Eur. Phys. J. Plus (2020) 135: 124
https://doi.org/10.1140/epjp/s13360-020-00150-z

Regular Article

Spinor fields in spherical symmetry: Einstein–Dirac and other space-times

¹ Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., Moscow, Russia 119361,
² Peoples’ Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6., Moscow, Russia 117198,
³ National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), Moscow, Russia
⁴ Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia 141980,

^* e-mail: bijan@jinr.ru

Received: 19 September 2019
Accepted: 19 November 2019
Published online: 23 January 2020

Abstract

We discuss the static, spherically symmetric Einstein-spinor field system in the possible presence of various spinor field nonlinearities. We take into account that the spinor field energy–momentum tensor (EMT) has in general some off-diagonal components, whose vanishing due to the Einstein equations substantially affects the form of the spinor field itself and the space-time geometry. In particular, the EMT structure with any spinor field nonlinearities turns out to be the same as that of the EMT of a minimally coupled scalar field with a self-interaction potential. Therefore, many results previously obtained for systems with such scalar fields are directly extended to the Einstein-spinor field system. Some special solutions are obtained and discussed, in particular a solution for the Einstein–Dirac system (which lacks asymptotic flatness) and some examples with spinor field nonlinearities.