On the Jeans Theorem and the “Tolman–Oppenheimer–Volkoff Equation” inR2Gravity

Abstract

Corda, Mosquera Cuesta and Lorduy Gòmez have shown that spherically symmetric stationary states can be used as a model for galaxies in the framework of the linearized R 2 gravity. Those states could represent a partial solution to the Dark Matter Problem. Here we discuss an improvement of this work. In fact, as the star density is a functional of the invariants of the associated Vlasov equation, we show that any of these invariants is in its turn a functional of the local energy and the angular momentum. As a consequence, the star density depends only on these two integrals of the Vlasov system. This result is known as the "Jeans theorem". In addition, we find an analogous of the historical Tolman-Oppenheimer-Volkov equation for the system considered in this paper.For the sake of completeness, in the final Section of the paper we consider two additional models which argue that Dark Matter could not be an essential element.

New perspectives on the TOV equilibrium from a dual null approach

“…since χ a does not admit components in S and γ ab does not depend on coordinates along N . Therefore, equation (25) implies that Θ χ = 0. Consequently, if there is an extra symmetry with orbits orthogonal to those of the maximally symmetric leaves of the foliation, the two-expansion of its generator vanishes.…”

“…Due to their evident relevance, many solutions for this type of configurations have been found [3][4][5][6][7][8][9][10][11][12][13][14][15], and more specifically, different formalisms [16][17][18][19][20] and solutions generating techniques have been developed [21,22]. Extensions of the TOV equation have also been investigated in the framework of modified gravity theories [23][24][25][26][27][28][29]. Yet a unified characterisation of the underlying features of the TOV equation has attracted little attention, and this is what concerns us in the present work.…”

Gravitational luminosity of a hot plasma in R^2 gravity

“…In [29] R 2 inflation is combined with the Dark Energy stage and in [30] an oscillating Universe, which is well tuned with some cosmological observations is discussed. Finally, in [31,32] the possibility to partially solve the Dark Matter problem in the linearized R 2 theory has been analyzed.…”

“…To obtain the gravitational luminosity of a plasma with the gravitational bremsstrahlung as a mechanism for the loss of its energy, one must multiply (31) with the electron flux vn e , ion density n i , and integrate over the impact parameter b [25,26]. Therefore, we obtain the luminosity L (energy loss per volume V ) of the plasma as…”

“…The key point here is that, exactly in order to match the PPN-restricted parameters for the action (1) and to be consistent with solar system tests, we have set the coupling constant of the R 2 term very small. Such a setting has been chosen also to match the Dark Matter model in [31,32]. This crucial point makes the contribution of Eq.…”