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We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three-dimensional backgrounds, including the BTZ black hole in string theory and…

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive…

We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near…

We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for…

We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition.…

We investigate the quasinormal modes of several families of higher-dimensional regular black holes arising in gravitational theories that incorporate an infinite tower of higher-curvature corrections to Einstein gravity. Our analysis…

The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional ${\cal N}=1$ supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the…

We establish a deep connection between the Prandtl equations linearised around a quadratic shear flow, confluent hypergeometric functions of the first kind, and the Schr\"odinger operator. Our first result concerns an ODE and a spectral…

We formulate the inverse spectral theory of infinite gap Hill's operators with bounded periodic potential as a Riemann--Hilbert problem on a typically infinite collection of spectral bands and gaps. We establish a uniqueness theorem for…

Linear perturbations of spherically symmetric spacetimes in general relativity are described by radial wave equations, with potentials that depend on the spin of the perturbing field. In previous work we studied the quasinormal mode…

In this paper we present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschild-black-hole background. The wave equa- tion in question is…

The vector Riemann-Hilbert problem is analyzed when the entries of its matrix coefficient are meromorphic and almost periodic functions. Three cases for the meromorphic functions, when they have (i) a finite number of poles and zeros…

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…

We revisit a deformed Jackiw-Teitelboim model with a hyperbolic dilaton potential, constructed in the preceding work [arXiv:1701.06340]. Several solutions are discussed in a series of the subsequent papers, but all of them are pathological…

We prove operator-norm resolvent convergence estimates for one-dimensional periodic differential operators with rapidly oscillating coefficients in the non-uniformly elliptic high-contrast setting, which has been out of reach of the…

The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic properties of the general solution, novel…

Quasinormal modes (QNMs) are usually characterized by their time dependence; oscillations at specific frequencies predicted by black hole (BH) perturbation theory. QNMs are routinely identified in the ringdown of numerical relativity…