scholarly journals Minimal coupling in presence of non-metricity and torsion

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Adrià Delhom
Keyword(s):  
Riemannian Space ◽  
Field Equations ◽  
Lagrange Equations ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Matter Fields

Abstract We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

scholarly journals SYMMETRIC TELEPARALLEL GRAVITY: SOME EXACT SOLUTIONS AND SPINOR COUPLINGS

2013 ◽  
Vol 28 (32) ◽  
pp. 1350167 ◽  
Author(s):  
MUZAFFER ADAK ◽  
ÖZCAN SERT ◽  
MESTAN KALAY ◽  
MURAT SARI
Keyword(s):  
Riemannian Space ◽  
Tangent Vector ◽  
Teleparallel Gravity ◽  
Coupling Coefficients ◽  
Field Equations ◽  
Minimal Coupling ◽  
Zero Curvature ◽  
Pp Wave ◽  
Teleparallel Theory ◽  
Parallel Transportation

In this paper, we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian space–time with nonzero nonmetricity, but zero torsion and zero curvature. First, we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then, we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry, the autoparallel curves coincide with those of the Riemannian space–times. Subsequently, we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving Lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our Lagrangian is equivalent to the Einstein–Hilbert Lagrangian for certain values of coupling coefficients. Thus, we arrive at calculating the field equations via independent variations. Then, we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally, we discuss a minimal coupling of a spin-1/2 field to STPG.

scholarly journals Cosmology with higher-derivative matter fields

2016 ◽  
Vol 13 (07) ◽  
pp. 1650102 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
Emmanuel N. Saridakis
Keyword(s):  
Dark Energy ◽  
Modified Gravity ◽  
State Parameter ◽  
De Sitter ◽  
Field Equations ◽  
Stiff Matter ◽  
Higher Derivative ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Matter Fields

We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry, we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher-derivatives of the matter energy density and pressure. For the cases of dust, radiation and stiff matter, we analyze the cosmological behavior, finding accelerating, de Sitter and non-accelerating phases, dominated by matter or dark-energy. Additionally, the effective dark-energy equation-of-state parameter can be quintessence-like, cosmological-constant-like or even phantom-like. The detailed study of these scenarios may provide signatures, that could distinguish them from other candidates of modified gravity.

scholarly journals Kerr–Schild–Kundt metrics in generic gravity theories with modified Horndeski couplings

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade ◽  
Çetin Şentürk
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Scalar Fields ◽  
Vacuum Field ◽  
Field Equations ◽  
Complete Proof ◽  
Universality Theorem ◽  
Covariant Derivatives ◽  
Matter Fields ◽  
Insight Into

AbstractThe Kerr–Schild–Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order covariant derivatives. There is yet no complete proof that these metrics are universal in the presence of matter fields such as electromagnetic and/or scalar fields. In order to get some insight into what happens when we extend the “universality theorem” to the case in which the electromagnetic field is present, as a first step, we study the KSK class of metrics in the context of modified Horndeski theories with Maxwell’s field. We obtain exact solutions of these theories representing the pp-waves and AdS-plane waves in arbitrary D dimensions.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

scholarly journals FERMIONIC AND SCALAR FIELDS AS SOURCES OF INTERACTING DARK MATTER–DARK ENERGY

2011 ◽  
Vol 20 (13) ◽  
pp. 2543-2558 ◽  
Author(s):  
SAMUEL LEPE ◽  
JAVIER LORCA ◽  
FRANCISCO PEÑA ◽  
YERKO VÁSQUEZ
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Analytical Solution ◽  
Scalar Fields ◽  
Nonminimal Coupling ◽  
Field Equations ◽  
Fermionic Field ◽  
Minimal Coupling ◽  
Constant Type

From a variational action with nonminimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the non-minimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

scholarly journals THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

2010 ◽  
Vol 25 (08) ◽  
pp. 1661-1698 ◽  
Author(s):  
ANZHONG WANG ◽  
N. O. SANTOS
Keyword(s):  
String Theory ◽  
Matter Field ◽  
Newtonian Potential ◽  
Field Equations ◽  
Hierarchy Problem ◽  
Large Extra Dimension ◽  
Gravitational Field Equations ◽  
Spatial Dimensions ◽  
Derivatives Of ◽  
Kaluza Klein

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

scholarly journals On higher covariant derivatives of the curvature tensors of Kählerian C-spaces

1983 ◽  
Vol 91 ◽  
pp. 1-18 ◽  
Author(s):  
Ryoichi Takagi
Keyword(s):  
Symmetric Spaces ◽  
Compact Type ◽  
Hermitian Symmetric Spaces ◽  
Covariant Derivatives ◽  
Higher Covariant Derivatives ◽  
Group Of Isometries ◽  
Complex Homogeneous Manifold ◽  
Curvature Tensors ◽  
Simply Connected ◽  
Derivatives Of

A compact simply connected complex homogeneous manifold is said briefly a C-space, which was completely classified by H. C. Wang [12]. A C-space is called to be Kählerian if it admits a Kählerian metric such that a group of isometries acts transitively on it. Hermitian symmetric spaces of compact type are typical examples of a Kählerian C-space. Let M be an arbitrary Kählerian C-space and R its curvature tensor. M. Itoh [6] expressed R in the language of Lie algebra and investigated various properties of R. In this paper, we study higher covariant derivatives of R.

scholarly journals Covariant extrinsic gravity and the geometric origin of dark energy

2015 ◽  
Vol 24 (03) ◽  
pp. 1550027 ◽  
Author(s):  
S. Jalalzadeh ◽  
T. Rostami
Keyword(s):  
Dark Energy ◽  
Density Parameter ◽  
Field Equations ◽  
Yang Mills ◽  
Geometric Origin ◽  
Model Independent ◽  
Bulk Space ◽  
Mills Field ◽  
Matter Fields ◽  
Good Agreement

In this paper, we construct the covariant or model independent induced Einstein–Yang–Mills field equations on a four-dimensional brane embedded isometrically in an D-dimensional bulk space, assuming the matter fields are confined to the brane. Applying this formalism to cosmology, we derive the generalized Friedmann equations. We derive the density parameter of dark energy in terms of width of the brane, normal curvature radii and the number of extra large dimensions. We show that dark energy could actually be the manifestation of the local extrinsic shape of the brane. It is shown that the predictions of this model are in good agreement with observation if we consider an 11-dimensional bulk space.

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