A study of the holonomy group of space-time is undertaken and related to the Segre and Petrov types of then Weyl and <I>E</I>-tensors respectively. Attention is then focused on the <I>E</I>-tensor, and a theorem is proved which states that any space-time <I>M</I> can be disjointly decomposed into open sets on which the Segre type of the <I>E</I>-tensor is constant, the union of which if dense in <I>M. </I>This theorem is then applied to prove a similar theorem for the Ricci tensor using the principal null directions of the <I>E</I>-tensor. Finally, a study of proper projective symmetry in null and non-null Einstein-Maxwell and static, spherically symmetric space-times is performed. A theorem is proved which states that no proper projective symmetry is possible in any null Einstein-Maxwell space-times. This result is then extended to the non-null case under some general restrictions. The static, spherically symmetric space-times are then considered, and those admitting proper projective symmetry are completely determined. The proper projective vector fields are also explicitly calculated.

Spinning-particle motion is studied, within the pole-dipole approximation, in algebraically special space-times of type N, III and D. The spin-curvature interaction is analysed for the Pirani and Tulczyjew spin supplementary conditions; for N and D types, the condition is related to a relative acceleration of two near observers separated in the direction of particle's spin. For Tulczyjew's condition, the momentum-velocity relation is also studied as well as its consequences for the spin-curvature interaction. Finally, the type of motion is mentioned for which both the supplementary conditions considered are equivalent.

[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.

The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73].

The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73]. / University of Bradford Research Studenship

This thesis presents an introduction to the three main fields that study time: physics, philosophy, and logics. A brief introduction to general relativity, thermodynamics and quantum physics is made. Also some of the basic ideas from the philosophy of time are explained and dualities connected to time are described, e.g. eternalism vs. presentism, determinism vs. indeterminism and the reality or unreality of time. As there is a huge number of temporal logics, only the main ideas that differentiate these logics from others are pointed out and some typical proofs are then shown. Special attention is then given to the relation between logics and physics, how the first can be used in the latter. Thereafter, Branching space-times and Branching continuation models are presented, which proved to be useful within quantum physics. Next, some basic terminology connected to general relativity and the A, P and T topologies are introduced . These are used together with the given models to investigate a possible combination.

Neste trabalho foi investigada a possibilidade de haver uma interação entre a energia e a matéria escuras. Adotamos um espaço-tempo de Friedmann-Robertson-Walker plano e dois modelos de energia escura interagente. No primeiro, o termo de interação, presente nas equações de conservação da energia e da matéria escuras, foi obtido a partir de argumentos fenomenológicos. No segundo, esse foi derivado de primeiros princípios. Ambos os modelos foram comparados com dados observacionais recentes e, em ambos os casos, obtivemos uma estimativa da constante de acoplamento diferente de zero com um desvio padrão de confiança. Além disso, em ambos os casos o sinal da constante de acoplamento é compatível com a energia escura se convertendo em matéria escura, fornecendo um alívio para o problema da coincidência. / In the present work the possibility of a dark energy interacting with dark matter has been investigated. We considered a flat Friedmann-Robertson-Walker space-time with two alternative interacting dark energy models. In the first, the interaction term, appearing in the energy conservation equations was introduced by purely phenomenological reasons. In the second, it has been obtained from a given Lagrangian density. In both cases we compared the results with recent observational data and obtained an estimate of the coupling constant, which is nonvanishing by one standard deviation. Moreover, in both cases the sign of the coupling constant is compatible with dark energy decaying into dark matter, providing an alleviation to the coincidence problem.

O que fazem profissionais de educação numa produção televisiva? Nesta pesquisa, por meio de 'conversas' com praticantespensantes que atuam em produção de TV, e no uso de outros documentos (programas editados, argumentos, textos e roteiros), busco responder a essa pergunta e compreender as redes de conhecimentos e significações relativas aos espaçostempos de ação desses profissionais, entendidos como entre-lugares de educação e comunicação. A pesquisa, na perspectiva dos estudos com os cotidianos, se articula ao GRPESQ Currículo, redes educativas e imagens, do Laboratório Educação e Imagem/ProPEd/UERJ, e busca apoio em conversas/narrativas com/de professores que trabalharam/trabalham em televisão em especial, no programa Salto para o Futuro integrando a equipe de educação da TV Escola (MEC), ou atuando como consultores de séries temáticas. Sobre o assunto, também foram ouvidos responsáveis pela assessoria pedagógica dos canais Encuentro e Pakapaka, na Argentina, em doutorado-sanduíche, com o apoio da Capes. Como fundamentação teórica, além de pesquisas com os cotidianos, a partir de textos de Michel de Certeau, de Nilda Alves e de Inês Barbosa de Oliveira, dos quais emergem algumas das noções que permeiam essa investigação, ressalto a contribuição de autores da sociologia, como Pierre Bourdieu e Boaventura de Sousa Santos e, ainda, de represe ntantes dos chamados estudos culturais, entre eles Jesús Martín-Barbero, Nestor Canclini, Stuart Hall, Homi Bhabha entre outros. A questão do outro, da alteridade, que permeia a tese, em sua tessitura com narrativas e imagens, busca inspiração também nos escritos e em conversas com Carlos Skliar e nos textos de Jorge Larrosa. As conclusões possíveis destacam a importância das ações desses profissionais (professores) nesses espaçostempos televisivos. / What do professionals in education do in a television production? This research is an attempt to answer this question not only through conversations with the practitioners engaged in television production but also through sources such as edited programmes, arguments , texts and scripts. In doing so, I intend to understand the net of knowledge and meanings related to the so called space-times of action (here understood as an in-between place belonging to both education and communication fields) of these professionals. This work, under the perspective of everyday life studies, is aligned with the research group entitled Curriculum, educational networks and images, from the Education and Image Laboratory of the post graduation program in Education (ProPEd) of the University of Rio de Janeiro State (UERJ). It concentrates in talks with and narratives of educators who worked and have been working either as members of TV Escola which belongs to the Ministry of Education (MEC) or consultants of a particular educational television program entitled Salto para o Futuro. The ones responsible for the pedagogical consultancy of the channels Encuentro and Pakapaka from Argentina have also been interviewed thanks to a doctorate program supported by Capes. The theoretical framework is based on the writings of Michel de Certeau, Nilda Alves and Ines Barbosa de Oliveira; besides them, the contributions of the sociological thinkers Pierre Bourdieu and Boaventura de Souza Santos as well as some representatives of cultural studies such as Jesús Martín Barbero, Nestor Canclini, Stuart Hall, Homi Bhabha, among others, have also been used. Issues about the other and alterity have found inspiration in Carlos Skliar and Jorge Larrosas texts. The possible conclusions made highlight the relevance of the actions of these professionals (teachers) in this space-time television environment

BALTAZAR, H. I. Métricas críticas do funcional volume e não-existência de múltiplos buracos negros em espaço-tempo estático. 2017. 67 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-07-12T19:24:59Z No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-07-13T12:17:45Z (GMT) No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) / Made available in DSpace on 2017-07-13T12:17:46Z (GMT). No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) Previous issue date: 2017-07-05 / This work is divided in two parts. In the first one we prove a Böchner type formula for critical metrics of the volume functional on compact manifolds with fixed metric on boundary (such critical metrics are called Miao-Tam critical metrics). As an application, we derive an integral formula that will be crucial to deduce a generalization of a result obtained by Miao and Tam in 2011 for the Einstein case. More precisely, we prove that a Miao-Tam critical metric with parallel Ricci curvature must be isometric to a geodesic ball in a simply connected space form Rn, Sn or Hn. Furthermore, in dimension 3, we prove that critical metrics with non-negative sectional curvature are precisely geodesic balls of R3 or S3. Moreover, we generalize a result due to Kim and Shin (2016), replacing the harmonic Weyl tensor condition by the second order divergence free Weyl tensor condition (i.e., div2W = 0), which is weaker that the former. To be precise, we shall show that a 4-dimensional Miao-Tam critical metric, with boundary isometric to a standard sphere S3 and satisfying div2W = 0 is isometric to a geodesic ball in a simply connected space form R4, S4 or H4. At the same time, we get some rigidity results for positive static triples. In the second part, we study static vacuum space-times, which can be seen as a special case of the V-static metrics for complete Riemannian manifolds with null scalar curvature. In this case, we focus our attention on four dimensions. We prove that there are no multiple black holes on static vacuum space-times with half harmonic Weyl tensor (i.e., divW+ = 0). / Esse trabalho está dividido em duas partes. A primeira delas está relacionada ao estudo de fórmulas tipo-Böchner para métricas críticas do funcional volume em variedades compactas com métrica fixada no bordo (estas são conhecidas como métricas críticas de Miao-Tam). Como aplicação, estabeleceremos uma fórmula integral que permitirá generalizar o resultado obtido por Miao e Tam em 2011 para o caso Einstein, mais precisamente, provaremos que métricas críticas de Miao-Tam com curvatura de Ricci paralelo são isométricas às bolas geodésicas em um espaço forma simplesmente conexo Rn, Sn ou Hn. Se nos restringirmos às variedades com dimensão 3, veremos que tais estruturas se mostram ainda mais rígidas, a saber, provaremos que métricas críticas com curvatura seccional não-negativa são precisamente as bolas geodésicas de R3 ou S3. Além disso, generalizamos o resultado obtido por Kim e Shin (2016) substituindo condição de harmonicidade do tensor de Weyl pela hipótese que o tensor de Weyl tem divergente de segunda ordem nulo (i.e., div2W = 0). Mais precisamente, mostraremos que métricas críticas de Miao-Tam em dimensão 4, com bordo isométrico a esfera S3 e satisfazendo div2W = 0, são isométricas às bolas geodésicas em um espaço forma simplesmente conexo R4, S4 ou H4. Concomitantemente, obtemos resultados de rigidez para triplas estáticas positivas. Na segunda parte do trabalho, estudaremos o espaço-tempo estático no vácuo, o qual pode ser visto como um caso especial das mátricas V-estáticas para variedades completas com curvatura escalar nula. Neste caso, restringiremos nosso estudo a quarta dimensão e provaremos que não existem múltiplos buracos negros em um espaço-tempo estático no vácuo com a parte autodual do tensor de Weyl harmônico (i.e., divW+ = 0).

O que fazem profissionais de educação numa produção televisiva? Nesta pesquisa, por meio de 'conversas' com praticantespensantes que atuam em produção de TV, e no uso de outros documentos (programas editados, argumentos, textos e roteiros), busco responder a essa pergunta e compreender as redes de conhecimentos e significações relativas aos espaçostempos de ação desses profissionais, entendidos como entre-lugares de educação e comunicação. A pesquisa, na perspectiva dos estudos com os cotidianos, se articula ao GRPESQ Currículo, redes educativas e imagens, do Laboratório Educação e Imagem/ProPEd/UERJ, e busca apoio em conversas/narrativas com/de professores que trabalharam/trabalham em televisão em especial, no programa Salto para o Futuro integrando a equipe de educação da TV Escola (MEC), ou atuando como consultores de séries temáticas. Sobre o assunto, também foram ouvidos responsáveis pela assessoria pedagógica dos canais Encuentro e Pakapaka, na Argentina, em doutorado-sanduíche, com o apoio da Capes. Como fundamentação teórica, além de pesquisas com os cotidianos, a partir de textos de Michel de Certeau, de Nilda Alves e de Inês Barbosa de Oliveira, dos quais emergem algumas das noções que permeiam essa investigação, ressalto a contribuição de autores da sociologia, como Pierre Bourdieu e Boaventura de Sousa Santos e, ainda, de represe ntantes dos chamados estudos culturais, entre eles Jesús Martín-Barbero, Nestor Canclini, Stuart Hall, Homi Bhabha entre outros. A questão do outro, da alteridade, que permeia a tese, em sua tessitura com narrativas e imagens, busca inspiração também nos escritos e em conversas com Carlos Skliar e nos textos de Jorge Larrosa. As conclusões possíveis destacam a importância das ações desses profissionais (professores) nesses espaçostempos televisivos. / What do professionals in education do in a television production? This research is an attempt to answer this question not only through conversations with the practitioners engaged in television production but also through sources such as edited programmes, arguments , texts and scripts. In doing so, I intend to understand the net of knowledge and meanings related to the so called space-times of action (here understood as an in-between place belonging to both education and communication fields) of these professionals. This work, under the perspective of everyday life studies, is aligned with the research group entitled Curriculum, educational networks and images, from the Education and Image Laboratory of the post graduation program in Education (ProPEd) of the University of Rio de Janeiro State (UERJ). It concentrates in talks with and narratives of educators who worked and have been working either as members of TV Escola which belongs to the Ministry of Education (MEC) or consultants of a particular educational television program entitled Salto para o Futuro. The ones responsible for the pedagogical consultancy of the channels Encuentro and Pakapaka from Argentina have also been interviewed thanks to a doctorate program supported by Capes. The theoretical framework is based on the writings of Michel de Certeau, Nilda Alves and Ines Barbosa de Oliveira; besides them, the contributions of the sociological thinkers Pierre Bourdieu and Boaventura de Souza Santos as well as some representatives of cultural studies such as Jesús Martín Barbero, Nestor Canclini, Stuart Hall, Homi Bhabha, among others, have also been used. Issues about the other and alterity have found inspiration in Carlos Skliar and Jorge Larrosas texts. The possible conclusions made highlight the relevance of the actions of these professionals (teachers) in this space-time television environment