The possibility of the no-hair theorem being violated

Recently, one of my articles got some interesting results about Kerr black hole superradiant stability. That result contained some conclusions that violated the “No Hair Theorem”. We know that the “No Hair Theorem” is the inference product of general relativity. I boldly believe that it may lead to a little progress in cosmological research.


I. INTRODUCTION
As stars evolve to the end, serious "collapse" will occur due to the inability to perform higher-level nuclear fusion to resist gravitational forces. The collapse result will be greatly different due to the gravitational gap caused by its mass.
For example, the sun will eventually become a white dwarf Stars that are more than three times larger than the Sun will eventually become "black holes". This limit is called the Oppenheimer limit. Currently, accepted theory holds that there are only three physical quantities that a black hole can measure: mass, charge, and angular momentum.
That is, for a black hole, once these three physical quantities are determined, the characteristics of the black hole are uniquely determined. This is called the black hole's no-hair theorem, or the uniqueness theorem of black holes.
On the other hand, once a black hole is formed, other physical information before the formation of the black hole is lost. There are no cubes, cones or other convex forms on the black hole. This is another way to understand the black hole's no-hair theorem.
Regge and Wheeler [13] proved that the Schwarzschild black holes are stable under disturbance. Due to the superradiation phenomenon, the stability of rotating black holes becomes more complicated. The superradiation effect allows the extraction of rotational and Coulomb energy from rotating or charged black holes. In 1972, Press and Teukolsky [12] proposed that It is possible to add a mirror to the outside of a black hole to make a black hole bomb (according to the current explanation, this is a scattering process involving classical mechanics and quantum mechanics [2,4,10,11]).
When a bosonic wave is impinging upon a rotating black hole, the wave reflected by the event horizon will be amplified if the wave frequency ω lies in the following superradiant regime [12,15,16] where m is azimuthal number of the bosonic wave mode, Ω H is the angular velocity of black hole horizon.This * Electronic address: wxchen4277@qq.com amplification is superradiant scattering. Therefore, through the superradiation process, the rotational energy or electromagnetic energy of a black hole can be extracted. If there is a mirror between the black hole's horizon and infinite space, the amplified wave will scatter back and forth and grow exponentially, which will cause the black hole's superradiant instability.
The no-hair theorem states that all black hole solutions of Einstein-Maxwell's gravitational and electromagnetic equations of general relativity can only be fully characterized by three classical parameters that can be observed from the outside: mass, charge, and angular momentum. All other information (metaphors about the "hair" that forms or falls into a black hole) "disappears" after the event horizon of the black hole, so external observers can never enter.
The no-hair theorem shows that for the disturbance incident on Kerr black hole, the geometry shown by its coupling with the black hole can be expressed by the parameters of the black hole.
That result contained some conclusions that violated the "No Hair Theorem"(This result shows that not all black hole solutions are only related to three black hole parameters).

II. DESCRIPTION OF THE KERR-BLACK-HOLE SYSTEM
The metric of the Kerr black hole [6,8,9] (in natural unit G=c=1) is Regarding the scalar field, we limit it with the Klein-Gordon equation Eigenvalues of the above formula and spherical harmonic functions(The integer parameters m and l ≥ |m| are the azimuthal and spheroidal harmonic indices of the scalar field modes) can be written as Substituting (6) According to the references [1,5,14],we get inequality(8) where l is the spherical harmonic index, m is the azimuthal harmonic index with −l ≤ m ≤ l and ω is the energy of the mode. The radial Klein-Gordon equation [5,14] obeyed by R lm is given by where and The inner and outer horizons of the black hole are and we get that The radial potential equation is transformed into a tortoise coordinate wave equation to solve the asymptotic behavior of the wave function.We use tortoise coordinate r * by equation dr * 2 dr 2 = r 2 ∆ and another radial function ψ = rR.We get the following radial wave equation where Then we get the asymptotic solutions for the radial wave equation below When there is a bound state of the scalar field.
When ϕ = ∆ 1 2 R, radial potential equation (9) can be transformed into the flat space-time wave equation velocity Ω H , the inequality fixed Kerr black hole-mass-scale scalar field configuration upper bound.
Although much research has been done on the superradiance of rotating black holes, even Kerr black holes have not been thoroughly studied.Hod proved [8] that one finds the upper bound on the scalar mass of fixed bound state field configuration, where γ = r− r+ , and the dimensionless function F = F(γ) is given by In Table 1 we present the dimensionless ratio µ numerical /µ bound , where µ numerical is the numerically computed field masses which mark the onset of the superradiant instabilities in the composed Kerr-black-hole-massive-scalar-field system, and µ bound is the analytically derived upper bound(21) on the superradiant instability regime of the composed black-hole-field system.One finds from Table 1 that the superradiant instability regime of the composed Kerr-blackhole-massive-scalar-field system is characterized by the relation µ numerical /µ bound < 1. Table 1: For µ 2 = y 2 ω 2 , when y > 4.352, there exists a certain interval to let the inequality be satisfied. So the Kerr black hole is superradiantly stable at that time [3].
Because y can theoretically be taken in the range of y > 4.352, we see that when y is relatively large(according to the properties of the boson, y can be very large), the superradiant stability interval of µ can always include some numerical solutions of the superradiant instability obtained by previous people. If I'm right, there might be something wrong with the no-hair theorem. This result shows that not all black hole solutions are only related to three black hole parameters.In this case, it also depends on the value of y .
We do a thinking experiment. When the incident disturbance parameter y satisfies the above conditions(y is very large, so µ can always include the numerical solutions of the superradiant instability ), if it can produce instability, then the no-hair theorem is still correct. If we observe that the Kerr black hole is stable, then the no-hair theorem is problematic.

V. SUMMARY
Recently, an article of mine has obtained interesting results about the superradiant stability of Kerr black holes.
The result contains some conclusions that violate the "no-hair theorem".I boldly believe that it may lead to a little progress in cosmological research.