Effects of nonlinearity of f (R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification
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Дата
2020
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E-ISSN
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Анотація
We study the effects associated with nonlinearity
of f (R) gravity and of the background perfect fluid manifested
in the Kaluza–Klein model with spherical compactification.
The background space-time is perturbed by a massive
gravitating source which is pressureless in the external
space but has an arbitrary equation of state (EoS) parameter
in the internal space. As characteristics of a nonlinear perfect
fluid, the squared speeds of sound are not equal to the background
EoS parameters in the external and internal spaces. In
this setting, we find exact solutions to the linearized Einstein
equations for the perturbed metric coefficients. For nonlinear
models with f
(R0) = 0, we show that these coefficients
acquire correction terms in the form of two summed Yukawa
potentials and that in the degenerated case, the solutions are
reduced to a single Yukawa potential with some “corrupted”
prefactor (in front of the exponential function), which, in
addition to the standard 1/r term, contains a contribution
independent of the three-dimensional distance r . In the linear
f
(R) = 0 model, we generalize the previous studies
to the case of an arbitrary nonlinear perfect fluid. We also
investigate the particular case of the nonlinear background
perfect fluid with zero speed of sound in the external space
and demonstrate that a non-trivial solution exists only in the
case of f
(R0) = 0.
Опис
Ключові слова
effects of nonlinearity, gravity and perfect fluid, Kaluza–Klein models, spherical compactification
Бібліографічний опис
European Physical Journal C