Roberto Casadio, Piero Nicolini
Non-commutative black holes are characterised by a minimum mass which would result in a remnant after the Hawking evaporation ends. We numerically study the decay of neutral non-commutative black holes for up to ten spatial dimensions and typical parameters that would make their production possible at the LHC. Neglecting possible accretion mechanism, we find that decay-times are extremely short.
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We study the shadow and energy emission rate of a spherically symmetric non-commutative black hole in Rastall gravity. Depending on the model parameters, the non-commutative black hole can reduce to the Schwarzschild black hole. Since the non-vanishing non-commutative parameter affects the formation of event horizon, the visibility of the resulting shadow depends on the non-commutative parameter in Rastall gravity. The obtained sectional shadows respect the unstable circular orbit condition, which is crucial for physical validity of the black hole image model.
Greybody factors for higher-dimensional non-commutative geometry inspired black holes
本文通过短程势和路径有序矩阵指数数值计算高维非对易几何启发黑洞的灰体因子，并比较其与Schwarzschild-Tangherlini黑洞在粒子通量和辐射功率上的差异。
The specific nonlinear vector $σ$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative'' vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair'' theorem.
Thermodynamics of high order correction for Schwarzschild-AdS black hole in non-commutative geometry
本文在非对易几何框架下研究具有Lorentz分布的Schwarzschild-AdS黑洞高阶修正热力学，发现高阶修正主导时其热力学行为趋近于普通Schwarzschild-AdS黑洞，并分析了Joule-Thomson效应。
Constraining Black Hole Parameters in Non-Commutative Geometry using Machine Learning
通过结合CUDA计算的机器学习技术，基于阴影行为约束非对易黑洞参数，并验证了模型与SgrA*_Keck观测的一致性。
It is shown that elementary black hole can not be distinguished from an elementary particle in the non-commutative space-times (space/space and space/time) at the Planck scale. But, the non-commutative space-times can not be ``directly'' measured in the elementary black hole system. A time-varying non-commutative parameter $θ(t)$ is suggested in accordance with the time-varying-G scenario. By identifying the elementary black hole with an elementary particle, the large hierarchy between the weak scale and Planck scale is naturally understood. For large black hole, the discrete spectrum of the h…
In this paper we employ the Horava-Lifshitz black holes solutions and obtain the corresponding Hamiltonian. It helps us to take new variables and it will be written by harmonic oscillator form. This leads us to apply non-commutative geometry to the new Hamiltonian and obtain the corresponding Lagrangian. And then, we take some information from Finsler geometry and write the Lagrangian of the different kinds of Horava-Lifshitz black holes. We show that the corresponding Lagrangian in non-commutative and Finsler geometry for above mentioned black holes completely coincidence together with some s…
Quantum features of a non-commutative Schwarzschild black hole
本文研究非交换Schwarzschild黑洞的量子特性，通过量子隧穿法计算粒子产生率和蒸发寿命，并推断非交换参数Θ的约束。
We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. De-localization of mass and charge is due to the presence of a "minimal length" in the spacetime fabric, coming from quantum gravitational effects, e.g. string induced non-commutative geometry. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner-Nordstrom geometry at large distance, and deSitter spacetime …
We compute the spectrum of quasinormal frequencies of five-dimensional black holes obtained in noncommutative geometry. In particular, we study scalar perturbations of a massive scalar field adopting the 6th order WKB approximation. We investigate in detail the impact of the mass of the scalar field, the angular degree and the overtone number on the spectrum. All modes are found to be stable.
Black Hole Radiation Sparsity and Bekenstein Entropy Loss in Non-Commutative Schwarzschild Spacetime
研究非对易引力框架下Schwarzschild黑洞的辐射稀疏性、Bekenstein熵损失和总粒子发射，发现辐射极稀疏且在蒸发末期发散。
This paper applies the first-order Seiberg-Witten map to evaluate the first-order non-commutative Kerr tetrad. The classical tetrad is taken to follow the locally non-rotating frame prescription. We also evaluate the tiny effect of non-commutativity on the efficiency of the Penrose process of rotational energy extraction from a black hole.
In this work, we study the thermodynamic properties on a non--commutative background via gravitational gauge field potentials. This procedure is accomplished after contracting de Sitter (dS) group, $\mathrm{SO}(4,1)$, with the Poincarè group, $\mathrm{ISO}(3,1)$. Particularly, we focus on a static spherically symmetric black hole. In this manner, we calculate the modified Hawking temperature and the other deformed thermal state quantities, namely, entropy, heat capacity, Helmholtz free energy and pressure. Finally, we also investigate the black hole evaporation process in such a context.
Comment on "Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity"
本评论指出一篇计算史瓦西非对易黑洞量子隧穿粒子产生的文献存在事件视界确定错误的问题，该错误影响了全部后续计算，且同一作者的其他多篇文献也存在相同问题，需进行修正。
Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole
本文研究了非交换黑洞的引力现象，推导测地线方程并分析薄吸积盘以模拟黑洞阴影，探讨了引力透镜在弱强偏折极限下对Sagittarius A*的应用，并计算了时间延迟及中微子湮灭、振荡和引力透镜效应。
Mutual Influence of Photon Sphere and Non-Commutative Parameter in Various Non-Commutative Black Holes: Part I- Towards evidence for WGC
本文研究非对易黑洞中光子球与非对易参数的相互影响，利用光子球对时空进行分类并约束非对易参数，证明引入爱因斯坦-玻恩-因费尔德场可增强模型与现实的物理一致性，并表明AdS BI模型可作为研究弱引力猜想效应的合适候选者。
Properties of an axisymmetric Lorentzian non-commutative black hole
本文利用改进的 Newman-Janis 方法将非对易几何中的球对称黑洞推广为旋转解，并系统分析其视界、热力学、测地线、阴影及标量准正规模态。
Using a noncommutative inspired anti-de Sitter-Einstein-Born-Infeld black hole with both non-commutative mass and charge distributions, we analyse a holographic superconductor in the context of the AdS/CFT correspondence. We show that the coupling of the Born-Infeld parameter and the noncommutative perturbations provides an enhancing mechanism for higher values of the expectation value of the condensate and that noncommutativity counter-balances nonlinearity of the electrodynamics to keep the ratio $ω_g/T_c \approx 8$.
Spontaneous localisation is a falsifiable, phenomenological, mechanism for explaining the absence of macroscopic position superpositions, currently being tested for in the laboratory. The theory of trace dynamics provides a possible theoretical origin for spontaneous localisation. We have recently proposed how to employ non-commutative geometry to include gravity in trace dynamics, and suggested the emergence of classical space-time geometry via spontaneous localisation. In our theory, which we call non-commutative matter gravity, a black hole arises from the spontaneous localisation of an ent…
In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of the system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent to the mentioned non-commutative Lagrangian under special c…
Axisymmetric black hole in a non-commutative gauge theory: classical and quantum gravity effects
本文研究了非交换规范理论中轴对称黑洞的经典和量子特性，通过修改的Newman-Janis程序推导出旋转解，并分析了其热力学性质、霍金辐射及引力透镜效应。
On the consistency of non-commutative geometry inspired Reissner-Nordström black hole solution
本文重新审视非对易几何启发的 Reissner-Nordström 黑洞解，指出原解未满足全部 Einstein 方程分量，并构造一致的改进能量-动量张量，修正强能量条件违反区域的预测。
We consider black hole interiors of arbitrary genus number within the paradigm of non-commutative geometry. The study is performed in two ways: One way is a simple smearing of a matter distribution within the black hole. The resulting structure is often known in the literature as a "model inspired by non-commutative geometry". The second method involves a more fundamental approach, in which the Hamiltonian formalism is utilized and a non-trivial Poisson bracket is introduced between the configuration degrees of freedom, as well as between the canonical momentum degrees of freedom. This is done…
The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
本文在非交换修正框架下研究了新黑洞解，探讨了非交换参数Θ对事件视界和表面重力的影响，并通过光子轨道分析黑洞阴影及引力透镜效应，结合事件视界望远镜数据和太阳系实验约束参数。
Effects of non-commutative geometry on black hole properties
本研究探讨了非对易黑洞解的特征，计算了其热力学性质，解析表达了蒸发后的寿命，并使用6阶WKB方法分析了准正规模式及引力透镜的偏折角。
Comment on "Thermodynamic properties of Schwarzschild black hole in non-commutative gauge theory of gravity"
该评论指出，非交换引力理论中Schwarzschild黑洞热力学分析存在计算错误，导致事件视界和表面重力定义不当，所有结果需重新检验。
Gravitational signatures of a non--commutative stable black hole
本文研究带质量变形的非对易黑洞，计算其热力学、准正规模式、测地线、阴影和偏转角，并利用Sgr A*观测约束非对易参数Θ。
In this work we describe a black hole, set on a non-commutative background. The model, which is relatively simple, is an exact solution of the Einstein Field Equations. Based on a proposition we put forward, we argue that introducing a matter density field on a non-commutative background sets up a mechanism that deforms the field into two distinct fields, one residing dominantly on the lattice tops (hereafter, on-cell) and the other residing dominantly in the inter-lattice regions (hereafter, off-cell). The two fields have different physical and themodynamic characterics which we describe, and…
We generalize the action found by 't Hooft, which describes the gravitational interaction between ingoing and outgoing particles in the neighbourhood of a black hole. The effect of this back-reaction is that of a shock wave, and it provides a mechanism for recovering information about the momentum of the incoming particles. The new action also describes particles with transverse momenta and takes into account the transverse curvature of the hole, and has the form of a string theory action. Apart from the Polyakov term found by 't Hooft, we also find an antisymmetric tensor, which is here relat…
Shadows of a Non-Commutative Black Hole under the Influence of a Magnetized Plasma
该研究考察磁化轴子–等离激元等离子体与非对易参数对黑洞阴影及能量发射率的影响。
The paper deals with non-thermal radiation spectrum by tunnelling mechanism with correction due to the generalized uncertainty principle (GUP) in the background of non-commutative geometry. Considering the reformulation of the tunnelling mechanism by Banerjee and Majhi, the Hawking radiation spectrum is evaluated through the density matrix for the outgoing modes. The GUP corrected effective temperature and the corresponding GUP corrected effective metric in non-commutative geometry are determined using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly the…
Constrained Scenarios of Non-Commutative Schwarzschild Black Holes with Global Monopoles from Van der Waals Behaviors
本研究结合热力学与光学，探究含整体单极子的非对易史瓦西黑洞的范德华行为，通过机器学习分析发现该模型与M87*黑洞的观测数据相匹配。
New Construction of Black Hole Solution in Non-Commutative Geometry and Their Thermodynamic Properties
通过Seiberg-Witten映射直接作用于相互作用势，构造了非对易Schwarzschild和Reissner-Nordstrom-like黑洞解，发现非对易性消除温度发散并诱导二级相变或Hawking-Page-like相变，稳定残余可作为冷暗物质候选者。
Quantum gravity effects on particle creation and evaporation in a non-commutative black hole via mass deformation
本文通过规范 de Sitter SO(4,1) 群和 Seiberg-Witten 映射研究质量形变下的引力非交换黑洞，分析了玻色子与费米子的 Hawking 辐射修正，推导了功率谱、Hawking 温度及黑洞蒸发寿命的解析表达式。
Thermodynamic properties and Joule-Thomson expansion of AdS black hole with Gaussian distribution in non-commutative geometry
本研究系统分析非对易几何中高斯分布AdS黑洞的热力学与焦耳-汤姆逊膨胀，发现其与洛伦兹分布黑洞热力学性质相似，但临界比值更高，零级相变效应更微弱。
On Modified First Law of Black hole Thermodynamics in The Non-Commutative Gauge Theory
本文在非对易引力规范理论中引入与 Θ 共轭的 NC 势修正黑洞热力学第一定律，揭示 NC Schwarzschild 黑洞的相变、蒸发末期行为及 Θ 的热力学变量作用。
Modeling the event horizon of a black hole by a fuzzy sphere it is shown that in the classical limit, for large astrophysical black-holes, the event horizon looks locally like a non-commutative plane with non-commutative parameter dictated by the Planck length. Some suggestions in the literature concerning black hole mass spectra are used to derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. We also suggest how the classical bounds on extremal black holes might be modif…
Lyapunov exponents and geodesic stability of Schwarzschild black hole in the non-commutative gauge theory of gravity
本文利用Lyapunov指数研究了引力规范理论下非对易Schwarzschild黑洞的测地线稳定性，发现粒子需无限固有时间到达奇点，揭示了新的稳定圆轨道与内层稳定光子球，并基于事件视界望远镜数据得出非对易参数量级为 $Θ^{\text{Phy}}\sim 10^{-32}m$。
We investigate solitonic black hole solutions in three dimensional noncommutative spacetime. We do this in gravity with negative cosmological constant coupled to a scalar field. Noncommutativity is realized with the Moyal product which is expanded up to first order in the noncommutativity parameter in two spatial directions. With numerical simulation we study the effect of noncommutativity by increasing the value of the noncommutativity parameter starting from commutative solutions. We find that even a regular soliton solution in the commutative case becomes a black hole solution when the nonc…
Optical Phenomena in a Non-Commutative Kalb-Ramond Black Hole Spacetime
本文研究非对易Kalb-Ramond黑洞时空中的光子轨道、阴影、弱场和强场偏转角，并利用EHT数据约束非对易参数Θ和洛伦兹破坏参数ℓ。
We address the issue of modelling quantum gravity effects in the evaporation of higher dimensional black holes in order to go beyond the usual semi-classical approximation. After reviewing the existing six families of quantum gravity corrected black hole geometries, we focus our work on non-commutative geometry inspired black holes, which encode model independent characteristics, are unaffected by the quantum back reaction and have an analytical form compact enough for numerical simulations. We consider the higher dimensional, spherically symmetric case and we proceed with a complete analysis …
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in higher dimensions with a source given by a static, spherically symmetric Gaussian distribution of mass. The resulting metric would describe a regular or curvature singularity free black hole in higher dimensions. The metric should smoothly interpolate between Schwarzschild geometry at large distance and de-Sitter spacetime at short distance. We will consider grav…
A Non-Commutative Kalb-Ramond Black Hole
本文在非对易Kalb-Ramond引力框架下提出新黑洞解，验证其非球对称性及正则性，推导热力学量并分析量子辐射，最终利用太阳系测试约束非对易和洛伦兹破坏参数。
Particle production induced by a Lorentzian non-commutative spacetime
本文研究了洛伦兹非对易黑洞的粒子产生、蒸发和灰体因子，发现非对易参数Θ会降低Hawking温度、减少玻色子和费米子的粒子产生密度并减小灰体因子，导致蒸发过程减缓。
The general theory of relativity is currently the accepted theory of gravity and as such, a large repository of test results has been obtained since its inception in 1915. However, in this paper we only focus on what are considered as the main tests but in non-commutative (NC) geometries. Using the coordinate coherent state formalism, we calculate the gravitational redshift, deflection, and time delay of light, separately, for NC inspired Schwarzschild and Riessner-Nordstrom black holes. We show the NC predictions have different behavior than the general relativity. We also provide an upper bo…
Non-commutative geometries have been proposed as an approach to quantum gravity and have led to the construction of non-commutative black holes, whose interior singularities are purportedly eliminated due to quantum effects. Here we find evidence that these black holes are in fact unstable, with infalling matter near the Cauchy (inner) horizon being subject to an infinite blueshift of the type that has been repeatedly demonstrated for the Reissner-Nordstr\(\ddot{\text{o}}\)m black hole. This instability is present even when an ultraviolet cutoff (induced by anticipated non-commutative geometri…
We synthesize and extend the previous ideas about appearance of both noncommutative and Finsler geometry in string theory with nonvanishing B--field and/or anholonomic (super) frame structures \cite{vstring,vstr2,vnonc,vncf}. There are investigated the limits to the Einstein gravity and string generalizations containing locally anisotropic structures modeled by moving frames. The relation of anholonomic frames and nonlinear connection geometry to M--theory and possible noncommutative versions of locally anisotropic supergravity and D--brane physics is discussed. We construct and analyze new cl…
Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in noncommutative geometry have shown that, in general relativity, the effects of noncommutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of…
It has recently been suggested that black hole remnants of primordial origin are not a viable dark matter candidate since they would have far too large a velocity due to the recoil of Hawking radiation. We re-examined this interesting claim in more details and found that it does not rule out such a possibility. On the contrary, for models based on non-commutativity of spacetime near the Planck scale, essentially the same argument can be used to estimate the scale at which non-commutativity effect becomes important. If dark matter "particles" are non-commutative black holes that have passed the…
We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for qua…
Non-commutative correction of ideal gas thermodynamics
本研究在κ-形变时空与彩虹引力背景下研究相对论理想气体热力学，通过引入形变哈密顿量与时间不变相空间体积修正构建修正配分函数，并探讨其对修正黑体辐射谱和德拜比热理论的影响。
It is increasingly widely believed that at high levels of resolution spacetime geometry may be inherently non-commutative. In this work we introduce an effective mechanism that maps matter fields onto a non-commutative background manifold. The mechanism, which is relevant at high densities in strongly gravitating systems (black holes, early universe) deforms a density field into two distinct fields, one residing dominantly on the lattice tops (hereafter, on-cell) and the other residing dominantly in the inter-lattice regions (hereafter, off-cell). The two fields have different physical and the…
Investigations of possible violations of the Pauli Exclusion Principle represent critical tests of the microscopic space-time structure and properties. Space-time non-commutativity provides a class of universality for several Quantum Gravity models. In this context the VIP-2 Lead experiment sets the strongest bounds, searching for Pauli Exclusion Principle violating atomic-transitions in lead, excluding the $θ$-Poincaré Non Commutative Quantum Gravity models far above the Planck scale for non-vanishing $θ_{μν}$ ``electric-like'' components, and up to $6.9 \cdot 10^{-2}$ Planck scales if $θ_{0i…
We propose a generalized star product which deviates from the standard product when the fields at evaluated at different space-time points. This produces no changes in the standard Lagrangian density in non-commutative space-time but produces a change in the cosmological power spectrum. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.
Quantum atmosphere effective radii for different spin fields from quantum gravity inspired black holes
本文计算了多种量子引力启发黑洞发射不同自旋无质量场的量子大气有效半径，发现等功率黑体有效半径通常无法准确表征量子大气的位置。
The entropy of charged black hole is calculated by using the partition function evaluated at radial geodesics confined under horizons. We establish two quantum phase states inside the black hole and a transition between them.
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.
In this work we study the Joule-Thomson expansion for uncharged black holes in a noncommutative scenario characterized by a parameter $θ$, which is present in the horizon function. We calculate the inversion temperature for some values of $θ$ and the isenthalpics for fixed masses. We find that the uncharged noncommutative black hole behaves as a charged commutative one.
In this paper, a four dimensional rotating Kaluza Klien (K-K) black hole was deformed using rainbow functions derived from loop quantum gravity and non-commutative geometry. We studied the thermodynamic properties and critical phenomena of this deformed black hole. The deformed temperature and entropy showed the existence of a Planckian remnant. The calculation of Gibbs free energy $ G$ for the ordinary and deformed black holes showed that both share a similar critical behaviour.
Thermodynamics of the BTZ black hole in noncommutative geometry is studied. We work out the Hawking temperature and entropy which reduce to their commutative limits when the noncommutativity parameter tends to zero. We also discuss the range of validity of the Hawking area law in the noncommutative case and provide graphical analysis. We see that the law is not valid unless the outer horizon is very large.
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