# Gravitational and electromagnetic radiation from collision of Kerr-Newman black holes

When black holes collide, they produce a gravitational wave, as has been recently established by LIGO. When a charge is accelerated, it creates an electromagnetic wave.

Does an accelerated massive charge, such as a Reissner-Nordstrom black hole, or, more generally, a Kerr-Newman black hole, produce electromagnetic radiation? If so, how will the radiation behave in the higly curved space-time surrounding such objects?

(EDIT: The answer to this question, as given by Lawrence B. Crowell, is yes- at $r>>r_s$ the spacetime is flat and must behave classically, so massive compact charges will still produce radiation when accelerated, and the radiation as precieved by an observer at infinity must match the classical predictions.)

Will two colliding Kerr-Newman black holes create an electromagnetic wave as well as a gravitational wave? If so, will the two waves be somehow correlated or mudulated by each other? Will they even coexist on the same plane? Will the spin of the black hole affect the produced radiation?

In short: how will the gravitational and electromagnetic radiation produced in a collision of two Kerr-Newman black holes behave, both independently and with respect to one another?

Thank you!

Consider the KN black hole at a distance. At sufficient distance the gravity field is Newtonian and the lines of electric field radially leave the charge source. If this is accelerating then the changing lines of electric field will still respond to generate Brehmsstralung radiation.

As for colliding charged black holes the energy associated with the electric field is converted into gravitational radiation. The reason is that the horizon area is determined by both mass and charge, with $r_+~=~m~+~\sqrt{m^2~-~Q^2}$. The area is reduced. The collision of two black hole with equal and opposite charge will result in a black hole for a Schwarszchild black hole with double the area. This is the idealization for constant entropy, which of course is not realistic. So more gravitational radiation must be emitted.

I should say that for the collision of two Schwarzschild black holes if entropy is constant, or total horizon area conserved, then $29$% of mass is converted to gravitational radiation. The LIGO black holes if you have followed this only convert about $5$% of their initial mass to gravitational radiation. What happens in the near field region is that a lot of gravitational radiation scatters back into the single new black hole.

As a result two oppositely charged black holes will convert most of the potential energy $U~=~-Q^2/r$ into gravitational radiation. There might be though some small amount of EM radiation produced. To nail that down would require a bit of analysis.

• Thank you! If EM radiation is produced, will it be polarized by the gravitational waves? – A. Ok Jun 21 '17 at 0:18
• If EM radiation is produced I have no idea what its characterization would be. – Lawrence B. Crowell Jun 21 '17 at 12:14