Local metrics admitting a principal Killing-Yano tensor with torsion

In this paper we initiate a classification of local metrics admitting the principal Killing--Yano tensor with a skew-symmetric torsion. It is demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and mutually commute. We reduce the classification problem to that of solving a set of partial differential equations, and we present some solutions to these PDEs. In even dimensions, three types of local metrics are obtained: one of them naturally generalizes the torsionless case while the others occur only when the torsion is present. In odd dimensions, we obtain more varieties of local metrics. The explicit metrics constructed in this paper are not the most general possible admitting the required symmetry, nevertheless, it is demonstrated that they cover a wide variety of solutions of various supergravities, such as the Kerr-Sen black holes of (un-)gauged abelian heterotic supergravity, the Chong-Cvetic-L\"u-Pope black hole solution of five-dimensional minimal supergravity, or the K\"ahler with torsion manifolds. The relation between generalized Killing--Yano tensors and various torsion Killing spinors is also discussed.Comment: 36pages, no figure

Effective field theory and classical equations of motion

Given a theory containing both heavy and light fields (the UV theory), a standard procedure is to integrate out the heavy field to obtain an effective field theory (EFT) for the light fields. Typically the EFT equations of motion consist of an expansion involving higher and higher derivatives of the fields, whose truncation at any finite order may not be well-posed. In this paper we address the question of how to make sense of the EFT equations of motion, and whether they provide a good approximation to the classical UV theory. We propose an approach to solving EFTs which leads to a well-posedness statement. For a particular choice of UV theory we rigorously derive the corresponding EFT and show that a large class of classical solutions to the UV theory are well approximated by EFT solutions. We also consider solutions of the UV theory which are not well approximated by EFT solutions and demonstrate that these are close, in an averaged sense, to solutions of a modified EFT.Comment: 47 pages; references update

On the backreaction of frame dragging

The backreaction on black holes due to dragging heavy, rather than test, objects is discussed. As a case study, a regular black Saturn system where the central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is considered. It is shown that there is a correlation between the sign of two response functions. One is interpreted as a moment of inertia of the black ring in the black Saturn system. The other measures the variation of the black ring horizon angular velocity with the central black hole mass, for fixed ring mass and angular momentum. The two different phases defined by these response functions collapse, for small central black hole mass, to the thin and fat ring phases. In the fat phase, the zero area limit of the black Saturn ring has reduced spin j^2>1, which is related to the behaviour of the ring angular velocity. Using the `gravitomagnetic clock effect', for which a universality property is exhibited, it is shown that frame dragging measured by an asymptotic observer decreases, in both phases, when the central black hole mass increases, for fixed ring mass and angular momentum. A close parallelism between the results for the fat phase and those obtained recently for the double Kerr solution is drawn, considering also a regular black Saturn system with J^{BH}\neq 0.Comment: 18 pages, 8 figure

Asymptotic properties of linear field equations in anti-de Sitter space

We study the global dynamics of the wave equation, Maxwell's equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove uniform boundedness of the natural energy as well as both degenerate (near the AdS boundary) and non-degenerate integrated decay estimates. Remarkably, the non-degenerate estimates "lose a derivative". We relate this loss to a trapping phenomenon near the AdS boundary, which itself originates from the properties of (approximately) gliding rays near the boundary. Using the Gaussian beam approximation we prove that non-degenerate energy decay without loss of derivatives does not hold. As a consequence of the non-degenerate integrated decay estimates, we also obtain pointwise-in-time decay estimates for the energy. Our paper provides the key estimates for a proof of the non-linear stability of the anti-de Sitter spacetime under dissipative boundary conditions. Finally, we contrast our results with the case of reflecting boundary conditions

Willingness to Pay to Reduce Future Risk

We elicit subjects’ willingness to pay to reduce future risk. In our experiments, subjects are given a cash endowment and a risky lottery. They report their willingness to pay to exchange the risky lottery for a safe one. Subjects play the lottery either immediately, eight weeks later, or twenty-five weeks later. Thus, both the lottery and the future are sources of uncertainty in our experiments. In two additional treatments, we control for future uncertainty with a continuation probability, constant and independent across periods, that simulates the chances of not returning to play the lottery after eight and twenty-five periods. We find evidence for present bias in both the time-delay sessions and the continuation probability sessions, suggesting that this bias robustly persists in environments including both risk and future uncertainty, and suggesting that the stopping rule may be a tool to continue study in this area without the need to delay payments into the future. Nous mesurons la volonté des participants de payer pour réduire les risques futurs. Au cours de nos séances expérimentales, les participants reçoivent une dotation en espèces et une loterie risquée. Ils signalent leur volonté de payer pour échanger la loterie risquée pour une loterie moins risquée. Les participants jouent à la loterie soit immédiatement, ou huit semaines plus tard, ou vingt-cinq semaines plus tard. Ainsi, dans ces expériences, la loterie et le futur forment deux sources d'incertitude. Lors de deux traitements additionnels, nous contrôlons l'aspect incertain de l'avenir avec une probabilité de continuation, constante et indépendante à travers les périodes, qui simule les chances de ne pas revenir jouer à la loterie après huit et vingt-cinq périodes. Nous avons trouvé des preuves d'un biais pour le présent à la fois dans les séances avec un délai temporel, que dans les séances avec une probabilité de continuation, ce qui suggère que cette tendance persiste avec vigueur dans les environnements comprenant de l'incertitude provenant à la fois du risque et du futur. Ceci suggère que cette règle d'arrêt peut constituer un outil efficace pour étudier ce domaine sans la nécessité de retarder les paiements dans le futur.Hyperbolic discounting, uncertainty, risk, experiments , escompte hyperbolique, incertitude, risque, expériences

Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

Abstract: We present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that L2-based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce L2-based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting

Semi-classical stability of AdS NUT instantons

The semi-classical stability of several AdS NUT instantons is studied. Throughout, the notion of stability is that of stability at the one-loop level of Euclidean Quantum Gravity. Instabilities manifest themselves as negative eigenmodes of a modified Lichnerowicz Laplacian acting on the transverse traceless perturbations. An instability is found for one branch of the AdS-Taub-Bolt family of metrics and it is argued that the other branch is stable. It is also argued that the AdS-Taub-NUT family of metrics are stable. A component of the continuous spectrum of the modified Lichnerowicz operator on all three families of metrics is found.Comment: 18 pages, 3 figures; references adde

Hidden symmetry in the presence of fluxes

We derive the most general first order symmetry operator for the Dirac equation coupled to arbitrary fluxes. Such an operator is given in terms of an inhomogenous form omega which is a solution to a coupled system of first order partial differential equations which we call the generalized conformal Killing-Yano system. Except trivial fluxes, solutions of this system are subject to additional constraints. We discuss various special cases of physical interest. In particular, we demonstrate that in the case of a Dirac operator coupled to the skew symmetric torsion and U(1) field, the system of generalized conformal Killing-Yano equations decouples into the homogenous conformal Killing-Yano equations with torsion introduced in [arXiv:0905.0722] and the symmetry operator is essentially the one derived in [arXiv:1002.3616]. We also discuss the Dirac field coupled to a scalar potential and in the presence of 5-form and 7-form fluxes.Comment: 13 pages, no figure

Optical Metrics and Projective Equivalence

Trajectories of light rays in a static spacetime are described by unparametrised geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the universe as static may determine the geometry of the light rays differently. More specifically, we classify Lorentzian metrics admitting more than one hyper--surface orthogonal time--like Killing vector and analyze the projective equivalence of the resulting optical metrics. These metrics are shown to be projectively equivalent up to diffeomorphism if the static Killing vectors generate a group $SL(2, \R)$, but not projectively equivalent in general. We also consider the cosmological $C$--metrics in Einstein--Maxwell theory and demonstrate that optical metrics corresponding to different values of the cosmological constant are projectively equivalent.Comment: 18 pages, two figures, final version, to appear in Physical Review