Proof of uniqueness of the Kerr-Newman black hole solution

Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields

“…Actually, as we also show, the rod structure in particular determines the topology of the horizon, which we show may be either be a 3-sphere S 3 , a ring S 2 × S 1 , or a Lens-space L(p, q). Our proof of these statements uses a known σ-model formulation of the reduced Einstein equations in 5 dimensions due to Maison [25], which is analogous to a formulation previously found by Mazur [27] and used in his uniqueness proof in 4 dimensions. We combine this technique with an elementary analysis of the global structure of the orbit space of the symmetries.…”

Slowly rotating supercompact Schwarzschild stars

“…Finally, the uniqueness theorem for the Kerr-Newmann [69] rotating charged black hole, was nailed down by Mazur [58] who showed that general black holes are characterized uniquely by three parameters; mass M , charge Q and angular momentum J. Moreover, the gravitational field of a stationary and charged black hole is determined only by the Kerr-Newman solution to the Einstein-Maxwell system, under the…”

“…In terms of the parameter k, defined above, this limit is equivalent to the condition 58) for the solution to be regular. We will go back to this point in the next chapter.…”

Editorial note to: Brandon Carter, Black hole equilibrium states Part II. General theory of stationary black hole states

“…The situation shortly after the Les Houches school was succinctly described (in "A brief History of Time") by Stephen Hawking [2] As well as the successive removal of restrictions on the validity of the theorem for the Kerr geometry in the pure vacuum case, work in more recent years, particularly by David Robinson [3], Paweł Mazur [4,5], and Gary Bunting [6] has obtained analogous results for the charged Kerr-Newman geometry in the Einstein-Maxwell case, and in doing so has also provided more elegant methods for deriving what was previously known about the pure vacuum case. 3 At Les Houches Carter was not only lecturing, but also conducting with James Bardeen and Stephen Hawking an intense research that resulted in a publication (next year) of their seminal paper [10] on the four laws of the black hole mechanics.…”

“…Indeed, Carter [12,13], a fully satisfactory physical interpretation of the Bekenstein-Hawking black hole entropy is still today a matter of an interesting debate, to which string theory contributes most forcefully. 4 The obvious question that a practical mind must ask is, what do these mathematically powerful results imply (if anything) for the real astrophysical black holes that have already been discovered in our Galaxy? Should one care about the enormously large Bekenstein-Hawking entropy of the astrophysical black holes when calculating their observable properties?…”