Physics

This paper analyzes how the generalized uncertainty principle (GUP) affects the thermodynamic properties in a regular black hole spacetime in the context of symmetric teleparallel gravity, with an arbitrary action f as a function of non-metric scalar $\mathcal{Q}$ and the boundary ${\mathcal{B}}_{\mathcal{Q}}$. We analyze a GUP-influenced semi-classical technique in regular black hole spacetime that incorporates the quantum tunneling mechanism. The GUP-influenced temperature results show that the GUP term reduced the vector particles’ radiation in the context of gravity. Moreover, we explore the GUP-influenced entropy as well as the GUP-influenced emission energy, it can help to explain the complex interactions between quantum gravity and astrophysics and highlights the important role of GUP-influenced thermodynamic properties (Hawking temperature, entropy and emission energy) in regular black hole spacetime in the context of gravity. We graphically analyze the effects of different parameters on black hole geometry.

The effect of the curvature of the boundary of semi-infinite cold plasma on the parameters and properties of surface oscillations localized near this boundary is considered. An analytical description of various cases of the impact of static deformation of the plasma boundary on the characteristics of the oscillating surface charge is obtained, and the results of the exact numerical solution of the initial equations are found to confirm the reliability of the derived analytical formulas. A significant role of the boundary perturbation shape in the formation of the spatial distribution of surface oscillation parameters is revealed. With the help of analytical formulas and precise numerical calculations, a description of this nonlinear interaction is presented. The availability of such a description is crucial both for determining the possibility of using the examined effect for specific applications and, on the other hand, for exciting it in plasma, which requires knowledge of the field structure features.

By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry.