Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models.Comment: 9 pages; v2: major changes; v3: misprints correcte

Homogeneous cosmologies from the quasi-Maxwell formalism

We show how to use the quasi-Maxwell formalism to obtain solutions of Einstein's field equations corresponding to homogeneous cosmologies - namely Einstein's universe, Godel's universe and the Ozsvath-Farnsworth-Kerr class I solutions - written in frames for which the associated observers are stationary.Comment: 15 pages, references adde

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first part of this series we established the well posedness of the characteristic problem, whereas in the second part we studied the stability of the radius function at the Cauchy horizon. In this third and final paper we show that, depending on the decay rate of the initial data, mass inflation may or may not occur. When the mass is controlled, it is possible to obtain continuous extensions of the metric across the Cauchy horizon with square integrable Christoffel symbols. Under slightly stronger conditions, we can bound the gradient of the scalar field. This allows the construction of (non-isometric) extensions of the maximal development which are classical solutions of the Einstein equations. Our results provide evidence against the validity of the strong cosmic censorship conjecture when $\Lambda>0$.Comment: 48 pages, 5 figures; v2: some presentation changes, mostly in the Introduction; v3: substantial changes in Section 5; v4: expanded Introduction; some presentation changes; matches final published versio

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom 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, we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos 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 by Dafermos, 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, we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.Comment: 44 pages, 13 figures; v2: a few small changes; v3: a paragraph was added in the Introduction, minor clarifications were made thoughout, the list of references was expanded, matches final published versio

Painleve-Gullstrand Coordinates for the Kerr Solution

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign error in the expression of the function delta correcte

Estándares territoriales de innovación : análisis de las regiones de Portugal

Competitiveness among regions and innovation dynamics are intimately related and depend on a solid and effective innovation system. This study aims to measure innovativeness in different Portuguese regions and to evaluate the nature of the innovation process and the relationship between innovativeness and its region of origin. To characterize the territorial innovation processes and to identify innovation patterns by regions, it analyzes their main distinctive factors, based on the Community Innovation Survey results for each region. Thus, it compares the Portuguese regions by verifying the existence of subjacent clusters and finding out the characteristics that distinguish the different groups of regions. The results point to the existence of four groups of regions, and the factors identified are related to the innovation process, namely objectives of innovation, sources of innovation, collaborative networks, triple helix performance, and obstacles to innovation.RESUMEN: La competitividad entre las regiones y la dinámica de la innovación están íntimamente relacionadas y dependen de un sistema de innovación sólida y eficaz. Este estudio tiene como objetivo medir la capacidad de innovación en diferentes regiones portuguesas y evaluar la naturaleza del proceso de innovación y la relación entre la capacidad de innovación y su región de origen. Para la caracterización de los procesos de innovación territoriales y identificar estándares de innovación en las regiones, este artículo analiza sus factores distintivos principales, con base en los resultados de las encuestas comunitarias sobre innovación para cada región. Por lo tanto, se comparan las regiones portuguesas mediante la verificación de la existencia de agrupaciones subyacentes y descubrir las características que distinguen a los diferentes grupos de regiones. Los resultados apuntan a la existencia de cuatro grupos de regiones, y los factores identificados están relacionados con el proceso de innovación, es decir, los objetivos de la innovación, las fuentes de innovación, redes de colaboración, el funcionamiento de la triple hélice, y los obstáculos a la innovación.info:eu-repo/semantics/publishedVersio

Inovação e desenvolvimento territorial: o papel do empreendedorismo social

DINÂMIA, Dezembro de 2009.Na era da globalização e da afirmação inequívoca da importância do desenvolvimento sustentável, realçados pelos diversos fóruns internacionais, suscitam-se diversas questões em torno da participação colectiva em matéria de desenvolvimento regional, designadamente quanto à importância do “terceiro sector” para reforçar o capital social e espessura institucional dos territórios mais expostos à desindustrialização por falta de competitividade externa, num esforço de mobilização da sociedade civil para vencer desafios comprometedores do bem-estar social das gerações vindouras. Neste artigo pretende-se efectuar uma revisão da literatura centrada na economia regional, territorial e da inovação, salientando a importância da economia social para a construção de um meio socialmente inovador. Procura-se dar particular destaque ao empreendedorismo social enquanto mecanismo que poderá contrariar a lógica dualista de competitividade regional inerente ao paradigma da “economia do conhecimento”, sendo esta potenciadora de um conflito entre eficiência e equidade (social e territorial) pelo risco de polarização geográfica do capital humano e da inovação que lhe está associado. Essa polarização inibe o potencial endógeno de crescimento da produção, do rendimento e do emprego das regiões empobrecidas.In the era of globalization and unequivocal affirmation of the importance of sustainable development, focused on various international forums, it raises several questions about the collective participation on Regional Development, particularly on the importance of "third sector" to reinforce social capital and institutional thickness of the territories more exposed to deindustrialization for lack of external competitiveness, in an effort to mobilize civil society to overcome challenges compromising the welfare of future generations. In this article it is purposed to make a literature review about regional, territorial and innovation economics, bringing to light the importance of social entrepreneurship as a mechanism that may counteract the dualistic logic of regional competitiveness inherent in the paradigm of "knowledge economy", which is leading to a conflict between efficiency and (social and territorial) equity for the inherent risk of capital human and innovation’ geographic polarization. This polarization inhibits the endogenous potential of growth of production, income and employment in depleted regions.FC

The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit

It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum ($l \gg 1$), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly-damped part of the spectrum in the large-$l$ regime. We confirm that, at leading order in $l$, the resonance frequency is linked to the orbital frequency, and the resonance damping to the Lyapunov exponent, of the relevant null orbit. We go somewhat further than previous studies to establish (i) a spin-dependent correction to the frequency at order $1 / l$ for equatorial ($m = \pm l$) modes, and (ii) a new result for polar modes ($m = 0$). We validate the approach by testing the closed-form approximations against frequencies obtained numerically with Leaver's method.Comment: 18 pages, 3 tables, 3 figure

Addendum to “Strong cosmic censorship: The nonlinear story”

We clarify a number of issues that arise when extending the analysis of strong cosmic censorship (SCC) to perturbations of highly charged Reissner-Nordström de Sitter (RNdS) spacetimes. The linear stability of the Cauchy horizon can be determined from the spectral gap of quasinormal modes, thus giving a clear idea of the ranges of parameters that are likely to lead to SCC violations for infinitesimally small perturbations. However, the situation becomes much more subtle once the nonlinear backreaction is taken into account. These subtleties have created a considerable amount of confusion in the literature regarding the conclusions one is able to derive about SCC from the available numerical simulations. Here we present new numerical results concerning charged self-gravitating scalar fields in spherical symmetry, correct some previous claims concerning the neutral case, and argue that the existing numerical codes are insufficient to draw conclusions about the potential failure of SCC for near extremal RNdS black hole spacetimes.info:eu-repo/semantics/acceptedVersio