Yes. (Note that this theorem excludes any quantum effects.)Hawking area theorem says that area of black hole generally never decrease.
Yes, but this only happens with a rotating black hole, and the hole also loses angular momentum in this process.Penrose process says that energy can be extracted from black hole. Energy extraction will decrease mass?
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.if mass is decreased then will area also decrease?
This has confused me more.. if both mass and angular momentum are decreasing then area must also decrease. How it end up increasing?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.
No. Look at the minus sign in front of ##a^2## in the heuristic formula I gave. If angular momentum decreases, the area increases.if both mass and angular momentum are decreasing then area must also decrease.
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.No. Look at the minus sign in front of ##a^2## in the heuristic formula I gave. If angular momentum decreases, the area increases.
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##.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.