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A covariant tapestry of linear GUP, metric-affine gravity, their Poincar\'e algebra and entropy bound by Ali, Ahmed Farag; Wojnar, Aneta is a scholarly article available to read on EtoBox.

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Motivated by the potential connection between metric-affine gravity and linear Generalized Uncertainty Principle (GUP) in the phase space, we develop a covariant form of linear GUP and an associated modified Poincar\'e algebra, which exhibits distinctive behavior, nearing nullity at the minimal length scale proposed by linear GUP. We use 3-torus geometry to visually represent linear GUP within a covariant framework. The 3-torus area provides an exact geometric representation of Bekenstein's universal bound. We depart from Bousso's approach, which adapts Bekenstein's bound by substituting the Schwarzschild radius ($r_s$) with the radius ($R$) of the smallest sphere enclosing the physical system, thereby basing the covariant entropy bound on the sphere's area. Instead, our revised covariant entropy bound is described by the area of a 3-torus, determined by both the inner radius $r_s$ and outer radius $R$ where $r_s\leq R $ due to gravitational stability. This approach results in a more precise geometric representation of Bekenstein's bound, notably for larger systems where Bousso's bound is typically much larger than Bekensetin's universal bound. Furthermore, we derive an equation th

Author

Ali, Ahmed Farag; Wojnar, Aneta

Published

2024

Language

EN