Influência de geometrias BTZ modificadas na termodinâmica e estabilidade de GRAVASTARS

Abstract

In the present thesis, we studied two complementary approaches: (i) a thin-shell GRAVASTAR in noncommutative BTZ geometry, implemented via a metric modified by the parameter θ; (ii) a GRAVASTAR in BTZ spacetime with a minimal length, which incorporates quantum effects through the ground-state density of the two-dimensional hydrogen atom and a Lorentzian distribution. Methodologically, the internal anti–de Sitter regions were connected to an external region described by the Schwarzschild–type BTZ metric using generalized thin-shell junction techniques, allowing a combined analysis of the junction equations, energy density and surface pressure. We verified that the resulting energy density and surface pressure guarantee the stability of the shell even with a vanishing cosmological constant for Lorentzian distributions and we determine the shell’s entropy in the minimal-length scenario. Moreover, the thermodynamic study revealed a positive heat capacity and the potential formation of a low-dimensional black-hole remnant. These results suggest that quantum effects regularize divergences and enrich the spacetime microstructure, offering a new theoretical framework for transitions between gravastars and black holes in lower-dimensional gravity.