https://doi.org/10.1140/epjc/s10052-017-5311-x
Regular Article - Theoretical Physics
Weak-field limit of Kaluza–Klein models with spherically symmetric static scalar field: observational constraints
1
The International Center of Future Science of the Jilin University, 2699 Qianjin St., Changchun City, 130012, China
2
Astronomical Observatory, Odessa National University, Dvoryanskaya st. 2, Odessa, 65082, Ukraine
3
Institut of Radio Astronomy of National Academy of Sciences of Ukraine, 4 Mystetstv str., Kharkov, 61002, Ukraine
* e-mail: a.chopovsky@yandex.ru
Received:
9
June
2017
Accepted:
17
October
2017
Published online:
30
October
2017
In a multidimensional Kaluza–Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter 
of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter 
. We define under which conditions can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have 
in the solar system, the mass of scalar field should be 
g 
eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: 
.
© The Author(s), 2017
