Green operators for low regularity spacetimes

In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well- posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs

The Black Hole: Scatterer, Absorber and Emitter of Particles

Accurate and powerful computational methods developed by the author for the wave scattering by black holes allow to obtain the highly non trivial total absorption spectrum of the Black Hole. As well as partial wave phase shifts and cross sections (elastic and inelastic), the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The exact total absorption spectrum of waves by the Black Hole has as a function of frequency a remarkable oscillatory behaviour characteristic of a diffraction pattern. This is an unique distinctive feature of the black hole absorption, and due to its r = 0 singularity. Ordinary absorptive bodies and optical models do not present these features. The unitarity optical theorem is generalized to the Black Hole case explicitly showing that absorption ocurrs only at the origin. All these results allow to understand and reproduce the Black Hole absorption spectrum in terms of Fresnel-Kirchoff diffraction theory: by the interference of the absorbed rays arriving at the origin through different optical paths. These fundamental features of the Black Hole Absorption will be present for generic higher dimensional Black Hole backgrounds, and whatever the low energy effective theory they arise from. In recent and increasing litterature devoted to compute absorption cross sections (grey body factors) of black holes (whatever ordinary, stringy, D-braned), the fundamental remarkable features of the Black Hole Absorption spectrum are overlooked.Comment: 19 pages Latex, 4 ps Figures, uses epsfig and psfra

Generalised hyperbolicity in spacetimes with string-like singularities

In this paper we present well-posedness results of the wave equation in $H^{1}$ for spacetimes that contain string-like singularities. These results extend a framework able to characterise gravitational singularities as obstruction to the dynamics of test fields rather than point particles. In particular, we discuss spacetimes with cosmic strings and the relation of our results to the Strong Cosmic Censorship Conjecture.Comment: Accepted for publication in Classical and Quantum Gravit

A salary system for the assignment problem

We propose a modification to the concept of the potential of agame à la Hart-Mas Colell to determine a salary system for theassignment problem. We obtain explicit formulas for the potentialof the assignment problem and for it's corresponding salarysystem. Also, we establish some properties of this salary systemand we give an interpretation in terms of the Shapley value.assignment problem

Additive Combination Spaces

We introduce a class of metric spaces called $p$-additive combinations and show that for such spaces we may deduce information about their $p$-negative type behaviour by focusing on a relatively small collection of almost disjoint metric subspaces, which we call the components. In particular we deduce a formula for the $p$-negative type gap of the space in terms of the $p$-negative type gaps of the components, independent of how the components are arranged in the ambient space. This generalizes earlier work on metric trees by Doust and Weston. The results hold for semi-metric spaces as well, as the triangle inequality is not used.Comment: 17 page

London, Libel Capital No Longer? The Draft Defamation Act 2011 and the Future of Libel Tourism

[Excerpt] “In the past decade, London emerged as the forum of choice for “libel tourists”—strategic, often foreign, plaintiffs who bring defamation actions in a jurisdiction with plaintiff-friendly libel laws, even if they and the defamatory material at issue lack a substantial connection with that jurisdiction. England’s defamation laws and procedures make it significantly easier for claimants to commence and prevail in libel actions than do the laws and procedures of many other countries, particularly the United States. As a result, English courts have entertained several high-profile defamation cases involving foreign parties who have only tenuous connections to England, such as disputes between a Saudi billionaire and a U.S. journalist; a Russian businessman and a U.S. magazine; and a French director and a U.S. publisher. Cases like these have cemented London’s reputation as the “libel capital of the world.” The establishment of that notorious title, reflecting the notion that England does not value free expression as highly as other countries, has helped ignite a movement to reform English libel laws and procedures. On March 15, 2011, the U.K. Ministry of Justice unveiled a draft bill entitled the Draft Defamation Act 2011, proposing a substantial overhaul of English libel laws as well as the procedures applied in libel actions. The Draft Act aims to combat the perception that England is a refuge for libel tourism by, among other reforms, requiring English courts to determine whether England is the most appropriate forum in which the action should be heard before exercising jurisdiction. The Draft Defamation Act comes less than one year after the enactment of the Securing the Protection of Our Enduring and Established Constitutional Heritage (“SPEECH”) Act of 2010 in the United States. The SPEECH Act prohibits U.S. courts, both state and federal, from recognizing or enforcing defamation judgments rendered by a foreign court unless that court applied a standard that was as protective of free speech as a U.S. court would have applied. In the context of libel tourism, this means that a libel tourist cannot force a U.S. author or publisher to comply with a foreign judgment unless a U.S. court finds that the judgment comported with First Amendment principles. This Note analyzes the efficacy of the Draft Defamation Act and its impact on the enforcement of English defamation judgments in U.S. courts. Specifically, it proposes that the Draft Act’s procedural clauses will effectively reduce the prevalence of libel tourism in England. Moreover, this Note argues that, in light of the Draft Act’s reforms as well as longstanding principles of international comity, U.S. courts should not narrowly construe the SPEECH Act to require exact congruence between U.S. and English defamation laws. Finally, this Note presents evidence suggesting that England’s problem of libel tourism could be supplanted by the new phenomenon of privacy tourism. Thus, in addition to modifying and enacting the Draft Defamation Act, English policymakers should consider reviewing and possibly reforming English privacy laws. This Note proceeds in four sections. Section II provides a background to issues related to libel tourism, including its prevalence in England and the U.S. response to it. Section III reviews the Draft Defamation Act’s procedural clauses related to libel tourism. Section IV analyzes the Draft Act’s potential to eradicate libel tourism and its effect on U.S. courts’ construction and application of the SPEECH Act. Section IV also proposes modifications to the Draft Act, including the adoption of a defamation-specific choice-of-law rule. Finally, Section V explores the interplay between English defamation and privacy laws, considering whether the Draft Act’s aim to eliminate libel tourism inadvertently opens the door to the development of privacy tourism