Penrose Process & Hawking Area Theorem Explained

In summary: Thanks!In summary, the Hawking area theorem states that the area of a black hole generally never decreases, excluding any quantum effects. The Penrose process allows for energy extraction from a black hole, which results in a decrease in mass and angular momentum. However, for a rotating black hole, the area does not just depend on mass but also on angular momentum, so the area may actually increase in the Penrose process. This is due to the minus sign in front of the angular momentum term in the area formula. Therefore, if both mass and angular momentum decrease, the area may still increase, as demonstrated in a hypothetical scenario.
  • #1
Sumarna
7
0
Hawking area theorem says that area of black hole generally never decrease. Penrose process says that energy can be extracted from black hole. Energy extraction will decrease mass? if yes then if mass is decreased then will area also decrease?
I am confusing things here :(
 
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  • #2
Sumarna said:
Hawking area theorem says that area of black hole generally never decrease.

Yes. (Note that this theorem excludes any quantum effects.)

Sumarna said:
Penrose process says that energy can be extracted from black hole. Energy extraction will decrease mass?

Yes, but this only happens with a rotating black hole, and the hole also loses angular momentum in this process.

Sumarna said:
if mass is decreased then will area also decrease?

No, because for a rotating hole the area does not just depend on the mass. It depends on, heuristically, ##\sqrt{M^2 - a^2}##, where ##a## is the hole's angular momentum per unit mass. In the Penrose process, ##M## decreases, but ##a## also decreases, in such a way that the horizon area ends up larger.
 
  • #3
PeterDonis said:
Yes. (Note that this theorem excludes any quantum effects.)
Yes, but this only happens with a rotating black hole, and the hole also loses angular momentum in this process.
No, because for a rotating hole the area does not just depend on the mass. It depends on, heuristically, ##\sqrt{M^2 - a^2}##, where ##a## is the hole's angular momentum per unit mass. In the Penrose process, ##M## decreases, but ##a## also decreases, in such a way that the horizon area ends up larger.
This has confused me more.. if both mass and angular momentum are decreasing then area must also decrease. How it end up increasing?
 
  • #4
Sumarna said:
if both mass and angular momentum are decreasing then area must also decrease.

No. Look at the minus sign in front of ##a^2## in the heuristic formula I gave. If angular momentum decreases, the area increases.
 
  • #5
PeterDonis said:
No. Look at the minus sign in front of ##a^2## in the heuristic formula I gave. If angular momentum decreases, the area increases.
Consider ##A=8\pi M(M+\sqrt{M^2-a^2})## which is area of rotating black hole. So if both mass M and angular momentum a are decreasing then area will increase? when i am decreasing these two terms, area is also decreasing.
 
  • #6
Sumarna said:
Consider ##A=8\pi M(M+\sqrt{M^2-a^2})## which is area of rotating black hole. So if both mass M and angular momentum a are decreasing then area will increase? when i am decreasing these two terms, area is also decreasing.

If ##a## is decreased enough the area will increase. For example start with ##M## and ##a## equal, then the area is ##A=8\pi M^2##. Now decrease ##M## to ##\frac34 M## and ##a## to zero, then the area will be ##A=9\pi M^2##.
 
  • #7
O yes now i get it
 

What is the Penrose Process?

The Penrose Process is a theoretical process in which energy can be extracted from a rotating black hole. It was proposed by mathematician Roger Penrose in 1969.

How does the Penrose Process work?

The Penrose Process involves sending a particle towards the rotating black hole, where it splits into two particles, with one particle falling into the black hole and the other escaping with more energy than the original particle had. This is possible due to the black hole's rotational energy.

What is the significance of the Hawking Area Theorem?

The Hawking Area Theorem, proposed by physicist Stephen Hawking in 1971, states that the area of a black hole's event horizon can never decrease, only increase or stay constant. This has implications for the irreversible nature of black holes.

What is the relationship between the Penrose Process and the Hawking Area Theorem?

The Penrose Process is related to the Hawking Area Theorem in that it can only occur if the black hole is rotating, and the amount of energy that can be extracted is limited by the area of the black hole's event horizon. This reinforces the idea that black holes can never decrease in size.

Are there any practical applications of the Penrose Process or Hawking Area Theorem?

Currently, there are no known practical applications of the Penrose Process or Hawking Area Theorem. However, they are important concepts in theoretical physics and have contributed to our understanding of black holes and the nature of space and time.

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