The Mathematical Theory of Black Holes

Hybrid approach to black hole perturbations from extended matter sources

“…(3.16) and (3.17), can be expressed in terms of the solutions Z ÿ in=out ' of the corresponding homogeneous RWZ Eqs. (3.7) through the Chandrasekhar transformation [25] in=out '…”

Non Linear Perturbations of Kerr Spacetime in External Regions and the Peeling Decay

“…1 What is known up to now relative to the whole outer region are some relevant uniform boundedness results for solutions to the wave equation in the Kerr spacetime used as a background spacetime (see Dafermos and Rodnianski [7], Klainerman [9]). 2 If we consider the existence problem in an external region sufficiently far from the Kerr event horizon for a slow rotating Kerr spacetime, the result is included in the version of Minkowski stability result proved by S. Klainerman and one of the present author, F. Nicolò, see [10] and also [6]. In this case F. Nicolò, recently proved [15], that the asymptotic behaviour of the Riemann components is in agreement with the "Peeling theorem" if the corrections to the Kerr initial data decay sufficiently fast.…”

“…Therefore, hereafter with r, we always mean the quantity defined in (2.42), a well-defined function of u and u. Finally, the norms we are using for the connection coefficients are, as in [10], or sup norms, | · | ∞ , or (p, S)-norms, | · | p,S , with p ∈ [2,4], where…”

From white dwarfs to black holes (commemorating the 70th anniversary of the theory of compact objects)

“…One could finish the article by Chandrasekhar's (1983) words, who investigated black hole theory for several years at the end of his life: "It is hardly probable that I would sin against the truth, confirming that black holes are the most perfect objects in the Universe, since we need only space and time concepts for their determination, as general relativity predicts that the black holes are described by the only one family of solutions, one could think that they are also the most simple". In accordance with Chandrasekhar's statement, a lot of researchers nowadays see the remarkable beauty (and simplicity) of black holes.…”