2012/02/29 by Maxim Eingorn, Alexander Zhuk · 7 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Equation of state #General relativity #Gravitation #Gravitational field #Gravitational potential #Internal energy #Kaluza–Klein theory #Mathematical physics #Omega #Physics #Quantum mechanics #Space (punctuation) #Spacetime #Yukawa potential #astro-ph.HE #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1016/j.physletb.2012.08.031
published in Physics Letters B 716(1), 176-178 (Elsevier BV) · 8 pages, no figures
openalex publication_date 2012/08/20 · arxiv created 2012/08/31 · arxiv updated 2012/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this Letter, we consider the six-dimensional Kaluza–Klein models with spherical compactification of the internal space. Here, we investigate the case of bare gravitating compact objects with the dustlike equation of state pˆ0=0 in the external (our) space and an arbitrary equation of state pˆ1=Ωεˆ in the internal space, where εˆ is the energy density of the source. This gravitating mass is spherically symmetric in the external space and uniformly smeared over the internal space. In the weak field approximation, the conformal variations of the internal space volume generate the admixture of the Yukawa potential to the usual Newtonʼs gravitational potential. For sufficiently large Yukawa masses, such admixture is negligible and the metric coefficients of the external spacetime coincide with the corresponding expressions of General Relativity. Then, these models satisfy the classical gravitational tests. However, we show that gravitating masses acquire effective relativistic pressure in the external space. Such pressure contradicts the observations of compact astrophysical objects (e.g., the Sun). The equality Ω=−1/2 (i.e. tension) is the only possibility to preserve the dustlike equation of state in the external space. Therefore, in spite of agreement with the gravitational experiments for an arbitrary value of Ω, tension (Ω=−1/2) plays a crucial role for the considered models.