What does research say about the Special and General Relativity Theory Teaching?

Na literatura da área de Ensino de Física encontramos diversos argumentos em defesa da inclusão, nos currículos escolares do Ensino Médio, de conteúdos de Física Moderna e Contemporânea. A Teoria da Relatividade Especial e Geral (ao lado da Mecânica Quântica) é um dos pilares da Física Moderna. Consideramos significativo e oportuno obter um panorama da produção acadêmica sobre o ensino e aprendizagem deste tópico. Nosso objetivo é sintetizar os avanços, as convergências e sinalizar perspectivas, com o intuito de contribuir para um avanço e defesa dos trabalhos futuros. Assim, procuramos resposta para a questão: Quais as contribuições da pesquisa em Ensino de Física para que a Teoria da Relatividade Especial e Geral (TREG) possa ser abordada no Ensino Médio?

Conservation laws and variational principles in general relativity /

"April 23, 1962."

Relativity, the electron theory, and gravitation,

Mode of access: Internet.

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Soliton collision in general relativity

An exact solution of the Einstein equations in vacuum representing two pairs of gravitational solitons propagating on an expanding universe is given and studied. It is suggested that the solitons evolve from quasiparticles to pure gravitational waves. Two of the four solitons collide and the focusing produced on null rays is studied. Although the spacetime following the collision is highly distorted, null rays do not focus to a singularity.

Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.

Quantum black holes: Nonperturbative corrections and no-veil scenario

A common belief is that further quantum corrections near the singularity of a large black hole should not substantially modify the semiclassical picture of black hole evaporation; in particular, the outgoing spectrum of radiation should be very close to the thermal spectrum predicted by Hawking. In this paper we explore a possible counterexample: in the context of dilaton gravity, we find that nonperturbative quantum corrections which are important in strong-coupling regions may completely alter the semiclassical picture, to the extent that the presumptive spacelike boundary becomes timelike, changing in this way the causal structure of the semiclassical geometry. As a result, only a small fraction of the total energy is radiated outside the fake event horizon; most of the energy comes in fact at later retarded times and there is no problem of information loss. This may constitute a general characteristic of quantum black holes, that is, quantum gravity might be such as to prevent the formation of global event horizons.

General relativity in two dimensions: A Hamilton-Jacobi analysis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Computational Aspects of the Calculation of Isometry Groups in General Relativity

We describe the ideas behind the package 'isometry', implemented in Maple to calculate isometry groups of dimensions 2, 3 and 4 in General Relativity. The package extends the functionality of previous programs written to perform invariant classification of space-times in General Relativity. Programming solutions used to surmount problems encountered with the calculation of eigenvectors and the determination of the signs of expressions are described. We also show how the package can be used to find the Killing vectors of a space-time.

Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Classic tests of General Relativity described by brane-based spherically symmetric solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stellar Models in General Relativity

Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 1012 Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition R < 3M is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed