Acceptability conditions and relativistic anisotropic generalized polytropes

Daniel Suárez-Urango (Escuela de Física, Universidad Industrial de Santander, Bucaramanga, 680002, Colombia) ; Justo Ospino (Departamento de Matemática Aplicada, Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Salamanca, Spain) ; Héctor Hernández (Escuela de Física, Universidad Industrial de Santander, Bucaramanga, 680002, Colombia; Departamento de Física, Universidad de Los Andes, Mérida, 5101, Venezuela) ; Luis Núñez (Escuela de Física, Universidad Industrial de Santander, Bucaramanga, 680002, Colombia; Departamento de Física, Universidad de Los Andes, Mérida, 5101, Venezuela)

This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $$P=\kappa {\rho }^{\gamma }+\alpha \rho -\beta $$ P = κ ρ γ + α ρ - β for a heuristic anisotropy. We integrated the corresponding Lane–Emden equation for several hundred models and found the parameter-space portion ensuring the physical acceptability of the configurations. Polytropes based on the total energy density are more viable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidates of astrophysical compact objects.

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      "source": "Springer", 
      "value": "This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state  $$P=\\kappa {\\rho }^{\\gamma }+\\alpha \\rho -\\beta $$  <math> <mrow> <mi>P</mi> <mo>=</mo> <mi>\u03ba</mi> <msup> <mrow> <mi>\u03c1</mi> </mrow> <mi>\u03b3</mi> </msup> <mo>+</mo> <mi>\u03b1</mi> <mi>\u03c1</mi> <mo>-</mo> <mi>\u03b2</mi> </mrow> </math>   for a heuristic anisotropy. We integrated the corresponding Lane\u2013Emden equation for several hundred models and found the parameter-space portion ensuring the physical acceptability of the configurations. Polytropes based on the total energy density are more viable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidates of astrophysical compact objects."
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Published on:
25 February 2022
Publisher:
Springer
Published in:
European Physical Journal C , Volume 82 (2022)
Issue 2
Pages 1-22
DOI:
https://doi.org/10.1140/epjc/s10052-022-10119-0
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: