Spherically symmetric solutions inf(R)theories of gravity obtained using the first order formalism

2000 ◽  
Vol 62 (4) ◽  
Author(s):  
D. E. Barraco ◽  
V. H. Hamity
Keyword(s):  
Spherically Symmetric ◽  
First Order ◽  
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.

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 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

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

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