Completely Deformed Complexity-free Anisotropic Fluid Sphere

TL;DR

This work addresses the challenge of modeling physically viable anisotropic compact stars within general relativity by combining the zero-complexity condition $Y_{\mathrm{TF}}=0$ with a density-like constraint inside the complete geometric deformation (CGD) framework. Using a Kohler-Chao-Tikekar seed metric, the authors employ CGD to decouple gravity into two interacting sectors, derive two fully deformed interior solutions, and analyze the energy exchange signal $\Delta E=\dfrac{u'}{2}(\sigma^{(s)}+P_r^{(s)})$ that governs coupling between sectors. The resulting models satisfy all standard energy conditions, exhibit positive anisotropy that enhances stability, and maintain Buchdahl-compactness limits, with masses compatible with observed compact stars. This CGD-based approach offers a robust route to realistic high-density interiors and suggests extensions to rotation, charge, and alternative gravity theories, broadening the scope of anisotropic stellar modeling in GR.

Abstract

In this work, we investigate the emergence of compact, anisotropic stellar structures through the gravitational decoupling scheme within the framework of complete geometric deformation. The study introduces a novel synthesis of two independent techniques, namely the zero-complexity factor and density-like constraints, applied simultaneously to determine the deformation functions. This dual implementation represents a new methodological step in stellar modeling, as it allows us to explicitly control the role of anisotropy and complexity in the internal structure of self-gravitating objects. Starting from a chosen metric ansatz as a seed solution, we demonstrate that the zero-complexity condition captures the gravitational response of compact matter in a fully tractable form. The complete deformation procedure then yields two new physically viable anisotropic solutions, passing all standard stability and energy condition tests. Our results show, for the first time, that the direction of energy transfer between the seed sector and the decoupled source is uniquely governed by the deformation parameter, providing direct physical insight into the coupling between known and generic gravitational fields. Furthermore, we find that anisotropy plays a decisive role in the stability criteria of these stars, highlighting its nontrivial influence on realistic stellar evolution. These results offer a new perspective on the modeling of high-density stellar interiors and open a pathway for extending gravitational decoupling analyses to more complex astrophysical scenarios.

Figures (7)

• Figure 1: Plots of $\sigma$ (left panel) and $P_{r}$ (right panel) for the completely deformed Kohler--Chao--Tikekar cosmological solution as functions of the radial coordinate $r$, for different values of the deformation parameter $\xi$: $\xi=0.0$ (solid pink), $\xi=0.1$ (space-dashed gold), $\xi=0.2$ (long-dashed red), $\xi=0.3$ (solid purple), $\xi=0.4$ (dotted black), $\xi=0.5$ (dashed green), and $\xi=0.6$ (dot-dashed cyan).
• Figure 2: Plots of $P_{t}$ (left panel) and $\Delta$ (right panel) as functions of the radial coordinate $r$ for different values of the deformation parameter $\xi$: $\xi=0.0$ (solid pink), $\xi=0.1$ (space-dashed gold), $\xi=0.2$ (long-dashed red), $\xi=0.3$ (solid purple), $\xi=0.4$ (dotted black), $\xi=0.5$ (dashed green), and $\xi=0.6$ (dot-dashed cyan).
• Figure 3: Plots of $\sigma+P_{r}$ (left panel) and $\sigma+P_{\bot}$ (right panel) versus $r$ for different values of the deformation parameter $\xi$. Legend is the same as in Fig. \ref{['1f']}.
• Figure 4: Plots of $\sigma-P_{r}$ (left panel) and $\sigma-P_{\bot}$ (right panel) against $r$ for various $\xi$ values subject to the Kohler-Chao-Tikekar model. Legend is the same as in Fig. \ref{['1f']}.
• Figure 5: Plot of $\sigma+P_{r}+2P_{\bot}$ as a function of $r$ for different $\xi$ values subject to the Kohler-Chao-Tikekar model. Legend is the same as in Fig. \ref{['1f']}.