Noncommutative Black Hole Research Articles

Fuzzy black hole models in f(G) Gravity

Abstract In this manuscript, we explore the concept of dark matter black holes, inspired by the Einasto density profile in the background of $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is a Gauss-Bonnet invariant. This work extends the scope beyond the noncommutative tiny black hole structure which incorporates dark matter as a constituent forming the black hole. Our investigation demonstrates the feasibility of constructing black hole solutions for various Einasto index values, $f(\mathcal{G})$ gravity parameters, and parameters of mass function adopting anisotropic fluid configuration to characterize the matter sector. Specifically, by adopting an equation of state in which the radial pressure equals the negative of the energy density, we derive black hole solutions exhibiting a horizon structure with the central singularity replaced by a regular de Sitter core akin to the Reissner-Nordstr"{o}m black holes. Furthermore, we explore an alternative scenario where the equation of state is nonlocal, resulting in the construction of self-gravitating fuzzy dark matter droplets together with the dark source $f(\mathcal{G})$ corrections.

Non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter: Plasma lensing and thermodynamics analysis

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.

Testing the non-commutative charged Schwarzschild black hole surrounded by perfect fluid dark matter for thermodynamical features and weak gravitational lensing

This paper is devoted in studying the thermodynamical properties and weak gravitational lensing in the context of a non-commutative charged Schwarzschild black hole surrounded by perfect fluid dark matter. In this context, we study the geometric mass and thermal temperature to discuss the viability of the charged black hole solution by evaluating the specific heat, the phase transition and stability of the configuration. We also study the energy emission process of the black hole. From the thermodynamical properties, we conclude that our studied black hole solution is thermally stable. Moreover, we discuss gravitational lensing in the weak plasma field by considering uniform as well as non-uniform plasma and evaluate the deflection angle where we observe that the deflection angle in the case of uniform plasma is greater than that in non-uniform plasma. We also have studied the image magnification from the source’s brightness and observed that in uniform plasma case, the source image is more magnified than the non-uniform plasma.

Observational signature of QPOs with particle motion around non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

We analyze the orbital and oscillatory motion of test particles in the vicinity of a non-commutative black hole submerged in perfect fluid dark matter and derive analytical solutions for the specific angular momentum and radial profiles of energy. Using the effective potential approach, we discuss the stability of circular orbits. Furthermore, we calculate the innermost stable circular orbits. The effective force acting on particles has also been discussed. We find the expressions for frequencies of radial and latitudinal harmonic oscillations as a function of the black hole mass and the model’s parameters. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. Furthermore, Periastron precession has been discussed. We demonstrate that the parameters of the model have a strong influence on particle motion around black holes. By using the observational data of four different X-ray binary systems GRO J1655-40, XTE J1550-564, XTE J1859+226, and GRS 1915+105, within the scope of Monte Carlo Markov Chain, we constrain the involved parameters α and β. It is necessary to mention that our presented investigations through graphical behavior are viable with required physical behavior.

Effects of non-commutative geometry on black hole properties

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.

Quasinormal modes in noncommutative Schwarzschild black holes: a spectral analysis

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous claims in the literature regarding the instability of these black holes but also reveal remarkable stability for both non-extreme and extreme Schwarzschild black holes under various perturbations.

Gravitational probe of ꝗuantum spacetime

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations.

Noncommutative Schwarzschild black hole surrounded by quintessence: Thermodynamics, Shadows and Quasinormal modes

In Campos et al. (2022), Campos et al studied the quasinormal modes and shadows of noncommutative Schwarzschild black holes. Since we know that the quintessence matter surrounding black holes has significant effects on the black hole quantities, in this study, we aimed to show this influence by revisiting the same problem in the presence of quintessence matter field. To this end, we first examined the thermodynamics of noncommutative Schwarzschild black holes embedded in quintessence matter using Hawking temperature, entropy, and specific heat functions. After that we discussed phase transition and stability features. We then investigated the shadow images in the presence of plasma. After visualizing these results qualitatively, we calculated the quasinormal modes in WKB and Mashhoon approximations and we demonstrated the impacts of quintessence matter and noncommutative spacetime on the whole quantities.

Thin-shell gravastar in a noncommutative BTZ geometry

In this paper, we build a thin-shell gravastar model within a noncommutative BTZ geometry. For this, we consider a noncommutative BTZ metric in the inner region and a geometry associated with a BTZ solution in the outer region, joined by the generalized join technique. After investigating the inner spacetime, surface and outer spacetime, we observe that there is a surface energy density and surface pressure, such as to make gravastar stable. This effect persists even when the cosmological constant is zero. Besides, we found a bound for the noncommutativity parameter. In addition, we examine the thermodynamics of the noncommutative BTZ black hole in Schwarzschild-type form in three-dimensional spacetime. We also check the stability condition by calculating the specific heat capacity, as well as for the formation of black hole remnants.

Noncommutative information is revealed from the static detector outside the black hole

We investigate the transition behavior of the two-level atom as the Unruh-DeWitt detector outside a noncommutative black hole. When the mass of the black hole is small enough, the difference between the commutative and noncommutative black hole can be distinguished. In particular, an evident fluctuation appearing at a far distance from the horizon by calculating the quantum Fisher information of the transition rate with regard to the local Hawking temperature provides a novel and interesting result about the information extraction of the noncommutativity for a small-mass black hole.

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.

4[formula omitted] AdS Einstein–Gauss–Bonnet black hole endowed with Lorentzian noncommutativity: [formula omitted] criticality, Joule–Thomson expansion, and shadow

In this article, we get a static, spherically symmetric 4D-AdS EGB black hole inspired by noncommutative geometry, where noncommutativity is expressed by a Lorentzian distribution. The noncommutativity correction has changed the relevant thermodynamic quantities. The cosmological constant Λ is interpreted as a dynamical pressure, and the noncommutative parameter Θ is treated as a thermodynamic variable to keep the first thermodynamic law and the Smarr formula in place. Our solution’s P−v criticality was investigated in the extended phase space, where the large/small black hole phase transition arises for the noncommutative 4D-AdS EGB black hole. That is, the noncommutativity parameter influences the phase transition as well as the critical pressure, horizon radius, and temperature; as a result, the critical ratio is also influenced and does not yet remain universal, as in the Van der Waals systems. The Joule–Thomson expansion has been studied in extended phase space. We acquired the inversion points (Pi,Ti) as a function of Θ, which allowed us to analyze the isenthalpic and inversion curves in the T−P plane and demonstrate the cooling and heating zones. In addition, it has been shown that the shadow radius is reduced when we increase the noncommutativity parameter, as is the peak of the associated energy emission rate, which decreases with the rise of the parameter Θ.

Greybody factors for higher-dimensional non-commutative geometry inspired black holes

Greybody factors are computed for massless fields of spin 0, 1/2, 1, and 2 emitted from higher-dimensional non-commutative geometry inspired black holes. Short-range potentials are used with path-ordered matrix exponentials to numerically calculate transmission coefficients. The resulting absorption cross sections and emission spectra are computed on the brane and compared with the higher-dimensional Schwarzschild–Tangherlini black hole. A non-commutative black hole at its maximum temperature in seven extra dimensions will radiate a particle flux and power of 0.72–0.81 and 0.75–0.81, respectively, times lower than a Schwarzschild–Tangherlini black hole of the same temperature. A non-commutative black hole at its maximum temperature in seven extra dimensions will radiate a particle flux and power of 0.64–0.72 and 0.60–0.64, respectively, times lower than a Schwarzschild–Tangherlini black hole of the same mass.

Hawking radiation and stability of the canonical acoustic black holes

In this paper we determine the Hawking temperature and entropy of a modified canonical acoustic black hole. In our results we obtain an entropy-area relation that has a logarithmic correction term in leading order. We also analyze the stability condition of the noncommutative canonical acoustic black hole and also with quantum corrections implemented by the generalized Heisenberg uncertainty principle.

Shadows and quasinormal modes of a charged non-commutative black hole by different methods

In this paper, we calculated the quasinormal modes (QNMs) of a charged non-commutative black hole in scalar, electromagnetic and gravitational fields by three methods. We gave the influence of non-commutative parameter $\theta$ and charge $Q$ on QNMs in different fields. Thereafter, we calculated the shadow radius of the black hole and provided the valid range of $\theta$ and $Q$ using the constraints on the shadow radius of $\text{M87}^{\ast}$ and $\text{Sgr A}^{\ast}$ from the Event Horizon Telescope (EHT). In addition, we estimated the ``relative deviation'' of the shadow radius ($\delta_{R_{s}}$) between non-commutative spacetime and commutative spacetime. We found that the maximum values of $\delta_{R_{s}}$ decreases with the increase of charge $Q$. In other words, the non-commutativity of spacetime becomes harder to distinguish as the charge of the black hole increases.

Absorption, scattering and shadow by a noncommutative black hole with global monopole

In this paper, we investigate the process of massless scalar wave scattering due to a noncommutative black hole with a global monopole through the partial wave method. We computed the cross section of differential scattering and absorption at the low frequency limit. We also calculated, at the high frequency limit, the absorption and the shadow radius by the null geodesic method. We showed that noncommutativity causes a reduction in the differential scattering/absorption cross section and shadow radius, while the presence of the global monopole has the effect of increasing the value of such quantities. In the limit of the null mass parameter, we verify that the cross section of differential scattering, absorption and shadow ray approach to a non-zero value proportional to a minimum mass.

Noncommutative Correction to the Entropy of Charged BTZ Black Hole

Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and it has logarithmic corrections and polynomials of logarithms of the black hole area.

Absorption and scattering of a high dimensional non-commutative black hole

In this work, we investigate the scattering of massless plane scalar waves by the high dimensional non-commutative Schwarzschild–Tangherlini black hole. We use the partial wave approach to determine the scattering and absorption cross sections in the incident wavelength range. Our numerical results demonstrate that the bigger the non-commutative parameter, the smaller the maximum value of the related partial absorption cross section, however the tendency is slightly. We also discovered that when the non-commutative parameter is weak, the absorption cross section of the high dimensional black hole oscillates in the low frequency zone. The total absorption cross section oscillates around the geometrical optical limit in the high frequency range, and the scattering characteristics of black holes with various parameters are visibly different. The influence on the differential scattering cross section is particularly pronounced at large angles.

The fuzzy BTZ

We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black hole carries a covariant differential calculus, satisfies Einstein’s equations and has a constant negative curvature. The construction passes through a larger space, the fuzzy anti-de Sitter, and implements discrete BTZ identifications as conjugations by a unitary operator. We derive the spectrum of the suitably regularised radial coordinate: it consists of a continuum of scattering states outside the horizon r+ and an infinite discrete set of bound states inside.

Noncommutative SUSY black holes

In this paper, we propose a generalization to the Schwarzschild metric and define noncommutative SUSY black holes. We introduce the noncommutative deformation to the minisuperspace variables and derive the noncommutative supersymmetric (SUSY) Wheeler–DeWitt (WDW) equation for the Schwarzschild black hole. We calculate the metric and find that the singularities are not removed.