Spherically symmetric solutions in
                    <i>f</i>
                    (
                    <i>R</i>
                    ) gravity via the Noether symmetry approach

Capozziello, Salvatore; Stabile, A.; Troisi, A.

doi:10.1088/0264-9381/24/8/013

Cited by 338 publications

(274 citation statements)

References 53 publications

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“…As discussed in detail in [119], we have assumed spherical symmetry in the the weak-field approximation of the field equations, which leads to a corrected Newtonian potential due to the strong non-linearity of higher order gravity. Note that Birkhoff's theorem does not hold, in general, in ) (R f gravity, and that spherically symmetric solutions different from the Schwarzschild one exist in these ETGs [120].…”

Section: Dark Matter As Curvaturementioning

confidence: 99%

A Bird's Eye View of f (R)-Gravity

Capozziello¹,

Laurentis²,

Faraoni³

2010

TOAAJ

112

135

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Abstract:The currently observed accelerated expansion of the Universe suggests that cosmic flow dynamics is dominated by some unknown form of dark energy characterized by a large negative pressure. This picture comes out when such a new ingredient, beside baryonic and dark matter, is considered as a source in the r.h.s. of the field equations. Essentially, it should be some form of un-clustered, non-zero vacuum energy which, together with (clustered) dark matter, should drive the global cosmic dynamics. Among the proposals to explain the experimental situation, the "concordance model", addressed as ! CDM, gives a reliable snapshot of the today observed Universe according to the CMBR, LSS and SNeIa data, but presents dramatic shortcomings as the "coincidence and cosmological constant problems" which point out its inadequacy to fully trace back the cosmological dynamics. On the other hand, alternative theories of gravity, extending in some way General Relativity, allow to pursue a different approach giving rise to suitable cosmological models where a late-time accelerated expansion can be achieved in several ways. This viewpoint does not require to find out candidates for dark energy and dark matter at fundamental level (they have not been detected up to now), it takes into account only the "observed" ingredients (i.e. gravity, radiation and baryonic matter), but the l.h.s. of the Einstein equations has to be modified. Despite of this modification, it could be in agreement with the spirit of General Relativity since the only request is that the Hilbert-Einstein action should be generalized asking for a gravitational interaction acting, in principle, in different ways at different scales. We survey the landscape of ) (R f theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of ) (R f -gravity (whereis a generic function of Ricci scalar R ), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.

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Section: Dark Matter As Curvaturementioning

confidence: 99%

A Bird's Eye View of f (R)-Gravity

Capozziello¹,

Laurentis²,

Faraoni³

2010

TOAAJ

112

135

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“…Furthermore, spherically symmetric solutions can be achieved starting from a point-like f (R)-Lagrangian [6]. Such a Lagrangian can be obtained by imposing the spherical symmetry directly in the action (1).…”

Section: The Noether Symmetry Approach and The Spherical Symmetrymentioning

confidence: 99%

Axially symmetric solutions in f ( R )-gravity

Capozziello

Laurentis

Stabile

2010

Class. Quantum Grav.

121

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Axially symmetric solutions for f (R)-gravity can be derived starting from exact spherically symmetric solutions achieved by Noether symmetries. The method takes advantage of a complex coordinate transformation previously developed by Newman and Janis in General Relativity. An example is worked out to show the general validity of the approach. The physical properties of the solution are also considered.PACS numbers: 98.80.-k, 95.35.+x, 95.35.+d, 04.50.+h

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“…Sanyal, Modak, Rubano and Piedipalumbo studied the Noether symmetry in the higher order gravity theory, and gave the correct quantum description of the theory [17]. Capozziello, Stabile and Troisi searched for spherically symmetric solutions of f(R) theories of gravity via the Noether symmetry approach [18]. Vakili investigated the Noether symmetries of generic f(R) cosmological model, and further using approach of Noether symmetry quantized a flat FRW cosmology of the f(R) gravity [19,20].…”

Section: Introductionmentioning

confidence: 99%

Noether Symmetries and Conserved Quantities of f(R) Cosmology Models Containing Time Transformation

Fu¹,

Guo²

2016

AdAp

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Abstract. According to the invariance of Hamilton action of the generic f(R) cosmological model under the infinitesimal transformations with respect to the time t, the scale factor a and the Ricci scalar R, the generalized variation principle of the f(R) cosmological model is presented. The definition and the criterion of Noether symmetry are given for this model. The Noether identical equation and the Noether theorem of generic f(R) cosmological models are obtained. The Lie group of transformation, the conserved quantity and the form of generic f(R) gravity are derived via the method of Noether symmetry. It is also shown that the resulting form of f(R) yields as conservative law of the cosmological scale factor. Finally, an example is discussed to illustrate these results.

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Spherically symmetric solutions in f ( R ) gravity via the Noether symmetry approach

Cited by 338 publications

References 53 publications

A Bird's Eye View of f (R)-Gravity

A Bird's Eye View of f (R)-Gravity

Axially symmetric solutions in f ( R )-gravity

Noether Symmetries and Conserved Quantities of f(R) Cosmology Models Containing Time Transformation

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