Non-trivial class of anisotropic compact stellar model in Rastall gravity

Abstract We investigated Rastall gravity, for an anisotropic star with a static spherical symmetry, whereas the matter-geometry coupling as assumed in Rastall Theory (RT) is expected to play a crucial role differentiating RT from General Relativity (GR). Indeed, all the obtained results confirm that RT is not equivalent to GR, however, it produces same amount of anisotropy as GR for static spherically symmetric stellar models. We used the observational constraints on the mass and the radius of the pulsar Her X-1 to determine the model parameters confirming the physical viability of the model. We found that the matter-geometry coupling in RT allows slightly less size than GR for a given mass. We confirmed the model viability via other twenty pulsars’ observations. Utilizing the strong energy condition we determined an upper bound on compactness $$U_\text {max}\sim 0.603$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>max</mml:mtext> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.603</mml:mn> </mml:mrow> </mml:math> , in agreement with Buchdahl limit, whereas Rastall parameter $$\epsilon =-0.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> . For a surface density compatible with a neutron core at nuclear saturation density the mass-radius curve allows masses up to $$3.53 M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3.53</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> . We note that there is no equation of state is assumed, however the model fits well with linear behaviour. We split the twenty pulsars into four groups according to the boundary densities. Three groups are compatible with neutron cores while one group fits perfectly with higher boundary density $$8\times 10^{14}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>8</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>14</mml:mn> </mml:msup> </mml:mrow> </mml:math> $$\hbox {g/cm}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>g/cm</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:math> which suggests that those pulsars may have quark-gluon cores.

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