Colliding rotating black holes

• TheMan112
In summary, when two black holes collide, they release a great deal of radiation and subsequently lose energy, resulting in a black hole with a lower total mass than the sum of the two original black holes. The amount of energy radiated is related to the area theorem, which states that the sum of the horizon areas of the initial black holes must be lower than the horizon area of the resulting black hole. The upper limit of the energy radiated is 50% of the combined original mass.
TheMan112
If two black holes with equal mass and angular momentum, but the latter in opposite directions were to collide, they would release a great deal of radiation and would subsequently lose energy and the resulting black hole would have a lower total mass than the two previous ones combined. But how can I calculate how much of their combined original mass would (at most) be released as radiation in the collision?

I know I should start from the "area-theorem". Unable to find it in my coursebook, I looked it up on wikipedia.

Hawking's Area theorem:

$$A_H=\frac{4\pi G^2}{c^4}((M + \sqrt{M^2-a^2})^2+a^2)$$

- This being the area of the eventhorizon of the black hole.

Is there some relation between the areas the two original black holes and the subsequently combined black hole?

If two black holes with equal mass and angular momentum, but the latter in opposite directions were to collide, they would release a great deal of radiation and would subsequently lose energy and the resulting black hole would have a lower total mass than the two previous ones combined.
Could you give a reference for this? My understanding is that two black holes colliding end up as one black hole with mass equal to the sum of the individual masses - nothing escaping.

mathman said:
Could you give a reference for this? My understanding is that two black holes colliding end up as one black hole with mass equal to the sum of the individual masses - nothing escaping.

I think it's pretty much an established fact of the theory, reference... this would be an example:

"It is shown that the collision of two black holes would result in the emission of electromagnetic radiation with a very distinctive wave form."

TheMan112 said:
But how can I calculate how much of their combined original mass would (at most) be released as radiation in the collision?
I know I should start from the "area-theorem". Unable to find it in my coursebook, I looked it up on wikipedia.
Hawking's Area theorem:
$$A_H=\frac{4\pi G^2}{c^4}((M + \sqrt{M^2-a^2})^2+a^2)$$
- This being the area of the eventhorizon of the black hole.
Is there some relation between the areas the two original black holes and the subsequently combined black hole?

The formula you give is not the area theorem, but the expression of the horizon area in terms of the Kerr black hole mass and angular momentum (assuming zero charge).

The area theorem states that the horizon area cannot decrease, which implies that the sum of the horizon areas of the initial black holes must be lower than the horizon area of the resulting black hole.

By substituting the above formula in this inequality it appears that the mass can decrease, provided that the area does not decrease. By conservation laws, the decrease in energy shall be equal to the energy radiated. The upper limit of the fraction of energy radiated is 50%, occurring when m1=m2=a1=a2 and a3=0.

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1. What are colliding rotating black holes?

Colliding rotating black holes are two black holes that are in the process of merging together. They are rotating around each other due to their angular momentum, and as they get closer, their gravitational pull increases, causing them to eventually merge into a single black hole.

2. How do colliding rotating black holes form?

Colliding rotating black holes form when two massive stars die and collapse into black holes that are in close proximity to each other. Over time, the black holes' orbits decay and they begin to spiral towards each other until they eventually collide.

3. What happens when colliding rotating black holes merge?

When colliding rotating black holes merge, they release a massive amount of energy in the form of gravitational waves. This energy causes the newly formed black hole to quickly rotate, emitting even more gravitational waves until it becomes stable.

4. Can we observe colliding rotating black holes?

Yes, we can observe colliding rotating black holes through the detection of gravitational waves. Scientists use specialized instruments, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), to detect these waves and study the mergers of black holes.

5. What can we learn from studying colliding rotating black holes?

Studying colliding rotating black holes can provide valuable insights into the nature of gravity and the behavior of matter in extreme conditions. It also helps us better understand the formation and evolution of black holes, as well as the role they play in shaping the universe.

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