# Colliding rotating black holes

1. Feb 23, 2008

### 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?

2. Feb 23, 2008

### mathman

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.

3. Feb 23, 2008

### TheMan112

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."

4. Feb 24, 2008

### xantox

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.

Last edited: Feb 24, 2008