- The Development of the Virial Method and. - The Beginning of the End XII. - The looseness of the whole argument was apparent. - 0 Y (µ) ψ (µ) dµ = 0) of the functional equations. - And hand iterations seemed out of the question. - First there was the paper on the polarization of the sunlit sky. - and George Backus was a member of the class.. - Savage was one of the new recruits.. - And finally there was the problem of the curved channel. - The problem was finally resolved in the pressure of the last weeks. - the various branches of the solution. - Wood of the Clarendon Press.. - This was the origin of the paper on “The potentials and the superpotentials of homogeneous ellipsoids” (7). - 1962 third-harmonic oscillations of the Jacobi ellipsoid. - of the Maclaurin spheroids in the post-Newtonian approximation.. - Once the problem of the Maclaurin sequence in the post-. - 1967 of the oscillations of rotating mass in the post-Newtonian theory. - of the post-post-Newtonian theory. - g was independent of the gauge chosen in the second post-Newtonian approximation;. - and the reduction of the equation θ αi ,i=0 . - the last section of the book. - The organization of the paper on the second post-Newtonian. - The completion of the second post-Newtonian approximation. - It was probably one of the more “eloquent”. - European Meeting of the I.A.U. - during the month following the end of the quarter.. - niversary celebrations of the University of Delhi. - and the matter of the Kerr metric was left inconclusive.. - normal modes of the Schwarzschild black hole. - During July, I was occupied with the transformation of the. - The deformed figures of the Maclaurin spheroids (continued), Ap. - The deformed figures, of the Jacobi ellipsoids (continued), Ap. - But the question of the general non-axisymmetric. - separation of the variables. - of the solution was accomplished with unexpected brusqueness. - of the derivation of the Kerr metric. - Swerdlow of the three Neugebauer volumes (18).. - (1) On the equations governing the axisymmetric perturbations of the Kerr black hole (S. - (7) On the equations governing the gravitational perturbations of the Kerr black hole (S. - (8) On the linear perturbations of the Schwarzschild and the Kerr black holes, Varenna Lectures. - (13) The gravitational perturbations of the Kerr black hole. - (16) On the discovery of the enclosed photograph of S. - Neugebauer, Bulletin of the American Mathematical Society.. - in the case of the Schwarzschild perturbations was “obvious. - The writing of the article required considerable concentration:. - (1) The gravitational perturbations of the Kerr black hole. - (5) On the metric perturbations of the Reissner–Nordstr¨ om black hole.. - In London, we stayed in the rooms of the Royal Society. - (2) The gravitational perturbations of the Kerr black hole: IV. - The completion of the solution (Proc. - a Regents Fellow of the Smithsonian Institution at Harvard. - a complete discussion of the Bianchi identities (including the Ricci terms). - Next, there was the matter of the geodesies. - The derivation of the relation in Sec. - (The two Equations (59) and (60) became essential for certain later developments: in the derivation of the Kerr–. - The treatment of the Penrose process in Sec. - and (2) the justification of the boundary conditions used in the super-radiant interval. - And there was the matter of the Prologue. - THE PERTURBATIONS OF THE SCHWARZSCHILD METRIC 1. - The Instability of the Inner Horizon VII. - The uniqueness of the Kerr Metric 5. - A General Description of the Geodesies 4. - THE PERTURBATIONS OF THE KERR METRIC I:. - THE PERTURBATIONS OF THE KERR METRIC II:. - The Reduction of the Equations 2. - Summary of the Solution 7. - THE PERTURBATIONS OF THE KERR METRIC III:. - THE PERTURBATIONS OF THE KERR METRIC IV:. - (e) A generalized version of the tetrad formalism 8. - (b) The representation of the Weyl, “the Ricci, and the Riemann tensors”. - An alternative derivation of the Schwarzschild metric. - 1) (i) Orbits of the first kind. - (γ) The post-Newtonian approximation (ii) Orbits of the second kind. - (b) The critical orbits (i) The cone of avoidance (c) The geodesies of the first kind. - (i) The asymptotic behavior of ϕ ∞ for P/3M → 1 and P 3M (d) The geodesies of the second kind. - THE PERTURBATIONS OF THE SCHWARZSCHILD BLACK HOLE 22. - (i) The reduction of the equations to a one-dimensional wave equation (ii) The completion of the solution. - (b) The completion of the solution of Equations and the phantom gauge. - The physical content of the theory. - The stability of the Schwarzschild black hole. - The quasi-normal modes of the Schwarzschild black hole. - The nature of the space-time. - (i) The completion of the solution. - The derivation of the Kerr metric. - (a) The tetrad components of the Riemann tensor. - The uniqueness of the Kerr metric. - The Kerr–Schild form of the metric. - The nature of the Kerr space-time. - (a) The reduction and the separability of the equations Φ 0 and Φ 2. - The completion of the solution. - (b) The asymptotic behavior of the solutions 75. - THE GRAVITATIONAL PERTURBATIONS OF THE KERR BLACK HOLE. - a statement of the problem. - The linearization of the remaining Bianchi identities. - The linearization of the commutation relations. - The solution of the integrability condition. - (a) The reduction of the solutions for Z 1 and Z 2. - The form of the solution in the Schwarzschild limit, a → 0. - (c) The nature of the potentials. - (d) The relation between the solutions belonging to the different potentials (e) The asymptotic behaviors of the solutions