Eur. Phys. J. Plus (2020) 135: 143
https://doi.org/10.1140/epjp/s13360-020-00222-0

Regular Article

The Tolman IV as quintessence star

¹ Facultad de Químico Farmacobiología de la Universidad Michoacana de San Nicolás de Hidalgo, Tzintzuntzan No. 173, Col. Matamoros, C.P. 58240, Morelia, Michoacán, Mexico
² Facultad de Ciencias Físico Matemáticas de la Universidad Michoacana de San Nicolás de Hidalgo, Edificio B, Ciudad Universitaria, C.P. 58030, Morelia, Michoacán, Mexico
³ Facultad de Ingenieria Civil de la Universidad Michoacana de San Nicolás de Hidalgo Edificio A, Ciudad Universitaria, C.P. 58030, Morelia, Michoacán, Mexico
⁴ Instituto Tecnológico Superior de Tacámbaro, Av. Tecnológico No 201, Zona el Gigante, C.P. 61650, Tacambaro, Michoacán, Mexico
⁵ Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario 100, Colonia Centro, C.P. 50000, Toluca, Estado de México, Mexico

^* e-mail: joaquin@fismat.umich.mx

Received: 6 December 2019
Accepted: 12 January 2020
Published online: 28 January 2020

Abstract

In this work, we present a model for stars formed by strange quark matter and quintessence with density which is characterized by a parameter and with negative radial and tangential pressures . The construction of the solution is done through the application of a theorem recently proposed for generating algebraic solutions starting from a solution to Einstein’s equations with a perfect fluid in a static and spherically symmetrical space time. The seed solution we employ is the Tolman IV, and we show that the density, radial pressure and tangential pressure of the resulting model are monotonic decreasing functions, as long as the radial and tangential speeds of sound satisfy the conditions of causality, conditions required so that the resulting model is physically acceptable, the stability of the system is guaranteed because it complies with Herrera’s cracking condition, that is to say . Additionally starting from the observational data of the mass for the strange star candidate SMC X-1, and assuming a value for the Bag’s constant , we obtain that the interval for the radius is  km, 8.593260 km].