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Peer-reviewed Open access
Jul 1, 2020

Uniqueness of static, isotropic low-pressure solutions of the Einstein–Vlasov system

Letters in Mathematical Physics
  • Maximilian Thaller
  • ,
  • Tomohiro Harada

Volume
110
Number
7
First page
1877
Last page
1901
Language
Publishing type
Research paper (scientific journal)
DOI
10.1007/s11005-020-01284-y

© 2020, The Author(s). In Beig and Simon (Commun Math Phys 144:373–390, 1992) the authors prove a uniqueness theorem for static solutions of the Einstein–Euler system which applies to fluid models whose equation of state fulfills certain conditions. In this article it is shown that the result of Beig and Simon (1992) can be applied to isotropic Vlasov matter if the gravitational potential well is shallow. To this end we first show how isotropic Vlasov matter can be described as a perfect fluid giving rise to a barotropic equation of state. This Vlasov equation of state is investigated, and it is shown analytically that the requirements of the uniqueness theorem are met for shallow potential wells. Finally the regime of shallow gravitational potential is investigated by numerical means. An example for a unique static solution is constructed, and it is compared to astrophysical objects like globular clusters. Finally we find numerical indications that solutions with deep potential wells are not unique.

Link information
DOI
https://doi.org/10.1007/s11005-020-01284-y
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082749366&origin=inward Open access
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85082749366&origin=inward
ID information
  • DOI : 10.1007/s11005-020-01284-y
  • ISSN : 0377-9017
  • eISSN : 1573-0530
  • SCOPUS ID : 85082749366

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