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I heard many times that there exists only one black hole solution for a given mass and angular momentum, but I know already that this is not true.

We all know that if we throw something into an existing black hole, its event horizon starts to ripple. So there are many solutions for a given mass and angular momentum, which can be distinguished by the shape of the event horizon.

The correct true statements about black holes are:

1. There exists only one

**stationary**solution for a given mass and angular momentum.

2. There are no

**periodic**(oscillating) solutions for any mass or angular momentum.

Now we know that any disturbance of event horizon will radiate gravitational waves, losing energy. That means, if we start from a disturbed solution, it will start approaching the only stationary solution.

Now my question is:

**will a disturbed black hole reach the stationary solution in finite time**or will it radiate energy forever?

Quote from "Black Holes in Higher Dimensions", Gary Horowits, p. 17:

*The Schwarzshild and Reisner-Nordstroem solutions have been shown to be stable to linearized perturbations. Black holes do not have ordinary normal modes since energy can be lost via radiation out to infinity or via waves falling through the horizon. If one considers perturbations with a harmonic time dependence exp(-i omega t) and imposes boundary conditions that the modes are purely outgoing at infinity and ingoing at the horizon then one finds solutions for a discrete set of complex omega. These are called quasinormal modes. The imaginary part of omega is negative, so these modes oscillate with exponentially decaying amplitude. A typical perturbation of the black hole decays exponentially for a while but falls off like power law at later times. This is a result of backscattering of the perturbation off the curvature around the black hole.*

What I understand is that holes can be oscillating, but with decaying amplitude. Nevertheless, in absence of some quantum effects the amplitude never goes to zero. That means

**classical black holes do have hair**. Once the hole got hair it never goes bald.