanics but will increase 1) if mass is added or 2) if spin or charge are reduced)

Or if spin or charge are *increased*. (The mass of a classical BH can't be reduced, so we don't have to consider that option.)
 

1. What is the horizon area of a blackhole?

The horizon area of a blackhole is the boundary surrounding the blackhole from which no light or matter can escape. It is often referred to as the event horizon and is a direct result of the intense gravitational pull of the blackhole.

2. How is the horizon area of a blackhole calculated?

The horizon area of a blackhole is calculated using the Schwarzschild radius formula, which takes into account the mass and the gravitational constant of the blackhole. The larger the mass of the blackhole, the larger its horizon area.

3. Can the horizon area of a blackhole change?

Yes, the horizon area of a blackhole can change. As a blackhole consumes more matter and increases in mass, its horizon area will also grow. Additionally, the merger of two blackholes can result in a larger combined horizon area.

4. What is the significance of the horizon area of a blackhole?

The horizon area of a blackhole is significant because it is directly related to the blackhole's entropy, a measure of its disorder. The larger the horizon area, the higher the entropy, which is a key concept in understanding the thermodynamics of blackholes.

5. Is the horizon area of a blackhole visible?

No, the horizon area of a blackhole is not visible to the naked eye. It is an abstract concept that defines the boundary of the blackhole's gravitational pull. However, scientists can indirectly study and measure the horizon area through various observations and calculations.

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