The Schwarzschild-de Sitter solution in five-dimensional general relativity briefly revisited

We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional Schwarzschild-de Sitter space can be locally and isometrically embedded. We show that this class of solutions is well-behaved in the limit of lambda approaching zero. Applying the same procedure to the de Sitter cosmological model in five dimensions we obtain a class of embedding spaces which are similarly well-behaved in this limit. These examples demonstrate that the presence of a non-zero cosmological constant does not in general impose a rigid relation between the (3+1) and (4+1)-dimensional spacetimes, with degenerate limiting behaviour.Comment: 7 page

Non-uniform Black Strings with Schwarzschild-(Anti-)de Sitter Foliation

We present some exact non-uniform black string solutions of 5-dimensional pure Einstein gravity as well as Einstein-Maxwell-dilaton theory at arbitrary dilaton coupling. The solutions share the common property that their 4-dimensional slices are Schwarzchild-(anti-)de Sitter spacetimes. The pure gravity solution is also generalized to spacetimes of dimensions higher than 5 to get non-uniform black branes.Comment: LaTeX 14 pages, 3 eps figures. V2: version appeared in CQ

Conformal invariance: from Weyl to SO(2,d)

The present work deals with two different but subtilely related kinds of conformal mappings: Weyl rescaling in $d>2$ dimensional spaces and SO(2,d) transformations. We express how the difference between the two can be compensated by diffeomorphic transformations. This is well known in the framework of String Theory but in the particular case of $d=2$ spaces. Indeed, the Polyakov formalism describes world-sheets in terms of two-dimensional conformal field theory. On the other hand, B. Zumino had shown that a classical four-dimensional Weyl-invariant field theory restricted to live in Minkowski space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS). This allows us to assert that a classical $SO(2,d)$-invariant field does not distinguish, at least locally, between two different $d$-dimensional CFSs.Comment: 5 pages, no figures. There are slight modifications to match with the published versio

Equivalence of three-dimensional spacetimes

A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede invariant classification of spacetimes of general relativity. The local geometry is completely determined by the curvature tensor and a finite number of its covariant derivatives in a frame where the components of the metric are constants. The results are presented in the framework of real two-component spinors in three-dimensional spacetimes, where the algebraic classifications of the Ricci and Cotton-York spinors are given and their isotropy groups and canonical forms are determined. As an application we discuss Goedel-type spacetimes in three-dimensional General Relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Goedel-type spacetimes is studied and the results are compared with previous works on four-dimensional Goedel-type spacetimes.Comment: 13 pages - content changes and corrected typo

Conformally flat spacetimes and Weyl frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker's interpretation of Nordstr\"om scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.Comment: LATEX - 18 page

General Relativity and Weyl Geometry

We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same gravitational phenomena. We show that in an arbitrary Weyl frame general relativity, which takes the form of a scalar-tensor gravitational theory, is invariant with respect to Weyl tranformations. A kew point in the development of the formalism is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke gravitational theory. In this scenario, the gravitational field is not described by the metric tensor only, but by a combination of both the metric and a geometrical scalar field. We illustrate this point by, firstly, discussing the Newtonian limit in an arbitrary frame, and, secondly, by examining how distinct geometrical and physical pictures of the same phenomena may arise in different frames. To give an example, we discuss the gravitational spectral shift as viewed in a general Weyl frame. We further explore the analogy of general relativity with scalar-tensor theories and show how a known Brans-Dicke vacuum solution may appear as a solution of general relativity theory when reinterpreted in a particular Weyl frame. Finally, we show that the so-called WIST gravity theories are mathematically equivalent to Brans-Dicke theory when viewed in a particular frame.Comment: LATEX, 22 page

Imigração e saúde: a (in)acessibilidade das mulheres imigrantes aos cuidados de saúde

A utilização dos serviços de saúde pelas populações imigrantes tem vindo a ser considerado um dos mais importantes indicadores da sua integração nas so- ciedades receptoras (Dias e col., 2009). No entanto, o conhecimento em torno da qualidade e da eficácia do acesso dos/as imigrantes aos cuidados de saúde, especialmente no que respeita às mulheres imigran- tes, é ainda escasso em Portugal (Fonseca e col., 2005). Embora os estudos nacionais tenham vindo, nas últimas décadas, a procurar traçar os diferentes perfis sociais das mulheres imigrantes em Portugal, sobretudo no que concerne às suas relações fami- liares ou laborais (Wall e col., 2005), a investigação no domínio da saúde é ainda parca e exclusora de uma análise centrada no género ou interseccional. Neste texto apresenta-se uma reflexão sobre os de- terminantes que condicionam a (in)acessibilidade das mulheres imigrantes aos cuidados de saúde, enfatizando-se os fatores que poderão estar a agir no sentido contrário à sua integração neste setor