New Yukawa-corrected Casimir wormholes in curvature-matter coupled gravitational framework

Abstract In this article, our primary objective is to construct new wormhole solutions by involving a Yukawa-corrected form of Casimir energy density in a well-motivated gravitational theory that allows the coupling of curvature and matter, namely the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> theory. To achieve this goal, a wormhole geometry exhibiting a spherically-symmetric nature is taken into account and anisotropic fluid is assumed to be the background ordinary matter source. We first consider the simple linear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> theory by assuming <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">F</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">T</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>ζ</mml:mi> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">T</mml:mi> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:math> (average pressure). Secondly, we utilize the conformal symmetries of the spherical-symmetric geometry for simplifying the resulting field equations and obtain the corresponding analytical form of the wormhole solution. In both cases, the viability of the proposed solutions is examined by checking the basic features of the wormhole shape model along with the validity of null energy constraints. Further, we study the volume integral quantifier (VIQ), exoticity factor and stability through the Tolman–Oppenheimer–Volkov (TOV) equation as well as the adiabatic index, active gravitational mass and complexity factor graphically. Lastly, we use a newly-proposed wormhole shape function to find the expressions of state variables and discuss the validity of energy bounds. We also explore the significance of this wormhole shape model through different quantities graphically. In all scenarios, the presented solutions are found to be new, promising and viable.