Stability of spherically symmetric solutions in modified theories of gravity

Abstract

In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our ''generalized variational principle,'' described in a previous work [M. D. Seifert and R. M. Wald, Phys. Rev. D 75, 084029 (2007)], to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s fR gravity, Jacobson and Mattingly's ''Einstein-aether theory,'' and Bekenstein's TeVeS theory. We find that in the presence of matter, fR gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-aether backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the ''kinetic terms'' of vacuum TeVeS theory are indefinite in a curved background, leading to an instability.

The Polarizations of Gravitational Waves

“…Finally, we briefly talk about the GW polarizations in Einstein-aether theory [29] as well as generalized TeVeS Theory [30][31][32]. These theories have more d.o.f., which excite more polarizations.…”

“…The vector field u µ has an action similar to that of the electromagnetic field. Later, it was generalized and replaced by the action for the aether field to solve some of the problems which TeVeS theory suffers from [31]. The new theory is simply called the generalized TeVeS theory, whose actions include Equation (40) and the one for the scalar field:…”

“…In fact, it cannot be used to identify the polarizations in Einstein-aether theory [29] or generalized Tensor-Vector-Scalar (TeVeS) theory [30][31][32], as the local Lorentz invariance is violated in both theories [33].…”

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

“…Although a considerable amount of work has gone into stability criteria, no study has been performed for investigating these criteria in the context of f (R) gravity. However, it should be noted that the dynamical stability of spherical systems, and also the stability of spherically symmetric solutions in f (R) gravity have been widely investigated (see Noureen & Zubair (2015) and Seifert (2007) and references therein for more details.) Certainly, the results of this paper could be useful in the numerical simulations of the disk galaxies in f (R) gravity.…”

Post-Newtonian parameters in the tensor-vector-scalar theory

“…These results also support our pathological situation. Thus, as it has been pointed out in these papers [15,16], we should consider Einstein-Aether type generalization for the vector field [11] if we consider TeVeS as an alternative to dark matter. It is, of course, very interesting to analyze PPN parameters and clarify the conditions for all the PPN parameters to be satisfied.…”