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Decay of the Maxwell field on the Schwarzschild manifold
 arXiv:0710.4102, J. Hyp. Diff. Eqns
"... We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate r ranges over 2M < r1 < r < r2, we obtain a decay rate of t −1 for all components of the Maxwell field. We use vector field m ..."
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We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate r ranges over 2M < r1 < r < r2, we obtain a decay rate of t −1 for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the ReggeWheeler tortoise coordinate is large, r ∗> ǫt, we obtain decay for the null components with rates of φ+  ∼ α  < Cr −5/2, φ0  ∼ ρ  + σ  < Cr −2 t − r∗  −1/2, and φ−1  ∼ α  < Cr −1 t − r∗  −1. Along the event horizon and in ingoing regions, where r ∗ < 0, and when t + r ∗> 1, all components (normalized with respect to an ingoing null basis) decay at a rate of Cu+ −1 with u+ = t + r ∗ in the exterior region. 1
Linear waves in the Kerr geometry: a mathematical voyage to black hole physics
 Bull. Amer. Math. Soc. (N.S
"... Abstract. This paper gives a survey of wave dynamics in the Kerr spacetime geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin s = 0, 1,1, 2, ..."
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Abstract. This paper gives a survey of wave dynamics in the Kerr spacetime geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin s = 0, 1,1, 2, cor 2 responding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the longtime dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open
Decay Rates for Spherical Scalar Waves in the Schwarzschild Geometry
, 2007
"... The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data, which is smooth and compactly supported outside the event h ..."
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The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data, which is smooth and compactly supported outside the event horizon. 1
Perturbation theory of spherically symmetric selfsimilar black holes
, 706
"... The theory of perturbations of spherically symmetric selfsimilar black holes is presented, in the NewmanPenrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is giv ..."
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The theory of perturbations of spherically symmetric selfsimilar black holes is presented, in the NewmanPenrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is given. Monopole and dipole modes are treated. The NewmanPenrose wave equations governing polar and axial spin0 perturbations are explored. PACS numbers: 04.20.q