Anisotropic strange star with Tolman–Kuchowicz metric under f(R, T) gravity

Abstract In the current article, we study anisotropic spherically symmetric strange star under the background of f ( R , T ) gravity using the metric potentials of Tolman–Kuchowicz type (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) as $$\lambda (r)=\ln (1+ar^2+br^4)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>ln</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:msup><mml:mi>r</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and $$\nu (r)=Br^2+2\ln C$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:msup><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mo>ln</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math> which are free from singularity, satisfy stability criteria and also well-behaved. We calculate the value of constants a , b , B and C using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) 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 ( $$p_r$$ <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 $$p_r(r)=\frac{1}{3}(\rho -4B_g)$$ <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:mfrac><mml:mn>1</mml:mn><mml:mn>3</mml:mn></mml:mfrac><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:mrow></mml:math> . Here quark pressure is responsible for generation of bag constant $$B_g$$ <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> . Motivation behind this study lies in finding out a non-singular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herrera’s cracking condition and also with Harrison–Zel $$'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:math> dovich–Novikov’s static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model.

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