Conservation laws for classical particles in anti-de Sitter-Beltrami space

Abstract

In this paper we consider the conservation laws for classical particles in AdS 4 . At first we parameterize a geodesic line and construct conserved quantities with analog of five dimensional Minkowski space-time M (2,3) .Consequently we change AdS 4 space to AdS-Beltrami space-time and write conserved quantities in the Beltrami coordinates. Finally we take a limit for small velocityẋ ≪ c and we get the conserved quantities in Lorentz-Fock space-time. And finally we give out the energy of the nonrelativistic noncosmological particle under the cosmological limit.

On the entropy corrected thermal features of black holes

“…Moreover, in figures 3, 6 and 9 we plotted Yukawa heat capacity, Non-local Gravity heat capacity and also Gradient field gravity capacity versus mass respectively which concluded that negative heat capacities for all three models as expected. Note that, since the heat capacity of a black hole can be either positive or negative due to the black holeʼs size (See [86][87][88] and some references therein), and in our cases, all heat capacities are obtained as negative values, it can be interpreted that these black holes are thermally unstable and tend to radiate energy, leading to a phase transition. These findings provide insights into the thermodynamic behavior of these modified gravity models and their relation to the classical understanding of black hole stability.…”

The Killing vectors and symmetry in $R$-spacetime

“…We show that the group of transformations (58)-(63) indeed contains the transformations which reduces to the ordinary Lorentz transformations in a certain limit [9], [10], [12]. Moreover we note that geodesics in anti-de Sitter spacetime in the Beltrami coordinates are described by linear functions [6]. The group of transformations (58)-( 63) are explained by linear-fractional functions which conserve linearity of geodesics.…”

“…These spacetime correspondingly are de Sitter or anti-de Sitter spacetime. In the case of antide Sitter spacetime metric in Beltrami coordinates there is a limit c → ∞ which reaches to the metric of R-spacetime [3], [4], [5], [6]. In this work we consider this metric and show that the R-spacetime is also a spacetime of maximal symmetry.…”