Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

Mohammad Hossein Zhoolideh Haghighi; Sohrab Rahvar; Mohammad Reza Rahimi Tabar

doi:10.3390/e23091158

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

Entropy (Basel). 2021 Sep 2;23(9):1158. doi: 10.3390/e23091158.

Authors

Mohammad Hossein Zhoolideh Haghighi^{1

2}, Sohrab Rahvar³, Mohammad Reza Rahimi Tabar^{3

4}

Affiliations

¹ Department of Physics, K.N. Toosi University of Technology, Tehran P.O. Box 15875-4416, Iran.
² School of Astronomy, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran.
³ Department of Physics, Sharif University of Technology, Tehran P.O. Box 11365-9161, Iran.
⁴ Institute of Physics and ForWind, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.

Abstract

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.

Keywords: Modified Newtonian Dynamics (MOND); binary systems; phase transition; structure formation.