Leandro Gomes - Academia.edu (original) (raw)

Papers by Leandro Gomes

Classical and Quantum Gravity, 2017

We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear... more We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear and the anisotropic pressure components as the basic variables, where the viscosity is driven by the (second-order) causal thermodynamics. A few exact solutions are presented, among which we mention the anisotropic versions of de Sitter/anti-de Sitter geometries as well as an asymptotically isotropic spacetime presenting an effectively constant cosmic acceleration without any cosmological constant. The qualitative analysis of the solutions for barotropic fluids with linear equations of state suggests that the behaviour is quite general.

International Journal of Modern Physics D

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact so... more Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter co...

Classical and Quantum Gravity

For any configuration of a static plane-symmetric distribution of matter along spacetime, there a... more For any configuration of a static plane-symmetric distribution of matter along spacetime, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for selfgravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.

We study the behavior of differential forms in a manifold having at least one of their maximal is... more We study the behavior of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some simple integrability conditions are ensured. We also classify possible 'canonical coordinates' for a certain class of forms with potential applications in classical field theory.

Neste trabalho, introduzimos uma nova classe de formas multilineares alternadas e de formas difer... more Neste trabalho, introduzimos uma nova classe de formas multilineares alternadas e de formas diferenciais, chamadas de formas polilagrangeanas (no caso de formas a valores vetoriais) ou multilagrangeanas (no caso de formas parcialmente horizontais em relação a um subespaço ou subfibrado dado), que são caracterizadas pela existência de um tipo especial de subespaço ou subfibrado maximal isotrópico chamado, respectivamente, de polilagrangeano ou multilagrangeano. Revela-se que estas constituem o arcabouço adequado para a formulação de um teorema de Darboux em nível algébrico. Combinando esta nova estrutura algébrica com propriedades padrão de integrabilidade (dω = 0) nos permite deduzir o teorema de Darboux no contexto geométrico (existência de coordenadas locais canônicas). Estruturas polissimpléticas e multissimpléticas, inclusive todas aquelas que aparecem no formalismo hamiltoniano covariante da teoria clássica dos campos, são contidas como caso especial.

We study the behaviour of differential forms in a manifold having at least one of their maximal i... more We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some

Reviews in Mathematical Physics, 2013

We propose new definitions of the concepts of a multisymplectic structure and of a polysymplectic... more We propose new definitions of the concepts of a multisymplectic structure and of a polysymplectic structure which extend previous ones so as to cover the cases that are of interest in mathematical physics: they are tailored to apply to fiber bundles, rather than just manifolds, and at the same time they are sufficiently specific to allow us to prove Darboux theorems for the existence of canonical local coordinates. A key role is played by the notion of "symbol" of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, thus clarifying the relation between these two closely related but not identical concepts.

Classical and Quantum Gravity, 2017

Classical and Quantum Gravity, 2017

We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear... more We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear and the anisotropic pressure components as the basic variables, where the viscosity is driven by the (second-order) causal thermodynamics. A few exact solutions are presented, among which we mention the anisotropic versions of de Sitter/anti-de Sitter geometries as well as an asymptotically isotropic spacetime presenting an effectively constant cosmic acceleration without any cosmological constant. The qualitative analysis of the solutions for barotropic fluids with linear equations of state suggests that the behaviour is quite general.

International Journal of Modern Physics D

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact so... more Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter co...

Classical and Quantum Gravity

For any configuration of a static plane-symmetric distribution of matter along spacetime, there a... more For any configuration of a static plane-symmetric distribution of matter along spacetime, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for selfgravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.

We study the behavior of differential forms in a manifold having at least one of their maximal is... more We study the behavior of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some simple integrability conditions are ensured. We also classify possible 'canonical coordinates' for a certain class of forms with potential applications in classical field theory.

Neste trabalho, introduzimos uma nova classe de formas multilineares alternadas e de formas difer... more Neste trabalho, introduzimos uma nova classe de formas multilineares alternadas e de formas diferenciais, chamadas de formas polilagrangeanas (no caso de formas a valores vetoriais) ou multilagrangeanas (no caso de formas parcialmente horizontais em relação a um subespaço ou subfibrado dado), que são caracterizadas pela existência de um tipo especial de subespaço ou subfibrado maximal isotrópico chamado, respectivamente, de polilagrangeano ou multilagrangeano. Revela-se que estas constituem o arcabouço adequado para a formulação de um teorema de Darboux em nível algébrico. Combinando esta nova estrutura algébrica com propriedades padrão de integrabilidade (dω = 0) nos permite deduzir o teorema de Darboux no contexto geométrico (existência de coordenadas locais canônicas). Estruturas polissimpléticas e multissimpléticas, inclusive todas aquelas que aparecem no formalismo hamiltoniano covariante da teoria clássica dos campos, são contidas como caso especial.

We study the behaviour of differential forms in a manifold having at least one of their maximal i... more We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some

Reviews in Mathematical Physics, 2013

We propose new definitions of the concepts of a multisymplectic structure and of a polysymplectic... more We propose new definitions of the concepts of a multisymplectic structure and of a polysymplectic structure which extend previous ones so as to cover the cases that are of interest in mathematical physics: they are tailored to apply to fiber bundles, rather than just manifolds, and at the same time they are sufficiently specific to allow us to prove Darboux theorems for the existence of canonical local coordinates. A key role is played by the notion of "symbol" of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, thus clarifying the relation between these two closely related but not identical concepts.

Classical and Quantum Gravity, 2017