scholarly journals Charged conformal Killing spinors

2015 ◽  
Vol 56 (1) ◽  
pp. 013510 ◽  
Author(s):  
Andree Lischewski
Keyword(s):  
Conformal Killing ◽  
Killing Spinors

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

scholarly journals Killing superalgebras for lorentzian five-manifolds

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrew Beckett ◽  
José Figueroa-O’Farrill
Keyword(s):  
Spin Manifold ◽  
Field Equations ◽  
Spinor Bundle ◽  
Killing Spinors ◽  
Spinor Connection ◽  
Spencer Cohomology ◽  
Definition Of ◽  
Supersymmetric Theories ◽  
Filtered Deformations

Abstract We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an $$ \mathfrak{sp} $$ sp (1)-valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.

INHERITING SPACELIKE CONFORMAL KILLING VECTORS IN STRING COSMOLOGY

2003 ◽  
Vol 12 (05) ◽  
pp. 885-892 ◽  
Author(s):  
HÜSNÜ BAYSAL
Keyword(s):  
General Relativity ◽  
Cosmic Strings ◽  
String Cosmology ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Conformal Killing Vectors

We study the consequences of the existence of spacelike conformal Killing vectors (SpCKV) parallel to xa for cosmic strings and string fluid in the context of general relativity. The inheritance symmetries of the cosmic strings and string fluid are discussed in the case of SpCKV. Furthermore we examine proper homothetic spacelike Killing vectors for the cosmic strings and string fluid.

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

scholarly journals Conformal geodesics on gravitational instantons

2021 ◽  
pp. 1-32
Author(s):  
MACIEJ DUNAJSKI ◽  
PAUL TOD
Keyword(s):  
Magnetic Field ◽  
Geodesic Flow ◽  
Isometry Group ◽  
Three Dimensional ◽  
First Integrals ◽  
Complete Integrability ◽  
Conformal Killing ◽  
Gravitational Instantons ◽  
Geodesic Equations ◽  
Jacobi Equations

Abstract We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the SO(3)–invariant gravitational instantons. On a hyper–Kähler four–manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self–dual magnetic field. In the case of the anti–self–dual Taub NUT instanton we integrate these equations completely by separating the Hamilton–Jacobi equations, and finding a commuting set of first integrals. This gives the first example of an integrable conformal geodesic flow on a four–manifold which is not a symmetric space. In the case of the Eguchi–Hanson we find all conformal geodesics which lie on the three–dimensional orbits of the isometry group. In the non–hyper–Kähler case of the Fubini–Study metric on $\mathbb{CP}^2$ we use the first integrals arising from the conformal Killing–Yano tensors to recover the known complete integrability of conformal geodesics.

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