Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes

TL;DR

This work applies the minimal geometric deformation (MGD) decoupling method to construct interior solutions for a static, circularly symmetric, electrically charged BTZ spacetime in $(2+1)$D. By decomposing the Einstein equations into an isotropic sector and a secondary $ heta$-sector driven by a deformation function $f(r)$, the authors derive both isotropic and conformally constrained interior solutions, and analyze their thermodynamics, curvature, and horizon structure. The isotropic case yields a closed deformation $f = f_0(-m + r^2 - Q^2 ext{ln} r)$ with explicit expressions for density and pressure, while the conformal case leads to a differential equation for $f$ without a closed-form solution. The results demonstrate the viability of interior charged BTZ models via MGD in $(2+1)$D and hint at broader implications for quantum gravity and AdS/CFT in lower dimensions.

Abstract

This work employs the minimal geometric deformation decoupling scheme to derive interior stellar solutions in the background of an electrically charged BTZ ansatz as a seed metric in three dimensions. In this respect, we impose two different equations of state to determine the deformation function and the new material contributions emerging from the additional field source. Furthermore, we describe the finiteness of all thermodynamic quantities of the presented stellar solutions, including the effective thermodynamical quantities, for varying values of the deformation parameter and total electric charge. We explore the new interior astrophysical solutions in three-dimensional gravity by analyzing the charged BTZ metric, admitting circular symmetry through the principles of geometric deformation. This study examines the impact of radial-metric deformation on the charged BTZ geometry and underscores the importance of stellar decoupling within the context of electrically charged dense distributions. It is shown that new physically acceptable solutions by incorporating any known three-dimensional spacetime as the isotropic basis are possible, which in turn enable one to analyze the quantum effects due to low degrees of freedom at lower dimensions.

Figures (5)

• Figure 1: The behavior of $\rho$ is shown for $\beta = 1$, with $f_{0} = -1.2$ (left panel) and $f_{0} = -2$ (right panel), for $Q=1$ (yellow dash-dotted line), $Q=2$ (red solid line), $Q=3$ (cyan dashed line), $Q=4$ (blue dotted line), $Q=5$ (pink dash-dotted line), and $Q=6$ (green space-dashed line).
• Figure 2: The variation of $\rho$ for $\beta=1$, $f_{0}=0.5$ (left panel) and for $f_{0}=0$ (right panel) for different values of $Q$. The legend is the same as in Fig. \ref{['1f']}.
• Figure 3: The behavior of $P$ for $\beta=1$, $f_{0}=-1.2$ (left panel) and for $f_{0}=-2$ (right panel) for different values of $Q$. The legend is the same as in Fig. \ref{['1f']}.
• Figure 4: The variation of $P$ for $\beta=1$, $f_{0}=0.5$ (left panel) and for $f_{0}=0$ (right panel) for different values of $Q$. The legend is the same as in Fig. \ref{['1f']}.
• Figure 5: Behavior of SEC for $\beta=1$ and $f_{0}=1$ for different values of $Q$. The legend is the same as in Fig. \ref{['1f']}.