On neutron stars in f(R) theories: Small radii, large masses and large energy emitted in a merger

Abstract

In the context of f (R) gravity theories, we show that the apparent mass of a neutron star as seen from an observer at infinity is numerically calculable but requires careful matching, first at the star's edge, between interior and exterior solutions, none of them being totally Schwarzschildlike but presenting instead small oscillations of the curvature scalar R; and second at large radii, where the Newtonian potential is used to identify the mass of the neutron star. We find that for the same equation of state, this mass definition is always larger than its general relativistic counterpart. We exemplify this with quadratic R 2 and Hu-Sawicki-like modifications of the standard General Relativity action. Therefore, the finding of two-solar mass neutron stars basically imposes no constraint on stable f (R) theories. However, star radii are in general smaller than in General Relativity, which can give an observational handle on such classes of models at the astrophysical level. Both larger masses and smaller matter radii are due to much of the apparent effective energy residing in the outer metric for scalar-tensor theories. Finally, because the f (R) neutron star masses can be much larger than General Relativity counterparts, the total energy available for radiating gravitational waves could be of order several solar masses, and thus a merger of these stars constitutes an interesting wave source.

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

“…More specifically, for the parameters space of quadratic f (R) models which are in agreement with theoretical constraints and cosmological data, the f (R) predictions for the neutron stars maximal mass ranged from 2-2.6 M ⊙ (see Table I) and therefore agreed with observed stars as those found in [16]. Similar results were found for the so-called Hu-Sawicki f (R) model [32]. Also, we have seen that, unlike previous works [61] which naively defined the mass as the matter integral over the star volume, we have shown how a more careful matching of interior and exterior regions causes the total gravitational mass to be unbounded for sufficiently large values of α (with specific values depending on the equation of state under consideration).…”

“…It is precisely this mode which can help to prevent the gravitational collapse and increase the gravitational mass as observed by a distant observer. Thus in the event of merging objects of this kind, the available energy would be higher than General Relativity counterparts and the emission of gravitational waves from such a configuration might be feasible and detectable by present and future interferometers [32,[62][63][64][65][66].…”

“…As a consequence, the spacetime region outside the star also contributes to the total gravitational mass as perceived by a distant observer (c.f. [32] for a thorough discussion on this issue). By analogy with scalar-tensor theory of gravity in which that region outside the star is referred to as the dilaton sphere (or disphere) [45], in the following we shall denote this domain as gravitational sphere (or gravisphere).…”

“…Neutron stars in the context of f (R) theories were primarily studied in [20,21] and then in abundant bibliography [22][23][24][25][26][27][28][29][30][31][32][33][34][35] for both scalar-tensor f (R) theories, as well as some closely-related theories. 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).…”

Constraining gravity with hadron physics: neutron stars, modified gravity and gravitational waves

“…In [36], we have explored neutron stars within f (R) theories. These are very popular to account for dark energy in cosmology: this is the limit of very tenuous density but very large sizes [38].…”