On the Six-dimensional Kerr Theorem and Twistor Equation

The Kerr theorem is revisited as part of the twistor program in six dimensions. The relationship between pure spinors and integrable 3-planes is investigated. The real condition for Lorentzian spacetimes is seen to induce a projective property in the space of solutions, reminiscent of the quaternionic structure of the 6-dimensional Lorentz group. The twistor equation (or Killing spinor equations generically) also has an interpretation as integrable null planes and a family of Einstein spacetimes with this property are presented in the Kerr-Schild fashion.Comment: JHEP style, 19 pages, minor corrections. Matches printed versio

Isomonodromy, Painlev\'e Transcendents and Scattering off of Black Holes

We apply the method of isomonodromy to study the scattering of a generic Kerr-NUT-(A)dS black hole. For generic values of the charges, the problem is related to the connection problem of the Painlev\'e VI transcendent. We review a few facts about Painlev\'e VI, Garnier systems and the Hamiltonian structure of flat connections in the Riemann sphere. We then outline a method for computing the scattering amplitudes based on Hamilton-Jacobi structure of Painlev\'e, and discuss the implications of the generic result to black hole complementarity.Comment: 40 pages, 4 figures, JHEP styl

The Technology of Skill Formation

his paper presents formal models of child development that capture the essence of recent findings from the empirical literature on child development. The goal is to provide theoretical frameworks for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies and for formulating policy. We start from the premise that skill formation is a life-cycle process. It starts in the womb and goes on throughout most of the adult life. Families and firms have a role in this process that is at least as important as the role of schools. There are multiple skills and multiple abilities that are important for adult success. Abilities are both inherited and created, and the traditional debate of nature versus nurture is outdated and scientifically obsolete. The technology of skill formation has two additional important characteristics. The first one is that IQ and behavior are more plastic at early ages than at later ages. Furthermore, behavior is much more malleable than IQ as individuals age. The second is that human capital investments are complementary over time. Early investments increase the productivity of later investments. Early investments are not productive if they are not followed up by later investments. The returns to investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very costlyhuman capital, life cycle of skill formation

Scalar quasinormal modes of Kerr-AdS5\mathbf{_5}

An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{AdS_5}$ black holes was previously proposed by the authors in ref. 1, in terms of transcendental equations involving the Painlev\'e VI (PVI) $\tau$ function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI $\tau$ function both in terms of conformal blocks (Nekrasov functions) and Fredholm determinants. We compare the results with standard numerical methods for the subcase of Schwarzschild black holes. We then derive asymptotic formulas for the angular eigenvalues and the quasinormal modes in the small black hole limit for generic scalar mass and discuss, both numerically and analytically, the appearance of superradiant modes.Comment: JHEP style, 42 pages, 3 figures, 3 tables; Updated discussion on the superradiant mode