Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

Abstract

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. Each d i -dimensional torus has its own scale factor C i , i ¼ 1; . . . ; N, which is characterized by a parameter i . We single out the physically interesting solution corresponding to a pointlike mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the pointlike mass soliton has dustlike equations of state in all spaces. We also obtain the parametrized post-Newtonian parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time-delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameters of the model: ¼ P N i¼1 d i i ¼ Àð2:1 AE 2:3Þ Â 10 À5 . The pointlike mass solution withcontradicts this restriction. The condition ¼ 0 satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes with i ¼ 0 belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state p i ¼ À"=2, i ¼ 1; . . . ; N, in the internal spaces and to the number of the external dimensions d 0 ¼ 3. The investigation of multidimensional static spherically symmetric perfect fluid with a dustlike equation of state in the external space confirms the above results.

Asymptotic latent solitons, black strings, and black branes inf(R)gravity

“…We have shown in our previous paper [10] that the most natural point-like massive source with the dust-like equations of state in all dimensions contradicts the experimental data. The similar situation takes place in multidimensional linear models [11,12]. In such linear models, latent solitons, in particular, black strings and black branes, satisfy the gravitational experiments at the same level of accuracy as General Relativity.…”

“…However, we have shown that such matter source contradicts the observations in the case of extra dimensions. The similar situation takes place in multidimensional linear models [11,12], where a point-like mass with dust-like equations of state in all spatial dimensions also contradicts the experimental data. However, latent solitons, in particular, black strings and black branes, satisfy the gravitational experiments at the same level of accuracy as General Relativity.…”

“…We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known results [11,12] of the linear theory. The second class of asymptotic solitons exists only in multidimensional nonlinear models.…”

“…in full analogy with the condition (31) for latent solitons in [11], where the parameter γ µ = 2ω µ + 1 and all d µ = 1. Then, we obtain from (18) the latent soliton condition: It is natural to suppose that in our asymptotic region…”

Many-body problem in Kaluza–Klein models with toroidal compactification

“…In our previous papers [19,25,26] devoted to KK models with toroidal compactification of the extra dimensions, we have shown that gravitating masses should have tension in the internal space to be in agreement with gravitational experiments in the Solar system. For example, black strings/branes with the parameter ω = −1/2 in the equation of state in the internal space satisfy this condition.…”