Bruno Carneiro da Cunha

Kerr-CFT from black-hole thermodynamics

We analyze the near-horizon limit of a general black hole with two commuting killing vector fields in the limit of zero temperature. We use black hole thermodynamics methods to relate asymptotic charges of the complete spacetime to those obtained in the near-horizon limit. We then show that some diffeomorphisms do alter asymptotic charges of the full spacetime, even though they are defined in the near horizon limit and, therefore, count black hole states. We show that these conditions are essentially the same as considered in the Kerr/CFT corresponcence. From the algebra constructed from these diffeomorphisms, one can extract its central charge and then obtain the black hole entropy by use of Cardy’s formula.

Isomonodromy, Painleve transcendents and scattering off of black holes

A bstractWe 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 Painlevé VI transcendent. We review a few facts about Painlevé 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 Painlevé, and discuss the implications of the generic result to black hole complementarity.

On the existence of monodromies for the Rabi model

We discuss the existence of monodromies associated with the singular points of the eigenvalue problem for the Rabi model. The complete control of the full monodromy data requires the taming of the Stokes phenomenon associated with the unique irregular singular point. The monodromy data, in particular the composite monodromy, are written in terms of the parameters of the model via the isomonodromy method and the tau-function of the Painleve V. These data provide a systematic way to obtain the quantized spectrum of the Rabi model.

Kerr scattering coefficients via isomonodromy

A bstractWe study the scattering of a massless scalar field in a generic Kerr background. Using a particular gauge choice based on the current conservation of the radial equation, we give a generic formula for the scattering coefficient in terms of the composite monodromy parameter σ between the inner and the outer horizons. Using the isomonodromy flow, we calculate σ exactly in terms of the Painlevé V τ -function. We also show that the eigenvalue problem for the angular equation (spheroidal harmonics) can be calculated using the same techniques. We use recent developments relating the Painlevé V τ -function to Liouville irregular conformal blocks to claim that this scattering problem is solved in the combinatorial sense, with known expressions for the τ -function near the critical points.

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 six-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.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 six-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.

On the Kerr-AdS/CFT correspondence

A bstractWe review the relation between four-dimensional global conformal blocks and field propagation in AdS5. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-AdS5 geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of c = 1 chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.

The isomonodromy method for black hole scattering

We summarize recent results by the authors [7, 8, 35] on the extraction of scattering amplitudes for scalar fields in Kerr/Kerr-de Sitter backgrounds. Analytical, closed forms are found in terms of the Painleve V and VI transcendents for generic values of the physical parameters.

Holography as Cutoff: a proposal for measure of inflationary universes

We propose the holographic principle as a dynamical cutoff for any quantum theory of gravity, incorporating ideas of effective field theory. This is done by viewing the holographic bound as a limit on the number of degrees of freedom that can be turned on before the geometrical picture of gravity loses applicability. We illustrate the proposal by revisiting the problem of defining a measure for homogeneous and isotropic space–times coupled to a scalar field and conclude by discussing the implications to the single scalar field inflationary model.

Note on tachyon moduli and closed strings

The collective behavior of the

Kerr–de Sitter greybody factors via isomonodromy

\mathrm{SL}(2,\mathbb{R})