scholarly journals Cosmological evolution and exact solutions in a fourth-order theory of gravity

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Order Theory ◽  
Cosmological Evolution ◽  
Theory Of Gravity

Stellar model in a fourth order theory of gravity

1998 ◽  
Vol 57 (2) ◽  
pp. 954-960 ◽  
Author(s):  
Daniel E. Barraco ◽  
Victor H. Hamity
Keyword(s):  
Fourth Order ◽  
Order Theory ◽  
Stellar Model ◽  
Theory Of Gravity

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

scholarly journals Poincaré gauge gravity: An overview

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840005 ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Gauge Theory ◽  
Exact Solutions ◽  
Current Status ◽  
Spacetime Geometry ◽  
Theory Of Gravity ◽  
Physical Consequences ◽  
Gauge Gravity ◽  
Dynamical Scheme ◽  
Gauge Theory Of Gravity

We review the basics and the current status of the Poincaré gauge theory of gravity. The general dynamical scheme of Poincaré gauge gravity (PG) is formulated, and its physical consequences are outlined. In particular, we discuss exact solutions with and without torsion, highlight the cosmological aspects, and consider the probing of the spacetime geometry.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

scholarly journals Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zulfiqar Ali ◽  
Syed Husnine ◽  
Imran Naeem
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Arbitrary Function ◽  
Mixed Derivative ◽  
Reduction Theory ◽  
Double Reduction ◽  
Derivative Term ◽  
Divergence Property

We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.

Canonical formulation of Pais–Uhlenbeck action and resolving the issue of branched Hamiltonian

2017 ◽  
Vol 14 (03) ◽  
pp. 1750038 ◽  
Author(s):  
Kaushik Sarkar ◽  
Nayem Sk ◽  
Ranajit Mandal ◽  
Abhik Kumar Sanyal
Keyword(s):  
Scalar Curvature ◽  
Canonical Transformation ◽  
Auxiliary Variable ◽  
Order Theory ◽  
Higher Order ◽  
End Points ◽  
Canonical Formulation ◽  
Higher Order Terms ◽  
Theory Of Gravity ◽  
Higher Order Theory

Canonical formulation of higher order theory of gravity requires to fix (in addition to the metric), the scalar curvature, which is acceleration in disguise, at the boundary. On the contrary, for the same purpose, Ostrogradski's or Dirac's technique of constrained analysis, and Horowit'z formalism, tacitly assume velocity (in addition to the co-ordinate) to be fixed at the end points. In the process when applied to gravity, Gibbons–Hawking–York term disappears. To remove such contradiction and to set different higher order theories on the same footing, we propose to fix acceleration at the endpoints/boundary. However, such proposition is not compatible to Ostrogradski's or Dirac's technique. Here, we have modified Horowitz's technique of using an auxiliary variable, to establish a one-to-one correspondence between different higher order theories. Although, the resulting Hamiltonian is related to the others under canonical transformation, we have proved that this is not true in general. We have also demonstrated how higher order terms can regulate the issue of branched Hamiltonian.

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