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

Abstract

In the framework of metric f (R) gravity, we find the dispersion relation for the propagation of tightly wound spiral density waves in the surface of rotating, selfgravitating disks. Also, new Toomre-like stability criteria for differentially rotating disks has been derived for both fluid and stellar disks.

Stability of differentially rotating disks in f(T) theory

“…(1) coincides with the well-known one considered in Newtonian gravity and the weak field limit of GR (see e.g. [6,7,28] and the references therein). This also supports the tetrad choice given in Eq.…”

“…[21,28], we restrict ourselves to the adiabatic approximation, in which the evolution of the universe is very slow in comparison with local dynamics. It means that we can choose the Minkowski metric η ab instead of Friedmann-Robertson-Walker (FRW) metric as the background metric [28]. In fact, the quantitative studies (e.g.…”

“…As mentioned in e.g. [21,28], the WKB approximation can be used in most cases without much loss of generality.…”

“…In the literature, the stability of differentially rotating disks were considered in some modified gravity theories, e.g. Modified Newtonian Dynamics (MOND) [26], Moffat's Modified Gravity (MOG) [27,36], f (R) theory [28], and so on. In the present work, we try to consider the stability of differentially rotating disks in another modified gravity theory, namely f (T ) theory [8,9,37].…”

Jeans analysis in energy–momentum-squared gravity

“…where the effective sound speed C 2 s = c 2 s + α * c 4 Σ 0 is defined in (53), again replacing α with α * . At the limit α * → 0, we have C s = c s and G = G. Therefore, as expected, the dispersion relation (100) reduces to the standard one in Newtonian gravity [62].…”