Weak-Field Limit of a Kaluza-Klein Model with a Nonlinear Perfect Fluid

Abstract

The main purpose of our paper is to construct a viable Kaluza-Klein model satisfying the observable constraints. To this end, we investigate the six-dimensional model with spherical compactification of the internal space. Background matter is considered in the form of a perfect fluid with non-linear equations of state both in the external/our and internal spaces and the model is set to include an additional bare cosmological constant Λ 6 . In the weak-field approximation, the background is perturbed by pressureless gravitating mass that is a static point-like particle. The non-linearity of the equations of state of a perfect fluid makes it possible to solve simultaneously a number of problems. The demand that the parameterized post-Newtonian parameter γ be equal to 1 in this configuration, first, ensures compatibility with gravitational tests in the Solar system (deflection of light and time delay of radar echoes) at the same level of accuracy as General Relativity. Second, it translates into the absence of internal space variations so that the gravitational potential coincides exactly with the Newtonian one, securing the absence of the fifth force. Third, the gravitating mass remains pressurless in the external space as in the standard approach to non-relativistic astrophysical objects and meanwhile, acquires effective tension in the internal space. *

Effects of nonlinearity of f(R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification

“…(106). In the case Ω = 0, we obtain the relation ζ = −1/(1+2ω 1 ), which exactly reproduces the corresponding results in paper [38].…”

“…We also suppose that the background perfect fluid is nonlinear, i.e., the background parametersω 0 andω 1 of the EoS in the external and internal spaces are not equal to the squared speed of sound in these spaces. The linear model f (R) = R with spherical compactification and nonlinear background perfect fluid was considered in [38]. Now, we generalize the study for some arbitrary function f (R).…”