arXiv subjects

P. Salgado

Publications and source records attributed to P. Salgado.

33 records · Page 2Linked to original sources

arXiv2016

Einstein-Hilbert action with cosmological term from Chern-Simons gravity

We propose a modification to the Lie algebra $S$-expansion method. The modification is carried out by imposing a condition on the $S$-expansion procedure, when the semigroup is given by a cyclic group of even order. The $S$-expanded algebras are called $S_{H}$-expanded algebras where $S=Z_{2n}$. The invariant tensors for $S_{H}$-expanded algebras are calculated and the dual formulation of $S_{H}$-expansion procedure is proposed. We consider the $S_{H}$-expansion of the five-dimensional $AdS$ algebra and its corresponding invariants tensors are found. Then a Chern-Simons Lagrangian invariant under the five-dimensional $AdS$ algebra $S_{H}$-expanded is constructed and its relationship to the general relativity is studied.

math-ph↗

arXiv2016

Generalized Galilean Algebras and Newtonian Gravity

The non-relativistic versions of the generalized Poincaré algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by $\mathcal{G}\mathfrak{B}_{n}$ and $\mathcal{G}\mathfrak{L}_{_{n}}$ respectively. Using a generalized Inönü--Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The $S$-expansion procedure allows us to find the $\mathcal{G}\mathfrak{B}_{_{5}}$ algebra from the Newton--Hooke algebra with central extension. The procedure developed in Ref. \cite{newton} allow us to show that the non-relativistic limit of the five dimensional Einstein--Chern--Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

hep-th↗

arXiv2016

Geometrical aspects of the Lie Algebra S-Expansion Procedure

In this article it is shown that S-Expansion procedure affects the geometry of a Lie group, changing it an leading us to the geometry of another Lie group with higher dimensionality. Is outlined, via an example, a method for determining the semigroup, which would provide a Lie algebra from another. Finally, it is proved that the Lie algebra obtained from another Lie algebra via S-Expansion is a non-simple Lie algebra. I

math-ph↗

arXiv2015

Chern-Simons Supergravity in D=3 and Maxwell superalgebra

We present the construction of the $D=3$ Chern-Simons supergravity action without cosmological constant from the minimal Maxwell superalgebra $s\mathcal{M}_{3}$. This superalgebra contains two Majorana fermionic charges and can be obtained from the $\mathfrak{osp}\left( 2|1\right) \otimes\mathfrak{sp}\left( 2\right) $ superalgebra using the abelian semigroup expansion procedure. The components of the Maxwell invariant tensor are explicitly derived.

hep-th↗

arXiv2015

Generalized supersymmetric cosmological term in N=1 Supergravity

An alternative way of introducing the supersymmetric cosmological term in a supergravity theory is presented. We show that the $AdS$-Lorentz superalgebra allows to construct a geometrical formulation of supergravity containing a generalized supersymmetric cosmological constant. The $N=1$, $D=4$ supergravity action is built only from the curvatures of the $AdS$-Lorentz superalgebra and corresponds to a MacDowell-Mansouri like action. The extension to a generalized $AdS$-Lorentz superalgebra is also analyzed.

hep-th↗

arXiv2015

Generalized Poincare algebras and Lovelock-Cartan gravity theory

We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincaré algebra $\mathfrak{B}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.

hep-th↗

arXiv2014

Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very Recently, it was shown that the generalized Inönü-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$ which correspond to the so called $B_{m}$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and only if $m\geq p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the $\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.

hep-th↗

arXiv2013

A generalized action for $\left( 2 + 1 \right)$-dimensional Chern--Simons gravity

We show that the so-called semi-simple extended Poincaré (SSEP) algebra in $D$ dimensions can be obtained from the anti-de~Sitter algebra $\mathfrak{so} \left( D-1,2 \right)$ by means of the $S$-expansion procedure with an appropriate semigroup $S$. A general prescription is given for computing Casimir operators for $S$-expanded algebras, and the method is exemplified for the SSEP algebra. The $S$-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern--Simons gravity in $2+1$ dimensions.

gr-qc↗

arXiv2013

Even-dimensional General Relativity from Born-Infeld gravity

It is an accepted fact that requiring the Lovelock theory to have the maximun possible number of degree of freedom, fixes the parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern-Simons form for the (A)dS group. In even dimensions, the action has a Born-Infeld-like form. Recently was shown that standard odd-dimensional General Relativity can be obtained from Chern-Simons Gravity theory for a certain Lie algebra B. Here we report on a simple model that suggests a mechanism by which standard even-dimensional General Relativity may emerge as a weak coupling constant limit of a Born-Infeld theory for a certain Lie subalgebra of the algebra B. Possible extension to the case of even-dimensional supergravity is briefly discussed.

hep-th↗

arXiv2004

On Magnetic solution to 2+1 Einstein--Maxwell gravity

The three--dimensional magnetic solution to the Einstein--Maxwell field equations have been considered by some authors. Several interpretations have been formulated for this magnetic spacetime. Up to now this solution has been considered as a two--parameter self--consistent field. We point out that the parameter related to the mass of this solution is just a pure gauge and can be rescaled to minus one. This implies that the magnetic metric has really a simple form and it is effectively one-parameter solution, which describes a distribution of a radial magnetic field in a 2+1 anti--de Sitter background space--time. We consider an alternative interpretation to the Dias--Lemos one for the magnetic field source.

hep-th↗

arXiv2003

Supergravity with cosmological constant and the AdS group

It is shown that the supersymmetric extension of the Stelle-West formalism permits the construction of an action for $(3+1)$-dimensional N=1 supergravity with cosmological constant genuinely invariant under the $OSp(4/1).$ Since the action is invariant under the supersymmetric extension of the $AdS$ group, the supersymmetry algebra closes off shell without the need for auxiliary fields. The limit case $m\to 0$, i.e.$(3+1)$ -dimensional N=1 supergravity invariant under the Poincaré supergroup is also discussed.

hep-th↗

arXiv2002

Self--dual Lorentzian wormholes in n--dimensional Einstein gravity

A family of spherically symmetric, static and self--dual Lorentzian wormholes is obtained in n--dimensional Einstein gravity. This class of solutions includes the n--dimensional versions of the Schwarzschild black hole and the spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we study the geometrical structure of the solution, and delineate the domains of the free parameters for which wormhole, naked singular geometries and the Schwarzschild black hole are obtained. It is shown that, in the lower dimensional Einstein gravity without cosmological constant, we can not have self--dual Lorentzian wormholes.

hep-th↗

arXiv2002

Higher dimensional gravity invariant under the Poincare group

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincarè translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451.

gr-qc↗

arXiv2001

Supergravity and the Poincare group

An action for 3+1-dimensional supergravity genuinely invariant under the Poincare supergroup is proposed. The construction of the action is carried out considering a bosonic lagrangian invariant under both local Lorentz rotations and local Poincare translations as well as under diffeomorphism, and therefore the Poincare algebra closes off-shell. Since the lagrangian is invariant under the Poincare supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.

gr-qc↗

arXiv2000

Viscous cosmologies in scalar-tensor theories for Kasner type metrics

In a viscous Bianchi type I metric of the Kasner form, it is well known that it is not possible to describe an anisotropic physical model of the universe, which satisfies the second law of thermodynamics and the dominant energy condition (DEC) in Einstein's theory of gravity. We examine this problem in scalar-tensor theories of gravity. In this theory we show that it is possible to describe the growth of entropy, keeping the thermodynamics and the dominant energy condition.

gr-qc↗