what is meant by Newtonian Polytrope?
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In the context of Newtonian gravity, polytropicequations of state are particularly useful to describe a greatvariety of situations their great success stemming mainly from thesimplicity of the equation of state and the ensuing mainequation (Lane-Emden). Polytropes in the context ofgeneral relativity have been considered in Refs. [7–15](and references therein). However, in this work, we restrictthe analysis to Newtonian polytropes.The theory of polytropes is based on the polytropicequation of state
▶P¼K¼K1þ1=n
;(1)where Pand denote the isotropic pressure and the mass(baryonic) density, respectively. Constants K,, and nare usually called the polytropic constant, polytropicexponent, and polytropic index, respectively.The polytropic equation of state may be used to modeltwo very different types of situations, namely:
i) When the polytropic constant Kis fixed and can becalculated from natural constants. This is the case ofa completely degenerate gas in the nonrelativistic(¼5=3;n¼3=2) and relativistic limit (¼4=3;n¼3). Polytropes of this kind are particularlyuseful to model compact objects such as whitedwarfs
HöPe ïT hèLps u
▶P¼K¼K1þ1=n
;(1)where Pand denote the isotropic pressure and the mass(baryonic) density, respectively. Constants K,, and nare usually called the polytropic constant, polytropicexponent, and polytropic index, respectively.The polytropic equation of state may be used to modeltwo very different types of situations, namely:
i) When the polytropic constant Kis fixed and can becalculated from natural constants. This is the case ofa completely degenerate gas in the nonrelativistic(¼5=3;n¼3=2) and relativistic limit (¼4=3;n¼3). Polytropes of this kind are particularlyuseful to model compact objects such as whitedwarfs
HöPe ïT hèLps u
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