A comparative study of wormhole geometries under two different modified gravity formalism
Sweeti Kiroriwal, Jitendra Kumar, S. K. Maurya, Sourav Chaudhary
Abstract
Abstract In the current article, we discuss the wormhole geometries in two different gravity theories, namely $$\texttt{F}(\texttt{Q, T})$$ <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> gravity and $$\texttt{F}(\texttt{R, T})$$ <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:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. In these theories, $$\texttt{Q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> is called a non-metricity scalar, $$\texttt{R}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> stands for the Ricci scalar, and $$\texttt{T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> denotes the trace of the energy–momentum tensor (EMT). The main goal of this study is to comprehensively compare the properties of wormhole solutions within these two modified gravity frameworks by taking a particular shape function. The conducted analysis shows that the energy density is consistently positive for wormhole models in both gravity theories, while the radial pressure is positive for $$\texttt{F}(\texttt{Q, T})$$ <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> gravity and negative in $$\texttt{F}(\texttt{R, T})$$ <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:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. Furthermore, the tangential pressure shows reverse behavior in comparison to the radial pressure. By using the Tolman-Oppenheimer-Volkov (TOV) equation, the equilibrium aspect is also described, which indicates that hydrostatic force dominates anisotropic force in the case of $$\texttt{F}(\texttt{Q, T})$$ <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> gravity theory, while the reverse situation occurs in $$\texttt{F}(\texttt{R, T})$$ <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:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, i.e., anisotropic force dominates hydrostatic force. Moreover, using the concept of the exoticity parameter, we observed the presence of exotic matter at or near the throat in the case of $$\texttt{F}(\texttt{Q, T})$$ <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> gravity while matter distribution is exotic near the throat but normal matter far from the throat in $$\texttt{F}(\texttt{R, T})$$ <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:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity case. In conclusion, precise wormhole models can be created with a potential NEC and DEC violation at the throat of both wormholes while having a positive energy density, i.e., $$\rho >0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> .