We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi-Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner-Nordström are dimension dependent (the extremal Reissner-Nordström case must be considered separately from the non-extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner-Nordström de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner-Nordström Anti-de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non-black hole spacetimes, such as pure de Sitter spacetimewhere there are quasinormal modes only in odd dimensions-and pure Anti-de Sitter spacetime-where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self-contained we also review earlier results in the literature.

Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically de Sitter and anti-de Sitter (Ads) spacetimes is provided). This calculation includes both the low-energy case -where the frequency of the scattered wave is small and real -and the asymptotic case -where the frequency of the scattered wave is very large along the imaginary axis -addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically de Sitter black holes the greybody e-print archive: http://lanl.arXiv.org/abs/0708.0017 TROELS HARMARK, JOSÉ NATÁRIO AND RICARDO SCHIAPPAfactor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically Ads black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure Ads spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically de Sitter black holes the greybody factors are given by non-trivial functions, while for asymptotically Ads black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).

The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrödinger-like equation to the complex plane and then performing a method of monodromy matching at the several poles in the plane. While this method was successfully used in asymptotically flat spacetime, as applied to both the Schwarzschild and Reissner-Nordstrøm solutions, its extension to non-asymptotically flat spacetimes has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild de Sitter and large Schwarzschild Anti-de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole spacetimes, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional spacetimes.

It is commonly believed that Alcubierre's warp drive works by contracting space in front of the warp bubble and expanding space behind it. We show that this contraction/expansion is but a marginal consequence of the choice made by Alcubierre, and explicitly construct a similar spacetime where no contraction/expansion occurs. Global and optical properties of warp drive spacetimes are also discussed.

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We prove that (possibly charged) test fields satisfying the null energy condition at the event horizon cannot overspin/overcharge extremal Kerr-Newman or Kerr-Newman-anti de Sitter black holes, that is, the weak cosmic censorship conjecture cannot be violated in the test field approximation. The argument relies on black hole thermodynamics (without assuming cosmic censorship), and does not depend on the precise nature of the fields. We also discuss generalizations of this result to other extremal black holes.

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the EinsteinMaxwell-scalar field system with a cosmological constant Λ, with the data on the outgoing initial null hypersurface given by a subextremal ReissnerNordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold.In the first paper of this sequence [4], we established well posedness of the characteristic problem with general initial data.In this second paper, we generalize the results of Dafermos [6] on the stability of the radius function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in [6], focusing on the level sets of the radius function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin.In the third and final paper [5], we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.