On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes

We consider the problem of quasinormal modes (QNM) for strongly hyperbolic systems on stationary, asymptotically anti-de Sitter black holes, with very general boundary conditions at infinity. We argue that for a time slicing regular at the horizon the QNM should be identified with certain H^k eigenvalues of the infinitesimal generator of the solution semigroup. Using this definition we are able to prove directly that the quasinormal frequencies form a discrete, countable subset of the complex plane, which in the globally stationary case accumulates only at infinity. We avoid any need for meromorphic extension, and the quasinormal modes are honest eigenfunctions of an operator on a Hilbert space. Our results apply to any of the linear fields usually considered (Klein-Gordon, Maxwell, Dirac etc.) on a stationary black hole background, and do not rely on any separability or analyticity properties of the metric. Our methods and results largely extend to the locally stationary case. We provide a counter-example to the conjecture that quasinormal modes are complete. We relate our approach directly to the approach via meromorphic continuation.Comment: 81 pages, 6 figures. V3: To appear in Comm. Math. Phy

Generalized hidden symmetries and the Kerr-Sen black hole

We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their relationship to Killing tensors and the separability of various field equations. We further demonstrate that the Kerr-Sen black hole spacetime of heterotic string theory, as well as its generalization to all dimensions, possesses a generalized closed conformal Killing-Yano 2-form with respect to a torsion identified with the 3-form occuring naturally in the theory. Such a 2-form is responsible for complete integrability of geodesic motion as well as for separability of the scalar and Dirac equations in these spacetimes.Comment: 33 pages, no figure

Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes

We study the global dynamics of free massive scalar fields on general, globally stationary, asymptotically AdS black hole backgrounds with Dirichlet-, Neumann- or Robin- boundary conditions imposed on $\psi$ at infinity. This class includes the regular Kerr-AdS black holes satisfying the Hawking Reall bound $r_+^2 > |a|l$. We establish a suitable criterion for linear stability (in the sense of uniform boundedness) of $\psi$ and demonstrate how the issue of stability can depend on the boundary condition prescribed. In particular, in the slowly rotating Kerr-AdS case, we obtain the existence of linear scalar hair (i.e. non-trivial stationary solutions) for suitably chosen Robin boundary conditions.Comment: 46 pages, 3 figures; V2 significant updat

The Einstein-Klein-Gordon-AdS system for general boundary conditions

We construct unique local solutions for the spherically-symmetric Einstein–Klein–Gordon–anti-de Sitter (AdS) system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. This paper furnishes a starting point for such global investigations. </jats:p

Aspherical photon and anti-photon surfaces

© 2016 The Authors In this note we identify photon surfaces and anti-photon surfaces in some physically interesting spacetimes, which are not spherically symmetric. All of our examples solve physically reasonable field equations, including for some cases the vacuum Einstein equations, albeit they are not asymptotically flat. Our examples include the vacuum C-metric, the Melvin solution of Einstein–Maxwell theory and generalisations including dilaton fields. The (anti-)photon surfaces are not round spheres, and the lapse function is not always constant

Genome-Wide Diet-Gene Interaction Analyses for Risk of Colorectal Cancer

Dietary factors, including meat, fruits, vegetables and fiber, are associated with colorectal cancer; however, there is limited information as to whether these dietary factors interact with genetic variants to modify risk of colorectal cancer. We tested interactions between these dietary factors and approximately 2.7 million genetic variants for colorectal cancer risk among 9,287 cases and 9,117 controls from ten studies. We used logistic regression to investigate multiplicative gene-diet interactions, as well as our recently developed Cocktail method that involves a screening step based on marginal associations and gene-diet correlations and a testing step for multiplicative interactions, while correcting for multiple testing using weighted hypothesis testing. Per quartile increment in the intake of red and processed meat were associated with statistically significant increased risks of colorectal cancer and vegetable, fruit and fiber intake with lower risks. From the case-control analysis, we detected a significant interaction between rs4143094 (10p14/near GATA3) and processed meat consumption (OR = 1.17; p = 8.7E-09), which was consistently observed across studies (p heterogeneity = 0.78). The risk of colorectal cancer associated with processed meat was increased among individuals with the rs4143094-TG and -TT genotypes (OR = 1.20 and OR = 1.39, respectively) and null among those with the GG genotype (OR = 1.03). Our results identify a novel gene-diet interaction with processed meat for colorectal cancer, highlighting that diet may modify the effect of genetic variants on disease risk, which may have important implications for prevention. © 2014