Noncommutative Black Hole Research Articles

A comparison of remnants in noncommutative Bardeen black holes

We derive the mass term of the Bardeen metric in the presence of a noncommutative geometry induced minimal length. In this setup, the proposal of a stable black hole remnant as a candidate to store information is confirmed. We consider the possibility of having an extremal configuration with one degenerate event horizon and compare different sizes of black hole remnants. As a result, once the magnetic charge $g$ of the noncommutative Bardeen solution becomes larger, both the minimal nonzero mass $M_0$ and the minimal nonzero horizon radius $r_0$ get larger. This means, subsequently, under the condition of an adequate amount of $g$, the three parameters $g$, $M_0$, and $r_0$ are in a connection with each other linearly. According to our results, a noncommutative Bardeen black hole is colder than the noncommutative Schwarzschild black hole and its remnant is bigger, so the minimum required energy for the formation of such a black hole at particle colliders will be larger. We also find a closely similar result for the Hayward solution.

Massive vector particles tunneling from noncommutative charged black holes and their GUP-corrected thermodynamics

In this paper, we investigate the tunneling process of charged massive bosons $W^{\pm }$ (spin-1 particles) from noncommutative charged black holes such as charged RN black holes and charged BTZ black holes. By applying the WKB approximation and by using the Hamilton-Jacobi equation we derive the tunneling rate and the corresponding Hawking temperature for those black holes configuration. Furthermore, we show the quantum gravity effects using the GUP on the Hawking temperature for the noncommutative RN black holes. The tunneling rate shows that the radiation deviates from pure thermality and is consistent with an underlying unitary theory.

Thermodynamics of noncommutative high-dimensional AdS black holes with non-Gaussian smeared matter distributions

Considering non-Gaussian smeared matter distributions, we investigate thermodynamic behaviors of the noncommutative high-dimensional Schwarzschild-Tangherlini anti-de Sitter black hole, and obtain the condition for the existence of extreme black holes. We indicate that the Gaussian smeared matter distribution, which is a special case of non-Gaussian smeared matter distributions, is not applicable for the 6- and higher-dimensional black holes due to the hoop conjecture. In particular, the phase transition is analyzed in detail. Moreover, we point out that the Maxwell equal area law maintains for the noncommutative black hole whose Hawking temperature is within a specific range, but fails for that whose the Hawking temperature is beyond this range.

Quantum-corrected finite entropy of noncommutative acoustic black holes

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.

Effective Potential in Noncommutative BTZ Black Hole

In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.

Particles and Scalar Waves in Noncommutative Charged Black Hole Spacetime

In this paper we have discussed geodesics and the motion of test particle in the gravitational field of non-commutative charged black hole spacetime. The motion of massive and massless particle have been discussed seperately. A comparative study of noncommutative charged black hole and usual Reissner–Nordström black hole has been done. The study of effective potential has also been included. Finally, we have examined the scattering of scalar waves in noncommutative charged black hole spacetime.

Stability of thin-shell wormholes from noncommutative BTZ black hole

In this paper, we construct thin-shell wormholes in (2 + 1)-dimensions from noncommutative BTZ black hole by applying the cut-and-paste procedure implemented by Visser. We calculate the surface stresses localized at the wormhole throat by using the Darmois–Israel formalism and we find that the wormholes are supported by matter violating the energy conditions. In order to explore the dynamical analysis of the wormhole throat, we consider that the matter at the shell is supported by dark energy equation of state (EoS) p = ωρ with ω < 0. The stability analysis is carried out of these wormholes to linearized spherically symmetric perturbations around static solutions. Preserving the symmetry we also consider the linearized radial perturbation around static solution to investigate the stability of wormholes which was explored by the parameter β (speed of sound).

Gravitational Aharonov–Bohm effect due to noncommutative BTZ black hole

In this paper we consider the scattering of massless planar scalar waves by a noncommutative BTZ black hole. We compute the differential cross section via the partial wave approach, and we mainly show that the scattering of planar waves leads to a modified Aharonov–Bohm effect due to spacetime noncommutativity.

Particle’s Motion Around a Non-Commutative Black Hole

In this paper, we study the motion of massive and massless test particles in the gravitational field of non-commutative black hole. Various other aspects are also analyzed. For our investigations, we use the non-commutative Schwarzschild black hole. The radial geodesic is found and we also study the effective potential. The motion of the test particle in static equilibrium as well as non-static equilibrium are presented using Hamilton-Jacobi formalism. Scattering of scalar waves in non-commutative black hole geometry is the final subject of our paper.

The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle

In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when λ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.

Thermodynamics of noncommutative geometry inspired black holes based on Maxwell-Boltzmann smeared mass distribution

In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole.

Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

Few years ago, Setare (2006) has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

Field Equations and Radial Solutions in a Noncommutative Spherically Symmetric Geometry

We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity. Field equations are derived in the framework of teleparallel gravity through Weitzenbock geometry. We solve these field equations by considering a mass that is distributed spherically symmetrically in a stationary static spacetime in order to obtain a noncommutative line element. This new line element interestingly reaffirms the coherent state theory for a noncommutative Schwarzschild black hole. For the first time, we derive the Newtonian gravitational force equation in the commutative relativity framework, and this result could provide the possibility to investigate examples in various topics in quantum and ordinary theories of gravity.

SOLUTIONS AND THERMODYNAMICS OF NONCOMMUTATIVE LIOUVILLE BLACK HOLE

Motivated by string theory results, we study Liouville black hole solutions and their thermodynamics on noncommutative space. In particular, we present explicit solutions of black hole equations of motion, then we find their classical properties such as the ADM-mass, the horizon geometry and the scalar Ricci curvature. Thermodynamic properties of such noncommutative black hole solutions including the Hawking temperature and entropy function are also discussed for three different regions of the moduli space of the theory.

Some aspects of entropic gravity in the presence of a noncommutative Schwarzschild-deSitter black hole

We study some features of entropic force approach in the presence of a noncommutative Schwarzschild-deSitter black hole. In this setup, there exists a similarity between the small and large scales. There are two finite cut-off in very short and long distances wherein the force and energy graph stop abruptly at those scales. We find that the existence of a deSitter core around the origin, induced by noncommutativity, in addition to a standard deSitter background at large scale may lead to a violation of the equivalence principle. Finally in order to directly observe the finite cut-off at short-scale gravity, caused by noncommutativity quantum fluctuations, we derive an effective gravitational constant.

SPACETIME NONCOMMUTATIVE EFFECT ON BLACK HOLE AS PARTICLE ACCELERATORS

We study the spacetime noncommutative effect on black hole as particle accelerators and, find that the particles falling from infinity with zero velocity cannot collide with unbound energy, either near the horizon or on the prograde ISCO when the noncommutative Kerr black hole is exactly extremal. Our results also show that the bigger of the spinning black hole's mass is the higher of center of mass energy that the particles obtain. For small and medium noncommutative Schwarzschild black hole, the collision energy depends on the black hole's mass.

Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

Gravitational energy of a noncommutative Vaidya black hole

In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

Noncommutative inspired Schwarzschild black hole, Voros product and Komar energy

The importance of the Voros product in defining a noncommutative Schwarzschild black hole is shown. The entropy is then computed and the area law is shown to hold upto order . The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy E for these black holes is then obtained and a deformation from the conventional identity E = 2STH is found at the order . This deformation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. Finally, the Smarr formula is worked out. Similar features also exist for a deSitter–Schwarzschild geometry.

Thermodynamics of noncommutative geometry inspired BTZ black hole based on Lorentzian smeared mass distribution

A noncommutative BTZ black hole is constructed in three-dimensional anti-de Sitter space. In this black-hole model, the noncommutative smearing is obtained by replacing the point-like source term with a Lorentzian distribution. We mainly investigate the thermodynamical properties of this black hole, including Hawking temperature, entropy, heat capacity and free energy.