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Stable relativistic polytropic objects with cosmological constant

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Abstract

The effects of the cosmological constant on the static equilibrium configurations and stability against small radial perturbations of relativistic polytropic spheres are investigated. This study numerically solves the hydrostatic equilibrium equation and the radial stability equation, both of which are modified from their standard form to introduce the cosmological constant. For the fluid, we consider a pressure p and an energy density \(\rho \), which are connected through the equation of state \(p=\kappa \delta ^{\varGamma }\) with \(\delta =\rho -p/(\varGamma -1)\), where \(\kappa \), \(\varGamma \) and \(\delta \) represent the polytropic constant, adiabatic index and rest mass density of the fluid, respectively. The dependencies of the mass, radius and eigenfrequency of oscillations on both the cosmological constant and the adiabatic index are analyzed. For ranges of both the central rest mass density \(\delta _c\) and the adiabatic index \(\varGamma \), we show that the stars have a larger (lower) mass and radius and a diminished (enhanced) stability when the cosmological constant \(\varLambda >0\) (\(\varLambda <0\)) is increased (decreased). In addition, in a sequence of compact objects with fixed \(\varGamma \) and \(\varLambda \), the regions constructed by stable and unstable static equilibrium configurations are recognized by the conditions \(\mathrm{d}M/\mathrm{d}\delta _c>0\) and \(\mathrm{d}M/\mathrm{d}\delta _c<0\), respectively.

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Acknowledgements

The authors thank Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), grant \(2013/26258-4\). PHRSM would like to thank FAPESP, grant \(2015/08476-0\).

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Authors and Affiliations

  1. Departamento de Ciencias, Universidad Privada del Norte, Avenida el Sol 461 San Juan de Lurigancho, 15434, Lima, Peru

    José D. V. Arbañil

  2. Departamento de Física, Instituto Tecnológico de Aeronáutica, Centro Técnico Aeroespacial, São José dos Campos, São Paulo, 12228-900, Brazil

    Pedro H. R. S. Moraes

  3. Instituto de Astronomia, Geofìsica e Ciências Atmosfèricas, Universidade de São Paulo, Rua do Matão 1226 Cidade Universitária, São Paulo, 05508-090, SP, Brazil

    Pedro H. R. S. Moraes

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Arbañil, J.D.V., Moraes, P.H.R.S. Stable relativistic polytropic objects with cosmological constant. Eur. Phys. J. Plus 135, 354 (2020). https://doi.org/10.1140/epjp/s13360-020-00368-x

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