Spherically symmetric solutions of modified field equations inf(R)theories of gravity

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
T. Multamäki ◽  
I. Vilja
Keyword(s):  
Spherically Symmetric ◽  
Field Equations ◽  
Spherically Symmetric Solutions ◽  
Theories Of Gravity

scholarly journals Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 68 ◽  
Author(s):  
Sebastian Bahamonde ◽  
Konstantinos Dialektopoulos ◽  
Ugur Camci
Keyword(s):  
Vector Fields ◽  
Selection Criterion ◽  
Alternative Theories Of Gravity ◽  
Spherically Symmetric ◽  
Lie Point Symmetries ◽  
Noether Symmetries ◽  
Symmetry Approach ◽  
Point Transformations ◽  
Spherically Symmetric Solutions ◽  
Theories Of Gravity

It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish those models of f ( R , G ) theory, with R and G being the Ricci and the Gauss–Bonnet scalars respectively, that are invariant under point transformations in a spherically symmetric background. In total, we find ten different forms of f that present symmetries and calculate their invariant quantities, i.e., Noether vector fields. Furthermore, we use these Noether symmetries to find exact spherically symmetric solutions in some of the models of f ( R , G ) theory.

The general static spherically symmetric solution in Einstein’s unified field theory

1952 ◽  
Vol 210 (1102) ◽  
pp. 427-434 ◽  
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Singular Surfaces ◽  
Field Equations ◽  
Unified Field ◽  
Spherically Symmetric Solution ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

The static spherically symmetric solutions of Einstein’s unified field equations previously given refer to an electric field alone or to a magnetic field alone. The general solutions in the case where both types of field exist together are now derived. After appropriate boundary conditions have been applied, the solutions may be interpreted to represent a magnetic field arising from a point pole, and an electric field arising from a dispersed charge distribution, but tending asymptotically to that of a point charge. The solutions have an infinity of singular surfaces, contain no arbitrary constant corresponding to the mass of the system, and in them the charge distributions contain both positive and negative electricity at different places. It appears that the only static spherically symmetric solutions likely to have any physical significance are certain of those referring to an electric field alone.

scholarly journals NON-MINIMAL RβF2-COUPLED ELECTROMAGNETIC FIELDS TO GRAVITY AND STATIC, SPHERICALLY SYMMETRIC SOLUTIONS

2011 ◽  
Vol 26 (20) ◽  
pp. 1487-1494 ◽  
Author(s):  
TEKIN DERELI ◽  
ÖZCAN SERT
Keyword(s):  
Variational Principle ◽  
Electromagnetic Fields ◽  
Lagrange Multipliers ◽  
Spherically Symmetric ◽  
Field Equations ◽  
First Order ◽  
Spherically Symmetric Solutions ◽  
Method Of Lagrange Multipliers ◽  
Electrically Charged ◽  
Static Spherically Symmetric Solutions

We investigate non-minimal RβF2-type couplings of electromagnetic fields to gravity. We derive the field equations by a first-order variational principle using the method of Lagrange multipliers. Then we present various static, spherically symmetric solutions describing the exterior fields in the vicinity of electrically charged massive bodies.

scholarly journals Nonstatic Spherically Symmetric Solutions for a Perfect Fluid in General Relativity

1976 ◽  
Vol 29 (2) ◽  
pp. 113 ◽  
Author(s):  
N Chakravarty ◽  
SB Dutta Choudhury ◽  
A Banerjee
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Dynamical Behaviour ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Spherically Symmetric Solutions ◽  
Spherically Symmetric Distribution ◽  
General Method

A general method is described by which exact solutions of Einstein's field equations are obtained for a nonstatic spherically symmetric distribution of a perfect fluid. In addition to the previously known solutions which are systematically derived, a new set of exact solutions is found, and the dynamical behaviour of the corresponding models is briefly discussed.

scholarly journals Static spherically symmetric solutions in a subclass of Horndeski theories of gravity

2018 ◽  
Vol 15 (09) ◽  
pp. 1850152 ◽  
Author(s):  
Lorenzo Sebastiani
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Integration Constant ◽  
Spherically Symmetric ◽  
Rotation Curves ◽  
Spherically Symmetric Solutions ◽  
Euclidean Action ◽  
Theories Of Gravity ◽  
Static Spherically Symmetric Solutions

In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole (BH) solution and we will study its thermodynamics by using the Euclidean Action. We will see that, in analogy with the case of General Relativity (GR), the integration constant of the solution can be identified with the mass of the BH itself. Other solutions will be discussed, by posing special attention on the possibility of reproducing the observed profiles of the rotation curves of galaxies. a

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