$\mathcal{N} = 2$ STRING GEOMETRY AND THE HEAVENLY EQUATIONS

García‐Compeán, Hugo

doi:10.1142/9789812772732_0018

Cited by 4 publications

(3 citation statements)

References 44 publications

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“…For r > r H the metric signature is Lorentzian, however, as we pass through the horizon (r < r H ) the radial component becomes negative and the metric signature changes to (−−++), exhibiting a spacetime with 2+2-signature [64,65,66,67,68,69,70]. Such a metric signature is physically interesting as it has applications in self-dual super-gravity and super-string theories [71,72,73,74,75,76,77,78,79,80], the analysis of spinors in 2 + 2 dimensions [81,82], cosmological models [83] and black hole like solutions [84]. Another type of solutions can be found by setting…”

Section: Class a Solutionsmentioning

confidence: 99%

Static vacuum solutions on curved space–times with torsion

Shabani

Ziaie

2018

Int. J. Mod. Phys. A

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The Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity naturally extends Einstein's general relativity (GR) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic relation between spacetime torsion and spin of matter which indeed deprives the torsion of its dynamical content. The Lagrangian of ECKS gravity is proportional to the Ricci curvature scalar constructed out of a general affine connection so that owing to the influence of matter energy-momentum and spin, curvature and torsion are produced and interact only through the spacetime metric. In the absence of spin, the spacetime torsion vanishes and the theory reduces to GR. It is however possible to have torsion propagation in vacuum by resorting to a model endowed with a non-minimal coupling between curvature and torsion. In the present work we try to investigate possible effects of the higher order terms that can be constructed from spacetime curvature and torsion, as the two basic constituents of Riemann-Cartan geometry. We consider Lagrangians that include fourth-order scalar invariants from curvature and torsion and then investigate the resulted field equations. The solutions that we find show that there could exist, even in vacuum, nontrivial static spacetimes that admit both black holes and naked singularities.

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Section: Class a Solutionsmentioning

confidence: 99%

Static vacuum solutions on curved space–times with torsion

Shabani

Ziaie

2018

Int. J. Mod. Phys. A

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“…In fact, the 2+2−signature emerges in several physical context, including self-dual gravity a la Plebanski (see Ref. [6] and references therein), consistent N = 2 superstring theory as discussed by Ooguri and Vafa [7], N = (2, 1) heterotic string [8]- [12]. Moreover, it has been emphasized [13]- [14] that Majorana-Weyl spinor exists in spacetime of 2 + 2−signature.…”

Section: -Introductionmentioning

confidence: 99%

The (2+2)-Signature and the (1+1)-Matrix-Brane

Nieto

2007

Mod. Phys. Lett. A

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We discuss different aspects of the 2 + 2-signature from the point of view of the quatl theory. In particular, we compare two alternative approaches to such a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime of a string. This analysis also reveals hidden discrete symmetries of the 2 + 2-brane action associated with the 2 + 2-dimensional sector of a 2 + 10-dimensional target background.

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“…Such metrics of (2, 2)-signature, through the last decades, have became not only mathematical interesting, but also physically, in several contexts like the self-dual type Plebanski gravity (see [25]), or Ooguri-Vafa formalism of superstring theory, [17,18,27]. Primarily this is a worthwhile reason to take into account Hermitian metrics g jk on a two-dimensional complex manifold.…”

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confidence: 99%

New Candidates for a Hermitian Approach of Gravity

Aldea

Munteanu

2013

Int. J. Geom. Methods Mod. Phys.

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In this paper, some possible candidates for the study of gravity are proposed in terms of complex Finsler geometry. These mainly concern the complex Hermitian versions of weakly gravitational metric and Schwarzschild metric. For the weakly gravitational fields, we state few interesting geometrical and physical aspects such as the conditions under which a complex Finsler metrics are projectively related to the weakly gravitational metric. In the Kähler case, the geodesic curves of the weakly gravitational metric are obtained. Some applications concerning the deformations of the weakly gravitational Hermitian metric to a complex Randers metric are described. Another candidate for gravity is given by so-called Hermitian Schwarzschild metric for which some geodesic curves are highlighted. The last part of the paper is devoted to a generalization of the complex Klein-Gordon equations, in terms of Quantum field theory on a curved space.

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$\mathcal{N} = 2$ STRING GEOMETRY AND THE HEAVENLY EQUATIONS

Cited by 4 publications

References 44 publications

Static vacuum solutions on curved space–times with torsion

Static vacuum solutions on curved space–times with torsion

The (2+2)-Signature and the (1+1)-Matrix-Brane

New Candidates for a Hermitian Approach of Gravity

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