Rabin Banerjee, Bibhas Ranjan Majhi, Sujoy Kumar Modak
Using a graphical analysis, we show that for the horizon radius $r_h\gtrsim 4.8\sqrtθ$, the standard semiclassical Bekenstein-Hawking area law for noncommutative Schwarzschild black hole exactly holds for all orders of $θ$. We also give the corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy when $r_h<4.8\sqrtθ$ till the extremal point $r_h=3.0\sqrtθ$.
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A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters $Θ^{μν}$. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of General Relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.
We show the importance of the Voros product in defining a noncommutative Schwarzschild black hole. The corrected entropy/area-law is then computed in the tunneling formalism. Two types of corrections are considered; one, due to the effects of noncommutativity and the other, due to the effects of going beyond the semiclassical approximation. The leading correction to the semiclassical entropy/area-law is logarithmic and its coefficient involves the noncommutative parameter.
We apply the generalization of the Parikh-Wilczek method to the tunneling of massive particles from noncommutative inspired Schwarzschild black holes. By deriving the equation of radial motion of the tunneling particle directly, we calculate the emission rate which is shown to be dependent on the noncommutative parameter besides the energy and mass of the tunneling particle. After equating the emission rate to the Boltzmann factor, we obtain the modified Hawking temperature which relates to the noncommutativity and recovers the standard Hawking temperature in the commutative limit. We also dis…
It is known that, in the noncommutative Schwarzschild black hole spacetime, the point-like object is replaced by the smeared object, whose mass density is described by a Gaussian distribution of minimal width $\sqrtθ$ with $θ$ the noncommutative parameter. The elimination of the point-like structures makes it quite different from the conventional Schwarzschild black hole. In this paper, we mainly investigate the area spectrum and entropy spectrum for the noncommutative Schwarzschild black hole with $0\leq θ\leq (\frac{M}{1.90412})^{2}$. By the use of the new physical interpretation of the quas…
Based on the perturbation expansion, we compute the noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole, where the noncommutative background is suitably constructed in terms of the Poincaré coordinate system. In particular, we find a reasonable tetrad with subtlety, which not only matches the metrics of the pure AdS spacetime and Schwarzschild-AdS black hole in the commutative case, but also makes the corrections real rather than complex in the noncommutative case. For the pure AdS spacetime, the nocommutative effect is only a loga…
In this paper we study through tunneling formalism, the effect of noncommutativity to Hawking radiation and the entropy of the noncommutative Schwarzschild black hole. In our model we have considered the noncommutativity implemented via the Lorentzian distribution. We obtain non-commutative corrections to the Hawking temperature using the Hamilton-Jacobi method and the Wentzel-Kramers-Brillouin (WKB) approximation. In addition, we found corrections of the logarithmic and other types due to noncommutativity and quantum corrections from the generalized uncertainty principle (GUP) for the entropy…
We investigate the behavior of a noncommutative radiating Schwarzschild black hole. It is shown that coordinate noncommutativity cures usual problems encountered in the description of the terminal phase of black hole evaporation. More in detail, we find that: the evaporation end-point is a zero temperature extremal black hole even in the case of electrically neutral, non-rotating, objects; there exists a finite maximum temperature that the black hole can reach before cooling down to absolute zero; there is no curvature singularity at the origin, rather we obtain a regular DeSitter core at shor…
In this contribution we present a noncanonical phase-space noncommutative (NC) extension of a Kantowski Sachs (KS) cosmological model to describe the interior of a Schwarzschild black hole (BH). We evaluate the thermodynamical quantities inside this NC Schwarzschild BH and compare with the well known quantities. We find that for a NCBH the temperature and entropy have the same mass dependence as the Hawking quantities for a Schwarzschild BH.
We study modifications of the Schwarzschild solution within the noncommutative gauge theory of gravity. In the present analysis, the deformed solutions are obtained by solving the field equations perturbatively, up to the second order in the noncommutativity parameter $Θ$, for both exterior and interior solutions of the equations of motion for $e_μ^a \left(x\right)$. Remarkably, we find that this new noncommutive solution is analogous to the Reissner-Nordström solution in the ordinary spacetime, in which the square of electric charge is replaced by the square of the noncommutativity parameter,…
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 $\frac{1}{\sqrtθ}e^{-M^2/θ}$. 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 $E=2ST_H$ is found at the order $\sqrtθe^{-M^2/θ}$. This deformation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. Finally, the Smarr form…
Quasinormal Modes in Noncommutative Schwarzschild black holes
本研究针对非对易修正的形变施瓦西黑洞，推导无质量标量场拟正模的类薛定谔主方程与修正有效势并数值求解，成果可助力未来高精度引力波探测，也为检验广义相对论、探究引力修正可探测性提供新工具。
A brief comment on the paper hep-th/0508051 (with the title mentioned above) by F. Nasseri.
We study the effects of noncommutative spaces on the horizon, the area spectrum and Hawking temperature of a Schwarzschild black hole. The results show deviations from the usual horizon, area spectrum and the Hawking temperature. The deviations depend on the parameter of space-space noncommutativity.
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $Λ$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The metrics and curvatures of the quantum Schwarzschild spacetime and the quantum Schwarzschild-de Sitter spacetime are computed. It is shown that up to the second order in the deformation parameter, the quantum spacetimes are solutions of a noncommutative Einstein equation which is proposed in this paper.
This work aims to implement the idea of noncommutativity in the subject of black holes. Its principal contents deal with a study of Schwarzschild black holes in a D-dimensional noncommutative space. Various aspects related to the non commutative extension are discussed and some non trivial results are derived.
Massive scalar field perturbations in noncommutative-geometry-inspired Schwarzschild black hole
本文基于非交换几何启发的Schwarzschild黑洞，采用三级WKB近似法计算大规模标量场扰动下的Quasinormal模式频率、灰体因子和吸收截面，研究其稳定性及参数影响。
In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole.
Noncommutative quasinormal modes of Schwarzschild black hole
本文基于非对易引力推导Schwarzschild黑洞轴向与极向微扰势，采用三种方法计算拟正则模，发现时空量子化打破二者经典等谱性而在eikonal极限恢复。
In this paper we investigate the problem of ordinary baryonic matter accretion onto the noncommutative geometry inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the noncommutative parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. Th…
The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.
We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordström black holes show that the area law holds upto order $\frac{1}{\sqrtθ}e^{-M^2/θ}$. 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 deviation from the standard identity $E=2ST_H$ is found at the order $\sqrtθe^{-M^2/θ}$. This deviation leads to a nonvanishing Komar energy at the e…
We calculate the Komar energy $E$ for a noncommutative Schwarzschild black hole. A deformation from the conventional identity $E=2ST_H$ is found in the next to leading order computation in the noncommutative parameter $θ$ (i.e. $\mathcal{O}(\sqrtθe^{-M^2/θ})$) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result $M=2ST_H$, where the mass ($M$) of the black hole is identifie…
We present a toy model of fuzzy Schwarzschild space slice (as a noncommutative manifold) which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of the $(r,θ)$ Schwarzschild coordinates (the so-called Flamm's paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-cohere…
We investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of a radiating Schwarzschild black hole. We show that evaporation process is in such a way that black hole reaches to a maximum temperature before its final stage of evolution and then cools down to a nonsingular remnant with zero temperature and entropy. We compare our results with more reliable results of string theory. This comparison Shows that GUP and space noncommutativity are similar concepts at least from view point of black hole thermodynamics.
A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.
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.
Recently, a new perspective of gravitational-thermodynamic duality as an entropic force arising from alterations in the information connected to the positions of material bodies is found. In this paper, we generalize some aspects of this model in the presence of noncommutative Schwarzschild black hole by applying the method of coordinate coherent states describing smeared structures. We implement two different distributions: (a) Gaussian and (b) Lorentzian. Both mass distributions prepare the similar quantitative aspects for the entropic force. Our study shows, the entropic force on the smalle…
We study the asymptotic quasi-normal modes for the scalar perturbation of the non-commutative geometry inspired Schwarzschild black hole in (3+1) dimensions. We have considered $M\geq M_0$, which effectively correspond to a single horizon Schwarzschild black hole with correction due to non-commutativity. We have shown that for this situation the real part of the asymptotic quasi-normal frequency is proportional to $\ln (3)$. The effect of non-commutativity of spacetime on quasi-normal frequency arises through the constant of proportionality, which is Hawking temperature $T_H(θ)$. We also consi…
We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be rejected as models for physical spacetimes because they contradict observations, we find also solutions that can be made compatible with low energy phenomenology, while exhibiting strong noncommutativity at very short distances and early times.
We emphasize the importance of the Voros product in defining a noncommutative inspired Reissner-Nordström black hole. The entropy of this black hole is then computed in the tunneling approach and is shown to obey the area law at the next to leading order in the noncommutative parameter $θ$. Modifications to entropy/area law is then obtained by going beyond the semi-classical approximation. The leading correction to the semiclassical entropy/area law is found to be logarithmic and its coefficient involves the noncommutative parameter $θ$.
Quasinormal modes of noncommutative geometry-inspired dirty black holes
本文用 Chebyshev 谱方法计算非对易几何“脏”黑洞在标量、电磁和引力微扰下的 QNMs，发现近极端区的过阻尼模及大质量极限向 Schwarzschild 的收敛。
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capture some essential structural features of spacetime at the Planck scale. Examples of noncommutative spacetimes were investigated in detail. These include quantisations of plane-fronted gravitational waves, quantum Schwarzschild spacetime and Schwarzschild-de Sitter spacetime, and…
We study the formation of the (noncommutative) Schwarzschild black hole from collapsing shell {of the} generalized matters containing polytropic and Chaplygin gas. We show that this collapsing shell depending on various parameters forms either a black hole or a naked singular shell with the help of the pressure.Furthermore, by considering the smeared gravitational sources, we investigate the noncommutative black holes formation. Though this mild noncommutative correction of matters cannot ultimately resolve the emergence of the naked singularity, we show that in some parameter region the colla…
We calculate leading long-distance noncommutative corrections to the classical Schwarzschild black hole which is sourced by a massive noncommutative scalar field. The energy-momentum tensor is taken up to ${\cal O}(\ell^4)$ in noncommutative parameter, and is treated in semiclassical (tree level) approximation. These noncommutative corrections can dominate classical post-post-Newtonian corrections providing $\ell > 1/M_P$, however, they are still too small to be observable in present-day experiments.
In this paper we investigate quasinormal modes (QNM) for a scalar field around a noncommutative Schwarzschild black hole. We verify the effect of noncommutativity on quasinormal frequencies by applying two procedures widely used in the literature. The first is the Wentzel-Kramers-Brillouin (WKB) approximation up to sixth order. In the second case we use the continuous fraction method developed by Leaver. Besides, we also show that due to noncommutativity, the shadow radius is reduced when we increase the noncommutative parameter. In addition, we find that the shadow radius is nonzero even at t…
We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then le…
Thermodynamic metric usually works only for those black holes with more than one conserved charge, therefore the Schwarzschild black hole was excluded. In this letter, we compute and compare different versions of offshell thermodynamic metric for the Schwarzschild-like black hole by introducing a new degree of freedom. This new degree of freedom could be the running Newton constant, a cutoff scale for regular black hole, a noncommutative deformation, or the deformed parameter in the nonextensive Tsallis-Renyi entropy. The onshell metric of the deformed Schwarzschild solution would correspond t…
In order to find a noncommutative analog of Schwarzschild or Schhwarzschild-de Sitter blackhole we investigate spherically symmetric spaces generated by four noncommutative coordinates in the frame formalism. We present two solutions which however do not posess the prescribed commutative limit. Our analysis indicates that the appropriate noncommutative space might be found as a subspace of a higher-dimensional space.
Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like mass…
We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Reissner-Nordström black-hole spacetime. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Our results show that with the increase of the parameter $\sqrt{\vartheta}$, the observables $θ_{\infty}$ and $r_m$ decrease, while $s$ increases. Our results also show that i) if $\sqrt{\vartheta}$ is strong, …
One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity regime and it is shown that the wave function vanishes in this limit.
We study the problem of a Schwarzschild-anti-deSitter black hole in a noncommutative geometry framework, thought to be an effective description of quantum-gravitational spacetime. As a first step we derive the noncommutative geometry inspired Schwarzschild-anti-deSitter solution. After studying the horizon structure, we find that the curvature singularity is smeared out by the noncommutative fluctuations. On the thermodynamics side, we show that the black hole temperature, instead of a divergent behavior at small scales, admits a maximum value. This fact implies an extension of the Hawking-Pag…
We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure. In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. …
We study a solution of the Einstein's equations generated by a self-gravitating, anisotropic, static, non-singular matter fluid. The resulting Schwarzschild like solution is regular and accounts for smearing effects of noncommutative fluctuations of the geometry. We call this solution regular Schwarzschild spacetime. In the presence of an Anti-deSitter cosmological term, the regularized metric offers an extension of the Hawking-Page transition into a van der Waals-like phase diagram. Specifically the regular Schwarzschild-Anti-deSitter geometry undergoes a first order small/large black hole tr…
Following the interpretation of matter source that the energy-momentum tensor of anisotropic fluid can be dealt with effectively as the energy-momentum tensor of perfect fluid plus linear (Maxwell) electromagnetic field, we obtain the regular higher-dimensional Reissner-Nordström (Tangherlini-RN) solution by starting with the noncommutative geometry inspired Schwarzschild solution. Using the boundary conditions that connect the noncommutative Schwarzschild solution in the interior of the charged perfect fluid sphere to the Tangherlini-RN solution in the exterior of the sphere, we find that the…
One key element to calculate thermodynamical properties for a black hole is the partition function. In this paper we have incorporated the idea of a two dimensional area in a noncommutative space and were able to calculate the partition function with such a spectra. Employing the canonical quantum statistics formalism we compute the temperature, entropy and time of evaporation for a Schwarzschild black hole.
We obtain a generalized Schwarzschild (GS-) and a generalized Reissner-Nordstrom (GRN-) black hole geometries in (3+1)-dimensions, in a noncommutative string theory. In particular, we consider an effective theory of gravity on a curved $D_3$-brane in presence of an electromagnetic (EM-) field. Two different length scales, inherent in its noncommutative counter-part, are exploited to obtain a theory of effective gravity coupled to an U(1) noncommutative gauge theory to all orders in $Θ$. It is shown that the GRN-black hole geometry, in the Planckian regime, reduces to the GS-black hole. However…
We revisit the tunneling process from a Schwarzschild black hole in the noncommutative spacetime and obtain the non-thermal tunneling probability. In such non-thermal spectrum, the correlations are discovered, which can carry the information about the noncommutativity. Thus this enlightens a way to find the noncommutative information in the Hawking radiation. The entropy is also shown to be conserved in the whole radiation process, which implies that the unitarity is held even for the Hawking radiation from noncommutative black holes.
In this paper we focus on the partial wave method with the aim of exploring the scattering of massless scalar waves due to the noncommutative Schwarzschild black hole via Lorentzian smeared mass distribution. We determine the phase shift analytically in low-frequency limit and we show that the scattering and absorption cross section is modified. Specially, we show that in the low-frequency limit the scattering/absorption cross section has its value decreased when we increase the value of the non-commutativity parameter. In addition, we have confirmed this result by solving the problem numerica…
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and physics of Planck scale, we emphasize the importance of underlying noncommutative space-time such as Snyder's or Yang's Lorentz-covariant quantized space-time. The background of Bekenstein-Hawking's Area-entropy law and Holographic principle is now substantially understood in terms of {\it Kinematical} Holographic Relation [KHR], which holds in Yang's quantized space-time as the result of the kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometr…
As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on the spacetime manifold. We derive conditions on those twists that allow a given symmetry reduction. A complete classification of admissible deformations is possible in a class of twists generated by commuting vector fields. As examples, we explicitly construct the families of vector fields that generate twists which are compatible with Friedmann-R…
We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\cal K}{2π}$ connecting the black hole temperature ($T_h$) with the surface gravity ($\cal K$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed for…
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 fo…
We investigated regular black holes with fuzzy sources in three and four dimensions. The density distributions of such fuzzy sources are inspired by noncommutative geometry and given by Gaussian or generalized Gaussian functions. We utilized mass functions to give a physical interpretation of the horizon formation condition for the black holes. In particular, we investigated three-dimensional BTZ-like black holes and four-dimensional Schwarzschild-like black holes in detail, and found that the number of horizons is related to the spacetime dimensions, and the existence of a void in the vicinit…
In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative B…
A semi-classical reasoning leads to the non-commutativity of the space and time coordinates near the horizon of Schwarzschild black hole. This non-commutativity in turn provides a mechanism to interpret the brick wall thickness hypothesis in 't Hooft's brick wall model as well as the boundary condition imposed for the field considered. For concreteness, we consider a noncommutative scalar field model near the horizon and derive the effective metric via the equation of motion of noncommutative scalar field. This metric displays a new horizon in addition to the original one associated with the S…
Deformed Reissner-Nordström, as well as Reissner-Nordström de Sitter, solutions are obtained in a noncommutative gauge theory of gravitation. The gauge potentials (tetrad fields) and the components of deformed metric are calculated to second order in the noncommutativity parameter. The solutions reduce to the deformed Schwarzschild ones when the electric charge of the gravitational source and the cosmological constant vanish. Corrections to the thermodynamical quantities of the corresponding black holes and to the radii of different horizons have been determined. All the independent invariants…
The accretion around the black hole plays a pivotal role in the theoretical analysis of black hole shadow, and of the black hole observation in particular. In this paper, we mainly study the shadow and observation characteristics of noncommutative Schwarzschild black holes wrapped by three accretion models, and then explore the influence of noncommutative parameters on the observation appearance and spacetime geometry of black holes. When the black hole is surrounded by an optically and geometrically thin accretion disk, it shows that the direct emissions always dominate the total observed int…
In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in {Friedmann-Robertson-Walker (FRW)} cosmology, where this "noncommutativity" provides a simple mechanism that can explain the origin of the cosmological constant. In this paper we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzsc…
Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Comparing to the Reissner-Norstr\"{om} black hole, we find that the inf…
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