Hydrostatic equilibrium and stellar structure inf(R)gravity

Abstract

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lané-Emden equation coming out from f (R)-gravity. Such an equation is obtained in metric approach by considering the Newtonian limit of f (R)-gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index n. The modified equation results an integro-differential equation, which, in the limit f (R) → R, becomes the standard Lané-Emden equation. We find the radial profiles of gravitational potential by solving for some values of n. The comparison of solutions with those coming from General Relativity shows that they are compatible and physically relevant.

Local stability of self-gravitating disks in f ( R ) $f(R)$ gravity

“…The weak field limit of this theory has been widely investigated, for a comprehensive review of the subject see (Sotiriou & Faraoni 2010;Nojiri & Odintsov 2011;De Felice & Tsujikawa 2010;Capozziello & De Laurentis 2011). The general action for this theory is given by…”

“…This situation is reminiscent of the difference between Jeans mass in modified gravity and Newtonian gravity. In fact in modified theories of gravity for which the gravitational force is stronger than that of Newtonian gravity, the Jeans mass is smaller than the standard case, for example see (Roshan & Abbassi 2014;Capozziello et al 2011). Therefore, comparing the two cases β = 0, α > 1 and α = 1, β > 0 (note that in both cases the gravitational force is stronger than the Newtonian gravitational force), we can conclude that in theories where the gravitational force in the weak field limit is stronger than that of Newtonian gravity, the required value of Toomre's parameter Q g for preventing gravitational collapse can be larger or smaller than the corresponding value in Newtonian gravity.…”

The realistic models of relativistic stars in f ( R ) = R + αR 2 gravity

“…Also the possibility of emergence of new types of astrophysical objects in the context of f (R) theories, such as stable stars with large magnetic fields, supermassive stars, among others (see for instance [36,37] for some proposals).…”

Dilatonic equation of hydrostatic equilibrium and neutron star structure

“…On the other hand, if one is interested in studying the structure and evolution of stars in different gravities, one should obtain the HEE in those gravity models. In recent years, the generalizations and modifications of this equation were of special interests for many authors (Heydarifard 2009;Astashenok 2013;Orellana 2013;Arbanil 2013;Doneva 2013;Goswami 2014;Lemos 2015;Yazadjiev 2014;Capozziello 2011;Capozziello 2012;Momeni 2015a). For more examples, we may note that the HEE equation in f (R) and f (G) gravities werediscussed in (Astashenok 2015b;Momeni 2015b;Astashenok 2015a;Abbas 2015), d-dimensional HEE in EN gravity was investigated in (Ponce 2000) and HEE of EN-Λ gravity with arbitrary dimensions was obtained in (Bordbar 2015).…”