66 research outputs found
Weak Gravitational Field in Finsler-Randers Space and Raychaudhuri Equation
The linearized form of the metric of a Finsler - Randers space is studied in
relation to the equations of motion, the deviation of geodesics and the
generalized Raychaudhuri equation are given for a weak gravitational field.
This equation is also derived in the framework of a tangent bundle. By using
Cartan or Berwald-like connections we get some types "gravito -
electromagnetic" curvature. In addition we investigate the conditions under
which a definite Lagrangian in a Randers space leads to Einstein field
equations under the presence of electromagnetic field. Finally, some
applications of the weak field in a generalized Finsler spacetime for
gravitational waves are given.Comment: 22 pages, matches version published in GER
Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
A generalized model of space-time is given, taking into consideration the
anisotropic structure of fields which are depended on the position and the
direction (velocity).In this framework a generalized FRW-metric the
Raychaudhouri and Friedmann equations are studied.A long range vector field of
cosmological origin is considered in relation to the physical geometry of
space-time in which Cartan connection has a fundamental role.The generalised
Friedmann equations are produced including anisotropic terms.The variation of
anisotropy is expressed in terms of the Cartan torsion tensor of the
Finslerian space-time.A possible estimation of the anisotropic parameter
can be achieved with the aid of the de-Sitter model of the empty flat universe
with weak anisotropy. Finally a physical generalisation for the model of
inflation is also studied.Comment: 21 pages- to appear in GR
Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR)
spacetime previously investigated by a subset of the present authors
(Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis et al.
in Eur Phys J C 81(11):990, 2021). We will examine the dynamical analysis of
geodesics which provides the derivation of the energy and the angular momentum
of a particle moving along a geodesic of SFR spacetime. This study allows us to
compare our model with the corresponding of general relativity (GR). In
addition, the effective potential of SFR model is examined and it is compared
with the effective potential of GR. The phase portraits generated by these
effective potentials are also compared. Finally we deal with the derivation of
the deflection angle of the SFR spacetime and we find that there is a small
perturbation from the deflection angle of GR. We also derive an interesting
relation between the deflection angles of SFR model and the corresponding
result in the work of Shapiro et al (Phys Rev Lett 92(12):121101, 2004). These
small differences are attributed to the anisotropic metric structure of the
model and especially to a Randers term which provides a small deviation from
the GR.Comment: 21 pages, 5 figure
Schwarzschild-like solutions in Finsler-Randers gravity
In this work, we extend for the first time the spherically symmetric
Schwarzschild and Schwarzschild-De Sitter solutions with a Finsler-Randers-type
perturbation which is generated by a covector . This gives a locally
anisotropic character to the metric and induces a deviation from the Riemannian
models of gravity. A natural framework for this study is the Lorentz tangent
bundle of a spacetime manifold. We apply the generalized field equations to the
perturbed metric and derive the dynamics for the covector . Finally,
we find the timelike, spacelike and null paths on the Schwarzschild-Randers
spacetime, we solve the timelike ones numerically and we compare them with the
classic geodesics of general relativity. The obtained solutions are new and
they enrich the corresponding literature.Comment: 13 pages, 2 figures, to be published in EPJ
Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors. We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally, we deal with the derivation of the deflection angle of the SFR spacetime and we find that there is a small perturbation from the deflection angle of GR. It comes from the anisotropic metric structure of the model and especially from a Randers term which provides a small deviation from GR
Spinors and space-time anisotropy
This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated anholonomic frames and nonlinear connection structures, the algebra and geometry of distinguished anisotropic Clifford and spinor spaces, their extension to spaces of higher order anisotropy and the geometry of gravity and gauge theories with anisotropic spinor variables. The book summarizes the authors' results and can be also considered as a pedagogical survey on the mentioned subjects
Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
A consistent theory of quantum gravity (QG) at Planck scale almost sure
contains manifestations of Lorentz local symmetry violations (LV) which may be
detected at observable scales. This can be effectively described and classified
by models with nonlinear dispersions and related Finsler metrics and
fundamental geometric objects (nonlinear and linear connections) depending on
velocity/ momentum variables. We prove that the trapping brane mechanism
provides an accurate description of gravitational and matter field phenomena
with LV over a wide range of distance scales and recovering in a systematic way
the general relativity (GR) and local Lorentz symmetries. In contrast to the
models with extra spacetime dimensions, the Einstein-Finsler type gravity
theories are positively with nontrivial nonlinear connection structure,
nonholonomic constraints and torsion induced by generic off-diagonal
coefficients of metrics, and determined by fundamental QG and/or LV effects.Comment: latex2e, 11pt, 34 pages, the version accepted to Class. Quant. Gra
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