An f(R) Gravitation for Galactic Environments

We propose [Sobouti, arXiv:astro-ph/0603302] an f(R) modification of GR, which admits of a modified Schwarzschild metric. In the weak field limit this amounts to adding a small logarithmic correction to the newtonian potential. A test star moving in such a spacetime acquires a constant speed at large distances. From observations of the velocity curves of spirals, this speed turns out to be proportional to the fourth root of the mass of the central body, in compliance with the Tully-Fisher relation. A variance of MOND emerges as a consequence of the formalism.

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An f(R) gravitation for galactic environments

Proceedings of the International Astronomical Union ◽

10.1017/s174392130700590x ◽

2006 ◽

Vol 2 (S238) ◽

pp. 451-452

Author(s):

Yousef Sobouti

Keyword(s):

Central Body ◽

Weak Field ◽

Newtonian Potential ◽

Logarithmic Correction ◽

Field Limit ◽

Weak Field Limit ◽

Asymptotic Speed ◽

Fourth Root ◽

Fisher Relation

AbstractWe propose an action-based f(R) modification of Einstein's gravity which admits of a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the Newtonian potential. A test star moving in such a spacetime acquires a constant asymptotic speed at large distances. This speed turns out to be proportional to the fourth root of the mass of the central body in compliance with the Tully-Fisher relation. A variance of MOND's gravity emerges as an inevitable consequence of the proposed formalism.

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GALACTIC AND ASTROPHYSICAL SIZES FROM SCALAR-TENSOR THEORY OF GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271804004669 ◽

2004 ◽

Vol 13 (02) ◽

pp. 359-371 ◽

Cited By ~ 1

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.

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NEWTONIAN LIMIT OF STRING-DILATON GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271803003347 ◽

2003 ◽

Vol 12 (05) ◽

pp. 843-852 ◽

Cited By ~ 8

Author(s):

S. CAPOZZIELLO ◽

G. LAMBIASE

Keyword(s):

Scalar Field ◽

Spiral Galaxies ◽

Weak Field ◽

The Self ◽

Newtonian Potential ◽

Nonminimal Coupling ◽

Dilaton Gravity ◽

Field Limit ◽

Weak Field Limit ◽

Flat Rotation Curves

We study the weak-field limit of string-dilaton gravity and derive corrections to the Newtonian potential having strength directly depends on the self interaction potential and the nonminimal coupling of the dilaton scalar field. We discuss also possible astrophysical applications of the results, in particular the flat rotation curves of spiral galaxies.

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A GENERAL SOLUTION IN THE NEWTONIAN LIMIT OF f(R)-GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732309030382 ◽

2009 ◽

Vol 24 (09) ◽

pp. 659-665 ◽

Cited By ~ 39

Author(s):

S. CAPOZZIELLO ◽

A. STABILE ◽

A. TROISI

Keyword(s):

General Solution ◽

Gravity Model ◽

General Result ◽

Weak Field ◽

Newtonian Limit ◽

Newtonian Potential ◽

Field Limit ◽

Weak Field Limit ◽

Theories Of Gravity ◽

Physical Consequences

We show that any analytic f(R)-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only f(R) = R allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.

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On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies withf(R)dark energy

Physical Review D ◽

10.1103/physrevd.87.063517 ◽

2013 ◽

Vol 87 (6) ◽

Cited By ~ 28

Author(s):

Timothy Clifton ◽

Peter Dunsby ◽

Rituparno Goswami ◽

Anne Marie Nzioki

Keyword(s):

Dark Energy ◽

Weak Field ◽

Field Limit ◽

Weak Field Limit

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Quantum Faraday Effect in the Universe

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194517600461 ◽

2017 ◽

Vol 45 ◽

pp. 1760046

Author(s):

Lídice Cruz Rodríguez ◽

Aurora Pérez Martínez ◽

Gabriella Piccinelli ◽

Elizabeth Rodríguez Querts

Keyword(s):

Faraday Effect ◽

Weak Field ◽

Field Limit ◽

Self Energy ◽

Weak Field Limit ◽

Resonant Behavior ◽

Degenerate Regime ◽

The Universe ◽

Resonant Mechanism ◽

Recombination Epoch

We study the Quantum Faraday rotation starting from the photon self-energy in the presence of a constant magnetic field. The Faraday angle is calculated in the non-degenerate regime and for weak field limit. Two physical scenarios, possibly characterized by these conditions, are the recombination epoch and the jets originated in pulsars. We discuss the resonant behavior that the Faraday angle exhibits in these scenarios and investigate the possibility of detecting cosmic magnetic fields through this resonant mechanism.

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The nature of the Raman damping constant and its effect upon resonant light scattering from molecular systems in the weak field limit

Solid State Communications ◽

10.1016/0038-1098(79)90993-1 ◽

1979 ◽

Vol 32 (1) ◽

pp. 39-42 ◽

Cited By ~ 1

Author(s):

J.M. Friedman

Keyword(s):

Light Scattering ◽

Weak Field ◽

Field Limit ◽

Molecular Systems ◽

Weak Field Limit

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Weak-field limit

Beyond Einstein Gravity ◽

10.1007/978-94-007-0165-6_5 ◽

2010 ◽

pp. 165-208

Author(s):

Salvatore Capozziello ◽

Valerio Faraoni

Keyword(s):

Weak Field ◽

Field Limit ◽

Weak Field Limit

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Jeans instability in non-minimal matter-curvature coupling gravity

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8189-y ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

Cláudio Gomes

Keyword(s):

Boltzmann Equation ◽

Dispersion Relation ◽

Weak Field ◽

Model Parameters ◽

Field Limit ◽

Modified Dispersion Relation ◽

Weak Field Limit ◽

Special Cases ◽

Jeans Instability ◽

Scalar Potentials

Abstract The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean’s criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.

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