scholarly journals Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1173
Author(s):  
Konstantin Osetrin ◽  
Ilya Kirnos ◽  
Evgeny Osetrin ◽  
Altair Filippov
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Spatial Homogeneity ◽  
Wave Variables ◽  
Quadratic Theory ◽  
Test Particles ◽  
Jacobi Formalism ◽  
Theory Of Gravity

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).

scholarly journals DISCUSSION ON SOME CHARACTERISTICS OF CHARGED BRANE-WORLD BLACK HOLES

2009 ◽  
Vol 24 (04) ◽  
pp. 719-739 ◽  
Author(s):  
M. KALAM ◽  
F. RAHAMAN ◽  
A. GHOSH ◽  
B. RAYCHAUDHURI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Field ◽  
Scalar Field ◽  
Brane World ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Effective Potentials ◽  
Test Particles ◽  
Jacobi Formalism

Several physical natures of charged brane-world black holes are investigated. Firstly, the timelike and null geodesics of the charged brane-world black holes are presented. We also analyze all the possible motions by plotting the effective potentials for various parameters for circular and radial geodesics. Secondly, we investigate the motion of test particles in the gravitational field of the charged brane-world black holes using the Hamilton–Jacobi formalism. We consider charged and uncharged test particles and examine their behavior in both static and nonstatic cases. Thirdly, the thermodynamics of the charged brane-world black holes are studied. Finally, it is shown that there is no phenomenon of superradiance for an incident massless scalar field for such a black hole.

scholarly journals Wave-like spatially homogeneous models of Stäckel spacetimes (2.1) type in the scalar-tensor theory of gravity

2020 ◽  
Vol 35 (33) ◽  
pp. 2050275
Author(s):  
Konstantin Osetrin ◽  
Altair Filippov ◽  
Evgeny Osetrin
Keyword(s):  
Scalar Field ◽  
Explicit Form ◽  
Scalar Tensor Theory ◽  
Tensor Theory ◽  
Test Particles ◽  
Homogeneous Wave ◽  
General Scalar ◽  
Spatially Homogeneous ◽  
Theory Of Gravity ◽  
The Universe

Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like spacetime models allow the existence of privileged coordinate systems where the eikonal equation and the Hamilton–Jacobi equation of test particles can be integrated by the method of complete separation of variables with the separation of isotropic (wave) variables on which the space metric depends (non-ignored variables). An explicit form of the scalar field and two functions of the scalar field that are part of the general scalar-tensor theory of gravity are found. The explicit form of the eikonal function and the action function for test particles in the considered models is given. The obtained solutions are of type III according to the Bianchi classification and type N according to the Petrov classification. Wave-like spatially homogeneous spacetime models can describe primordial gravitational waves of the Universe.

scholarly journals Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity

2020 ◽  
Vol 17 (12) ◽  
pp. 2050184
Author(s):  
Evgeny Osetrin ◽  
Konstantin Osetrin ◽  
Altair Filippov ◽  
Ilya Kirnos
Keyword(s):  
Eikonal Equation ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Scalar Tensor Theory ◽  
Tensor Theory ◽  
Test Particles ◽  
Petrov Classification ◽  
Homogeneous Models ◽  
Theory Of Gravitation ◽  
Spatially Homogeneous

All classes of spatially homogeneous spacetime models in the generalized scalar–tensor theory of gravitation are found to allow the integration of the equations of motion of test particles and the eikonal equation by the method of separation of variables by type (3.1). Three classes of exact solutions are obtained that relate to Shapovalov wave-like spacetime models. The resulting spacetime models are of types IV, VI and VII according to the Bianchi classification and type N according to Petrov classification.

scholarly journals TENSOR–SCALAR TORSION

2001 ◽  
Vol 16 (03) ◽  
pp. 113-119 ◽  
Author(s):  
CHARRO GRUVER ◽  
RICHARD HAMMOND ◽  
P. F. KELLY
Keyword(s):  
Angular Momentum ◽  
Scalar Field ◽  
Conservation Law ◽  
Torsion Tensor ◽  
Equations Of Motion ◽  
Exterior Derivative ◽  
Field Equations ◽  
Theory Of Gravity ◽  
Rotational Angular Momentum

A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank-two potential plus the dual of the gradient of a scalar field. Field equations for the theory are derived by demanding that the action be stationary under variations with respect to the metric, the antisymmetric potential, and the scalar field. A material action is introduced and the equations of motion are derived. The correct conservation law for rotational angular momentum plus spin is observed to hold in this theory.

scholarly journals Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

2020 ◽  
Vol 17 (14) ◽  
pp. 2050186
Author(s):  
Valeriy Obukhov
Keyword(s):  
Jacobi Equation ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Type Equation ◽  
Parabolic Type ◽  
Complete Separation ◽  
Test Particles ◽  
Charged Test Particle ◽  
Charged Test ◽  
Hamilton Jacobi Equation

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

scholarly journals A NON-GEODESIC MOTION IN THE R-1 THEORY OF GRAVITY TUNED WITH OBSERVATIONS

2008 ◽  
Vol 23 (02) ◽  
pp. 109-114 ◽  
Author(s):  
CHRISTIAN CORDA
Keyword(s):  
Dark Matter ◽  
High Order ◽  
Ricci Scalar ◽  
Geodesic Motion ◽  
General Picture ◽  
Test Particles ◽  
Pioneer Anomaly ◽  
Theories Of Gravity ◽  
Theory Of Gravity

In the general picture of high order theories of gravity, recently, the R-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R-1 function of the Ricci scalar and the matter Lagrangian. The result is a non-geodesic motion of test particles which, in principle, could be connected with Dark Matter and Pioneer anomaly problems.

GALACTIC AND ASTROPHYSICAL SIZES FROM SCALAR-TENSOR THEORY OF GRAVITY

2004 ◽  
Vol 13 (02) ◽  
pp. 359-371 ◽  
Author(s):  
GIUSEPPE BASINI ◽  
MARCO RICCI ◽  
FULVIO BONGIORNO ◽  
SALVATORE CAPOZZIELLO
Keyword(s):  
Scalar Field ◽  
Spiral Galaxies ◽  
Weak Field ◽  
Newtonian Potential ◽  
Scalar Tensor Theory ◽  
Field Limit ◽  
Weak Field Limit ◽  
Tensor Theory ◽  
Flat Rotation Curves ◽  
Theory Of Gravity

We investigate the weak-field limit of scalar-tensor theory of gravity and show that results are directly depending on the coupling and self-interaction potential of the scalar field. In particular, corrections are derived for the Newtonian potential. We discuss astrophysical applications of the results, in particular the flat rotation curves of spiral galaxies.

Sign in / Sign up

Export Citation Format

Share Document