Two Parameter Deformation of Embedding Class-I Compact Stars in Linear $f(Q)$ Gravity

Abstract

Recent multi-messenger observations, including gravitational wave detections of compact objects in the neutron star-black hole mass-gap region and precise measurements of high-mass pulsars, motivate mechanisms capable of enlarging the stellar mass window without arbitrarily stiffening the equation of state (EOS) toward the causal limit. In linear $f(Q)$ gravity of the form $f(Q)=β_1 Q+β_2$, the theory is dynamically equivalent to General Relativity at the geometric level and modifies stellar structure solely through a uniform rescaling of the matter sector governed by $β_1$. Consequently, linear $f(Q)$ alone does not introduce new geometric families of stellar solutions or alter classical compactness bounds. To overcome this structural limitation, we incorporate gravitational decoupling within an embedding class-I (Karmarkar) Vaidya-Tikekar configuration in linear $f(Q)$ gravity. While similar VT-based decoupling constructions exist in GR, the present framework introduces a controlled two-parameter deformation characterized by $(ε,β_1)$: the decoupling parameter $ε$ governs geometric deformation and EOS stiffness, whereas $β_1$ independently rescales the matter sector without altering the metric structure. This separation permits a direct comparison between GR and linear $f(Q)$ gravity at fixed geometric deformation, thereby isolating pure coupling-driven mass enhancement. We determine the admissible parameter domain from regularity, matching, causality and compactness requirements and derive an analytic compactness bound for the decoupled embedding class-I configuration. The combined action of $ε$ and $β_1$ enlarges the accessible stellar mass window while preserving physical acceptability, allowing configurations compatible with recent high-mass pulsars and mass-gap candidates without exceeding causal limits.

Figures (17)

• Figure 1: Structural distinction between GR-based decoupling and linear $f(Q)$ decoupling. In GR, mass and compactness change arise solely from geometric deformation $\epsilon$. In linear $f(Q)$ gravity, $\epsilon$ modifies geometry (and hence compactness), while $\beta_1$ independently shifts the mass scale without affecting compactness.
• Figure 2: Radial variation of the total energy density $\rho^{tot}$ for for different values of $\epsilon$. We assume $K=2$, $\beta_1 = 0.9$ and $\beta_2=0$.
• Figure 3: Radial variation of the total radial pressure $P_r^{tot}$ for different values of $\epsilon$. We assume $K=2$, $\beta_1 = 0.9$ and $\beta_2=0$.
• Figure 4: Radial variation of the total tangential pressure $P_t^{tot}$ for different values of $\epsilon$. We assume $K=2$, $\beta_1 = 0.9$ and $\beta_2=0$.
• Figure 5: Radial variation of anisotropy $\Delta$ for different values of $\epsilon$. We assume $K=2$, $\beta_1 = 0.9$ and $\beta_2=0$.