https://doi.org/10.1140/epjp/i2018-12345-x
Regular Article
An algorithm to generate anisotropic rotating fluids with vanishing viscosity
1
Dipartimento di Fisica Nucleare, Subnucleare e delle Radiazioni, Università degli Studi Guglielmo Marconi, Via Plinio 44, I-00193, Rome, Italy
2
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, I-00133, Roma, Italy
3
INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Napoli, Italy
* e-mail: viaggiu@axp.mat.uniroma2.it
Received:
17
September
2018
Accepted:
25
October
2018
Published online:
27
December
2018
Starting with generic stationary axially symmetric spacetimes depending on two spacelike isotropic orthogonal coordinates x1, x2, we build anisotropic fluids with and without heat flow but with wanishing viscosity. In the first part of the paper, after applying the transformation ,
(with
regular functions) to general metrics coefficients
with
, being
the Einstein’s tensor, we obtain that
. Therefore, the transformed spacetime is endowed with an energy-momentum tensor
with expression
heat term (where
is the metric and
,
are functions depending on the physical parameters of the fluid), i.e. without viscosity and generally with a non-vanishing heat flow. We show that after introducing suitable coordinates, we can obtain interior solutions that can be matched to the Kerr one on spheroids or Cassinian ovals, providing the necessary mathematical machinery. In the second part of the paper we study the equation involving the heat flow and thus we generate anisotropic solutions with vanishing heat flow. In this frame, a class of asymptotically flat solutions with vanishing heat flow and viscosity can be obtained. Finally, some explicit solutions are presented with possible applications to a string with anisotropic source and a dark energy-like equation of state.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018