Regular Article - Theoretical Physics
Virial theorem for a cloud of stars obtained from the Jeans equations with second correlation moments
Oles Honchar Dnipro National University, Haharin 72 ave., 49010, Dnipro, Ukraine
2 Institute of Physics, Research Centre of Theoretical Physics and Astrophysics, Silesian University in Opava, Bezrucovo nam. 13, 746 01, Opava, Czech Republic
3 Institute of Experimental and Applied Physics, Czech Technical University in Prague, 128 00, Prague, Czech Republic
4 Department of Physics, University of Illinois at Urbana Champaign, 1110 West Green St., 61801, Urbana, IL, USA
Accepted: 19 June 2023
Published online: 11 July 2023
A hydrodynamic model for small acoustic oscillations in a cloud of stars is built, taking into account the self-consistent gravitational field in equilibrium with a non-zero second correlation moment. It is assumed that the momentum flux density tensor should include the analog of the anisotropic pressure tensor and the second correlation moment of both longitudinal and transverse gravitational field strength. The non-relativistic temporal equation for the second correlation moment of the gravitational field strength is derived from the Einstein equations using the first-order post-Newtonian approximation. One longitudinal and two transverse branches of acoustic oscillations are found in a homogeneous and isotropic star cloud. The requirement for the velocity of transverse oscillations to be zero provides the boundary condition for the stability of the cloud. The critical radius of the spherical cloud of stars is obtained, which is precisely consistent with the virial theorem.
© The Author(s) 2023
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