Structure, maximum mass, and stability of compact stars in $$f(\mathcal {Q,T})$$ gravity

Abstract

Abstract We investigate the properties of compact objects in the f ( Q , T ) theory, where $$\mathcal {Q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> is the non-metricity scalar and $${ \mathcal {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> is the trace of the energy–momentum tensor. We derive an interior analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the linear form of $$f(\mathcal {Q}, { \mathcal {T}})=\mathcal {Q}+\psi { \mathcal {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>+</mml:mo> <mml:mi>ψ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> , where $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021, $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> is set to a maximum negative value of $$\psi _1=\psi / \kappa ^2=-0.04$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ψ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>κ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.04</mml:mn> </mml:mrow> </mml:math> , where $$\kappa ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>κ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition $$c_s^2\le \frac{c^2}{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>≤</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mn>3</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> . The effective equation of state is similar to the quark matter equation of state, and involves the presence of an effective bag constant. When $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> is negative, the star has a slightly larger size as compared to GR stars with the same mass. The difference in the predicted star size between the theory with a negative $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> and GR for the same mass is attributed to an additional force appearing in the hydrodynamic equilibrium equation. The maximum compactness allowed by the strong energy condition for $$f(\mathcal {Q}, { \mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory and for GR is $$C = 0.514$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.514</mml:mn> </mml:mrow> </mml:math> and 0.419, respectively, with the $$f(\mathcal {Q}, { \mathcal {T}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> prediction about $$10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> higher than the GR one. Assuming a surface density at saturation nuclear density of $$\rho _{\text {nuc}} = 4\times 10^{14}~\hbox {g}/\hbox {cm}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>nuc</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>14</mml:mn> </mml:msup> <mml:mspace/> <mml:mtext>g</mml:mtext> <mml:mo>/</mml:mo> <mml:msup> <mml:mtext>cm</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> , the maximum mass of the star is $$4.66 M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4.66</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> , with a radius of 14.9 km.