Quark stars in massive gravity might be candidates for the mass gap objects

Abstract

Abstract We have investigated the structural properties of strange quark stars (SQSs) in a modified theory of gravity known as massive gravity. In order to obtain the equation of state (EOS) of strange quark matter, we have employed a modified version of the Nambu–Jona-Lasinio model (MNJL) which includes a combination of NJL Lagrangian and its Fierz transformation by using weighting factors $$(1-\alpha )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$\alpha .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Additionally, we have also calculated dimensionless tidal deformability $$(\Lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in massive gravity. To constrain the allowed values of the parameters appearing in massive gravity, we have imposed the condition $$\Lambda _{1.4 {M}_{\odot }}\lesssim 580 .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mn>1.4</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mn>580</mml:mn> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Notably, in the MNJL model, the value of $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> varies between zero and one. As $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> increases, the EOS becomes stiffer, and the value of $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> increases accordingly. We have demonstrated that by softening the EOS with increasing the bag constant, one can obtain objects in massive gravity that not only satisfy the constraint $$\Lambda _{1.4 {M} _{\odot }}\lesssim 580,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mn>1.4</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mn>580</mml:mn> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> but they also fall within the unknown mass gap region $$(2.5{M}_{\odot }-5{M}_{\odot }).$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2.5</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> To establish that the obtained objects in this region are not black holes, we have calculated Schwarzschild radius, compactness, and $$\Lambda _{{M_{TOV}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>TOV</mml:mi> </mml:mrow> </mml:msub> </mml:msub> </mml:math> in massive gravity.

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