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Slimane Zaim

Publications and source records attributed to Slimane Zaim.

At least 19 recordsLinked to original sources
arXiv2026

A new non-commutative correction to the thermodynamics and evaporation of the Schwarzschild black hole in non-commutative gauge theory

We investigate the modified thermodynamic properties of a deformed Schwarzschild black hole arising from new noncommutative corrections to the tetrad fields obtained through the Seiberg-Witten map. By deriving the corrected event horizon radius, we evaluate the corresponding thermodynamic quantities, including the Hawking temperature, entropy, heat capacity, Helmholtz free energy, and pressure. We also examine the evaporation process of the black hole within this noncommutative framework. The behavior of the heat capacity reveals a rich thermodynamic structure consisting of three distinct phases: two unstable phases with negative heat capacity, corresponding to a large black hole and a small black hole, separated by an intermediate stable phase with positive heat capacity. Our analysis also shows that the Schwarzschild black hole in noncommutative geometry possesses a finite lifetime that exceeds that of its classical counterpart, owing to the effective contribution of noncommutativity to the black hole mass. The noncommutative correction naturally introduces a fundamental length scale, {\Theta}=1,6.10^-35 m, which is of the order of the Planck length.

gr-qc↗
arXiv2025

Non-commutative geometry and thermodynamics of the Schwarzschild-AdS black hole

We investigate the thermodynamic properties of a Schwarzschild-AdS black hole within the framework of noncommutative geometry. We derive and analyze the black hole's thermodynamic functions, showing that they depend critically on the noncommutativity parameter denoted as {\Theta}, while still satisfying the first law of thermodynamics. Stability analysis reveals that the noncommutative Schwarzschild-AdS black hole undergoes a phase transition at a critical point. Moreover, the thermodynamic behavior closely resembles that of a van der Waals fluid, with the noncommutativity introducing a correction term to the black hole's surface temperature. Our results indicate that the noncommutativity parameter {\Theta} is of the order of the Planck scale and functions as a novel thermodynamic variable within the system.

gr-qc↗
arXiv2025

On the scalar tachyons creation in noncommutative de Sitter space-time

We investigate tachyon production in noncommutative de Sitter space by solving the deformed Klein-Gordon equation. Using the Bogoliubov transformation method, we compute the number density of created scalar tachyons and demonstrate that their spectrum follows a thermal distribution. Our analysis reveals that noncommutativity reduces the effective temperature of tachyon production, analogous to its effect on ordinary particle creation. Furthermore, we establish that the role of the noncommutative parameter in tachyon production is functionally equivalent to that of an electric field in standard particle production in de Sitter space.

hep-th↗
arXiv2024

Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole

In this work, we derive non-commutative corrections to the Schwarzschild-Anti-de Sitter solution up to the first and second orders of the non-commutative parameter $\Theta$. Additionally, we obtain the corresponding deformed effective potentials and the non-commutative geodesic equations for massive particles. Through the analysis of time-like non-commutative geodesics for various values of $\Theta$, we demonstrate that the circular geodesic orbits of the non-commutative Schwarzschild-Anti-de Sitter black hole exhibit greater stability compared to those of the commutative one. Furthermore, we derive corrections to the perihelion deviation angle per revolution as a function of $\Theta$. By applying this result to the perihelion precession of Mercury and utilizing experimental data, we establish a new upper bound on the non-commutative parameter, estimated to be on the order of $10^{-66}\,\mathrm{m}^2$.

gr-qc↗
arXiv2023

Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg-Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale $\Theta\sim l_{planck}$. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking-Page phase transition in the NC gauge theory.

gr-qc↗
arXiv2023

Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

gr-qc↗
arXiv2022

Particle creation in cosmological space-time by a time-dependent electric field

In this work, we calculate the particle creation density in a cosmological anisotropic Bianchi I universe, by solving the Klein-Gordon and Dirac equations in the presence of a time-dependent electric field using the semi-classical method. We show that the particles distribution becomes thermal under the influence of the electric field when the electric interaction proportional to the Ricci scalar of curved space-time

gr-qc↗
arXiv2022

On Modified First Law of Black hole Thermodynamics in The Non-Commutative Gauge Theory

In this paper, we investigated the thermodynamic properties of Schwarzschild black hole (SBH) in the non-commutative (NC) gauge theory of gravity. According to our previous work, we modify the first law of the black hole (BH) thermodynamics by the physical quantity (NC potential) $\mathcal{A}$ which is the conjugate to the NC parameter $\Theta$, which leads to this expression $d\hat{M}=\hat{T}d\hat{S}+\mathcal{A}d\Theta$. Our result shows that the NC SBH has a phase transition, and the non-commutativity affected this transition. And the NC potential $\mathcal{A}$ is effective only in the final stage of the BH evaporation, where it increases the Gibbs free energy at this stage, and the NC parameter in this study can represent the tension of the spacetime. Then the study of the pressure of the SBH in the modified first law of the BH thermodynamic shows a second-order phase transition, and the critical value of the thermodynamical variables are related to each value of $\Theta$, and that leads to this parameter to play the same role as a thermodynamical variable.

gr-qc↗
arXiv2022

Thermodynamic Properties of Schwarzschild Black Hole in Non-Commutative Gauge Theory of Gravity

In this paper, we used the non-commutative (NC) gauge theory of gravity to investigate the thermodynamic properties of a deformed Schwarzschild black hole (SBH). Our results present a new scenario of black hole evaporation. As a first step, we described the Arnowitt-Deser-Misner (ADM) mass, the Hawking temperature, and the entropy of NC SBH. The non-commutativity removes the divergence behavior of temperature, and the result shows a difference in the pole-equator temperature. These corrections also reveal a new fundamental length at the Planck scale order, $\Theta \approx 2.257 \times 10^{-35}\,m$. In the last stage of evaporation, the NC correction exposes a remnant entropy $\hat{S}_0$ of the NC SBH. Then, the description of the heat capacity and the Gibbs free energy of the deformed black hole shows the effect of the NC gauge theory on the thermodynamic stability and the phase transitions. Finally, we investigate the influence of the black hole pressure on the stability and the phase transition of SBH in NC spacetime. In this study, we found that the NC parameter plays a similar role to the thermodynamic variables. The results show a second-order phase transition of NC SBH.

gr-qc↗
arXiv2021

Geodesic equation in non-commutative gauge theory of gravity

In this work, we construct a non-commutative (NC) gauge theory of gravity for any metric with spherical symmetries, where we use a non-diagonal tetrad field. The deformed gauge potentials (tetrad fields) and the components of deformed metric are computed to the second order in the NC parameter $\Theta^{\mu\nu}$, as the application to the Schwarzschild black hole we show that the NC geometry removes the singularity at the origin of the black hole, and increase the event horizon. The non-commutativity correction to the effective potential of the Schwarzschild metric is also computed and we show how this geometry affects the stability condition which it found the NC parameter plays the same role as the mass that can be used to explain the dark matter and we show that the NC Schwarzschild space-time has new stable circular orbits appear near the event horizon that is not allowed by Schwarzschild space-time. The geodesic equations in the NC space and the corrections to the periastron advance in terms of $\Theta$ are obtained. We have also specified the problem of Mercury's perihelion and used the experimental data to estimate the NC parameter $\Theta$, then we show that $\Theta$ of the order $10^{-25}s.kg^{-1}$ gives observable corrections to the movement at a large scale. We show that the NC propriety of the spacetime appears at the High Energy.

gr-qc↗
arXiv2020

Hartmann potential with a minimal length and generalized recurrence relations for matrix elements

In this work we study the Schrödinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of deformation $β$ and show that some degenerate states are removed. We give analytic expressions for the solutions of the diagonal matrix elements. Finally, we derive a generalized recurrence formula for the angular average values.

quant-ph↗
arXiv2018

Non-commutative DKP equation and pair creation in curved space-time

This study is about the application of the non-commutativity on the DKP equation up to first order in $θ$ for the process of pair-creation of bosons from vacuum in (1+1) curved space-time. The density of particles created in the vacuum can be calculated with the help of the Bogoliubov transformations. The non-commutative density of created particles is found to decrease as $\frac{1% }{\sqrt{θ}}\sim Λ_{NC},$, so that the rate of particle creation increases whenever a non-commutativity parameter is small and this corresponds to the spirit of quantum mechanics.

hep-th↗
arXiv2016

Non-commutative space time of the relativistic equations with a Coulomb potential using Seiberg-Witten map

We present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon and Dirac equations in a non-commutative space-time up to first-order of the non-commutativity parameter using the Seiberg-Witten maps. We thus find the non-commutative modification of the energy levels and by comparing with the the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of non-commutativity, we show that the fundamental length ($\sqrtΘ$) is compatible with the value of the electroweak length scale ($l$). Phenomenologically, this effectively confirms the presence of gravity at this level.

hep-th↗
arXiv2016

2D Schrödinger Equation with Mixed Potential in Noncommutaive Complex space

We obtain exact solutions of the 2D Schrödinger equation for Hydrogen atom with the lenear and Harmonic Potentials in noncommutative complex space, using the Power-series expansion method. Hence we can say that the Schrödinger equation in noncommutative complex space describes to the particles with spin (1/2)in an external uniform magnitic field. Where the noncommutativity play the role of magnetic field with created the total magnetic moment of particle with spin 1/2, who in turn shifted the spectrum of energy. Such effects are similar to the Zeeman splitting in a commutative space.

quant-ph↗
arXiv2015

Negative heat capacity for a Klein-Gordon oscillator in non-commutative complex phase space

We obtain exact solutions to the two-dimensional Klein-Gordon oscillator in a non-commutative complex phase space to first order in the non-commutativity parameter. We derive the exact non-commutative energy levels and show that the energy levels split to $2m$ levels. We find that the non-commutativity plays the role of a magnetic field interacting automatically with the spin of a particle induced by the non-commutativity of complex phase space. The effect of the non-commutativity parameter on the thermal properties is discussed. It is found that the dependence of the heat capacity $C_V$ on the non-commutative parameter gives rise to a negative quantity. Phenomenologically, this effectively confirms the presence of the effects of self-gravitation induced by the non-commutativity of complex phase space.

hep-th↗
arXiv2015

Anisotropic universe space-time non-commutativity and scalar particle creation in the presence of a constant electric field

We study the effect of the non-commutativity on the creation of scalar particles from vacuum in the anisotropic universe space-time. We derive the deformed Klein-Gordon equation up to second order in the non-commutativity parameter using the general modified field equation. Then the canonical method based on Bogoliubov transformation is applied to calculate the probability of particle creation in vacuum and the corresponding number density in the $k$ mode. We deduce that the non-commutative space-time introduces a new source of particle creation.

hep-th↗
arXiv2014

2D Schrödinger Equation with Singular Even-Power and Inverse-Power Potentials in Non Commutative Complex space

We obtain exact solutions of the 2D Schrödinger equation with the Singular Even-Power and Inverse-Power Potentials in non-commutative complex space, using the Power-series expansion method. Hence we can say that the Schrödinger equation in non-commutative complex space describes to the particles with spin (1/2)in an external uniform magnitic field. Where the noncommutativity play the role of magnetic field with created the total magnetic moment of particle with spin 1/2, who in turn shifted the spectrum of energy. Such effects are similar to the Zeeman splitting in a commutative space.

quant-ph↗