Charged compact star in f(R, T) gravity in Tolman–Kuchowicz spacetime

Abstract In this current study, our main focus is on modeling the specific charged compact star SAX J 1808.4-3658 (M = 0.88 $$M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> , R = 8.9 km) within the framework of $$f(R,\,T)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> modified gravity theory using the metric potentials proposed by Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) and the interior spacetime is matched to the exterior Reissner–Nordström line element at the surface of the star. Tolman–Kuchowicz metric potentials provide a singularity-free solution which satisfies the stability criteria. Here we have used the simplified phenomenological MIT bag model equation of state (EoS) to solve the Einstein–Maxwell field equations where the density profile ( $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> ) is related to the radial pressure ( $$p_{\mathrm{r}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> ) as $$p_{\mathrm{r}}(r) = (\rho - 4B_{\mathrm{g}})/3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . Furthermore, to derive the values of the unknown constants $$a,\, b,\, B,\, C$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>B</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>C</mml:mi> </mml:mrow> </mml:math> and the bag constant $$B_{\mathrm{g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> , we match our interior spacetime to the exterior Reissner–Nordström line element at the surface of stellar system. In addition, to check the physical validity and stability of our suggested model we evaluate some important properties, such as effective energy density, effective pressures, radial and transverse sound velocities, relativistic adiabatic index, all energy conditions, compactness factor and surface redshift. It is depicted from our current study that all our derived results lie within the physically accepted regime which shows the viability of our present model in the context of $$f(R,\,T)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> modified gravity.

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