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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.29 n.2 San José Jul./Dec. 2022
http://dx.doi.org/10.15517/rmta.v29i2.46390
Artículo
Cosmological exact solutions of Petrov type D. a mixture of two fluids: dark energy and radiation
Soluciones cosmológicas exactas del tipo Petrov D. una mezcla de dos fluidos: energía oscura y radiación
1Universidad de Costa Rica, Centro de Investigaciones Espaciales (CINESPA) y Escuela de Física, San José, Costa Rica; rodrigo.alvarado@ucr.ac.cr
2Universidad de Costa Rica, Escuela de Física, San José, Costa Rica; andres.angulosibaja@ucr.ac.cr
3Universidad de Costa Rica, Escuela de Física, San José, Costa Rica; mauricio.vargasobando@ucr.ac.cr
In this paper, two exact solutions of the Einstein's equations are obtained for an anisotropic and homogeneous symmetry of Petrov Type D, the difference between both solutions lies in how relevant is the expansión that is presented initially, either on an axis or on a perpendicular plane. Both solutions represent a mixture of two fluids with minimum interaction: dark energy (P = -µ) and radiation (P = µ/3). The singularities and the influence that these fluids have on this metric are studied; the Hubble parameters, the deceleration parameter and the role that these fluids representon them are determined and analyzed. Additionally, their temperatura and the role that both play on this magnitude are determined.
Keywords: cosmology; exact solution; Einstein; temperature; Hubble; deceleration parameter; Kretschmann; singularity.
En este trabajo se obtienen dos soluciones exactas de las ecuaciones de Einstein para una simetría anisotrópica y homogénea del Tipo Petrov D, la diferencia entre ambas soluciones radica en que tan relevante es la expansión que se presenta inicialmente, ya sea en un eje o en un plano perpendicular. Dichas soluciones representan una mezcla de dos fluidos con mínima interacción: energía oscura (P = -µ) y radiación (P = µ/3). Se estudia las singularidades y la influencia que estos fluidos tienen en esta métrica; así como el parámetro de Hubble, el parámetro de desaceleración y la influencia que estos fluidos tienen en ellos. Además, se determina su temperatura y el papel que ambos juegan en esta magnitud.
Palabras clave: cosmología; solución exacta; Einstein; temperatura; Hubble; parámetro de deceleración; Kretschmann; singularidad.
Acknowledgments
The authors would like to express their gratitude to the referees, whose recommendations and comments contributed to improve the paper's quality, as well as other reviewers for their valuable contributions to the article's content.
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Received: April 20, 2021; Revised: May 12, 2022; Accepted: May 30, 2022
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