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电影黑洞的英语作文In the realm of science fiction, black holes have long captured the imagination of filmmakers and audiences alike. These cosmic phenomena, characterized by their immense gravitational pull and the mystery surrounding what lies within, have been the subject of numerous films. Theportrayal of black holes in cinema often serves as a metaphor for the unknown, the infinite, and the unexplored.One of the earliest and most iconic representations of a black hole can be found in the 1979 film "The Black Hole." This Disney production was a pioneer in its use of special effects to depict the gravitational anomalies and the eerie silence that surrounds these cosmic bodies. The film's black hole was portrayed as a gateway to another dimension, sparking the curiosity of viewers about the possibilitiesthat lie beyond our known universe.In more recent years, Christopher Nolan's "Interstellar" (2014) took a more scientifically accurate approach to black holes. The film featured a black hole named Gargantua, which was designed in consultation with physicist Kip Thorne. The depiction of Gargantua showcased the effects of gravitational lensing and the distortion of time, providing viewers with a more grounded and scientifically plausible understanding of black holes.The narrative of "Interstellar" revolves around a group ofexplorers who venture through a wormhole near Saturn insearch of a new home for humanity. The film's exploration of love, time, and the human spirit against the backdrop of a black hole adds a layer of emotional depth to the scientific concepts presented.Another notable film that explores the concept of black holes is "Event Horizon" (1997). This science fiction horror film tells the story of a spaceship that disappears into a black hole and returns with a malevolent presence on board. While less scientifically accurate, "Event Horizon" uses the black hole as a plot device to delve into themes of fear, isolation, and the unknown.The portrayal of black holes in cinema has evolved over time, reflecting both the advancements in our understanding ofthese celestial bodies and the creative imaginations of filmmakers. Whether used as a metaphor for the unknown or asa backdrop for exploring the human condition, black holes continue to captivate audiences and inspire filmmakers topush the boundaries of storytelling.。
Investigating the Nature of DarkMatterThe phrase “dark matter” has become a buzzword in modern astrophysics as well as popular culture, and yet we still know very little about what dark matter really is. It is a mysterious substance that makes up 27% of the universe and that cannot be observed directly, but can only be inferred from the gravitational effects it has on visible matter. Therefore, dark matter is a topic of intense research and debate in the scientific community. In this article, we will explore the key aspects of dark matter and the different ways scientists are working to uncover its nature.What is Dark Matter?As mentioned, dark matter is a substance that does not emit, absorb or reflect light, hence its name. It does not interact strongly with electromagnetic forces, but it does with gravity, which is why its presence can be inferred from the gravitational effects it has on visible matter. One of the most well-known examples of this is the rotation curve of spiral galaxies. According to the laws of classical mechanics, the velocity of stars and gas in a galaxy should decrease as one moves away from the center, as the gravitational attraction of the visible matter decreases. However, observations have shown that the velocity remains constant or even increases, suggesting that there is an invisible mass that is causing this anomaly. This invisible mass is the dark matter.Another piece of evidence for the existence of dark matter is the distribution of matter in the universe as revealed by the cosmic microwave background radiation, which is the afterglow of the Big Bang. The pattern of temperature fluctuations in this radiation shows that the matter in the universe is not distributed evenly, but is rather clumped up in large structures such as galaxies and clusters of galaxies. However, this clumping up cannot be explained solely by the gravitational influence of visible matter; there must be an additional source of gravity, i.e. dark matter, to explain the observed distribution.Moreover, measurements of the large-scale structure of the universe, such as the distribution of galaxies and galaxy clusters, also point to the existence of dark matter.What is Dark Matter Made of?Despite its importance in shaping the structure of the universe, the identity of dark matter remains unknown. There are several hypotheses about what dark matter might be made of, but none of them has been conclusively proven yet. One popular hypothesis is that dark matter is composed of weakly interacting massive particles (WIMPs), which are hypothetical particles that would interact with normal matter only through the weak nuclear force and gravity. The idea is that WIMPs were produced in the early universe when it was hot and dense, and have been moving around freely ever since. If they collide with normal matter, they would transfer some of their energy and momentum, producing detectable signals. In fact, several experiments have been designed to detect WIMP interactions, such as the Large Underground Xenon (LUX) experiment and the Super Cryogenic Dark Matter Search (SuperCDMS).Another hypothesis is that dark matter is made of axions, which are theoretical particles that were originally proposed to explain a different problem in physics, the strong CP problem. The idea is that axions would be very light and weakly interacting, making them difficult to detect, but would still affect the motion of galaxies and other cosmic structures. The Axion Dark Matter eXperiment (ADMX) is currently searching for evidence of axions in a laboratory at the University of Washington.A third hypothesis is that dark matter is composed of primordial black holes, which are black holes that were formed by the collapse of a density fluctuation in the early universe. The idea is that these black holes could have a mass range that would make them more likely to be dark matter, and that their interactions with normal matter could produce observable effects. However, this hypothesis is less favored by most researchers, as the formation and stability of such black holes would require very specific conditions.ConclusionDespite decades of research, the nature of dark matter remains one of the most intriguing and elusive topics in astrophysics. It remains a theoretical construct that cannot be directly observed, but its effects on the motion and structure of the cosmos are undeniable. Researchers are continuing to study dark matter using a variety of tools and techniques, from telescopes that measure gravitational lensing to underground experiments that look for WIMP interactions. The hope is that someday we will finally be able to unravel the mystery of what dark matter is made of, and in doing so, gain a better understanding of the universe and our place in it.。
介绍黑洞的英语作文短片1Black holes are one of the most mysterious and fascinating objects in the universe. They possess incredibly powerful gravitational forces that are so strong that not even light can escape from them. This makes them impossible to observe directly. However, scientists have found ingenious ways to detect their presence indirectly. One such method is by observing the effects of a black hole on nearby matter. When matter gets close to a black hole, it is heated to extremely high temperatures and emits intense radiation that can be detected by telescopes.For instance, the study of the X-ray emissions from the accretion disks around black holes has provided valuable insights. The famous Cygnus X-1, for example, is one of the earliest and most studied black hole candidates. Another important achievement is the detection of gravitational waves produced by the merger of two black holes. This groundbreaking discovery not only confirmed the existence of black holes but also opened up a new window for studying the universe.In conclusion, despite the challenges in directly observing black holes, the progress made in understanding them through indirect means has been remarkable, and continues to deepen our knowledge of the universe's most extreme phenomena.2Black holes are one of the most mysterious and fascinating phenomena in the universe. They are formed through a complex process that involves the collapse of massive stars. When a star much larger than our sun runs out of fuel and can no longer support its own weight, it undergoes a gravitational collapse. The core of the star collapses inward with such tremendous force that it creates an object with an incredibly strong gravitational pull, from which nothing, not even light, can escape.In many science fiction movies, black holes are depicted in various imaginative ways. They are often shown as portals to other dimensions or as cosmic monsters that swallow entire galaxies. These depictions not only entertain us but also fuel our curiosity about the unknown.The study of black holes has opened up new frontiers in our understanding of the universe. It challenges our current theories of physics and forces us to think beyond the boundaries of conventional knowledge. The mystery and allure of black holes continue to captivate scientists and enthusiasts alike, driving us to explore the vastness of space and uncover its deepest secrets.3Black holes are one of the most mysterious and fascinating phenomena in the universe. They have a profound impact on thesurrounding spacetime. The gravitational pull of a black hole is so intense that it can distort spacetime to an extreme degree. This distortion causes objects near the black hole to experience extreme gravitational forces and behave in unusual ways.For example, consider the theory of gravitational lensing. When light passes near a black hole, its path is bent due to the gravitational distortion of spacetime. This effect has been observed and studied in various astronomical observations, providing valuable evidence for our understanding of black holes and their influence.Another interesting aspect is the concept of the event horizon. Once an object crosses this boundary, it is impossible for it to escape the gravitational pull of the black hole. This idea has led to many scientific experiments and hypotheses aimed at exploring the nature and properties of black holes.Scientists have also proposed the idea of extracting energy from black holes through a process known as the Penrose process. This theoretical concept involves the conversion of rotational energy of the black hole into usable energy.In conclusion, the study of black holes and their effects on spacetime continues to expand our knowledge of the universe and challenges our understanding of fundamental physics.Black holes have long fascinated scientists and the public alike. The study of black holes has a rich history that dates back to Einstein's theory of relativity. According to this theory, massive objects can distort spacetime to such an extent that a black hole can form.For many years, black holes were theoretical entities. But with the advancement of technology, we have been able to observe and study them more closely. Modern telescopes and observatories have provided us with valuable data and images.The discovery of gravitational waves, predicted by Einstein's theory, has also opened new doors in the study of black holes. When two black holes merge, they produce gravitational waves that can be detected on Earth.Scientists are constantly working to understand the nature of black holes, their formation, and their effects on the universe. They are using advanced computer simulations and mathematical models to gain deeper insights.In conclusion, our understanding of black holes has come a long way from theoretical concepts to actual observations and discoveries. The journey is far from over, and there is still much to learn and explore about these mysterious cosmic objects.Black holes are one of the most mysterious and fascinating objects in the universe. They have a gravitational pull so strong that nothing, not even light, can escape. The study of black holes has opened up new frontiers in our understanding of the cosmos.The future development of black hole research holds immense potential and scientific value. One exciting area is the combination of black hole studies with quantum mechanics. This could help us solve some of the most profound questions in physics, such as the nature of space and time at the most fundamental level.For instance, researchers are exploring how the extreme gravitational environment near a black hole might affect the behavior of quantum particles. This could lead to a revolutionary understanding of the interplay between gravity and quantum physics, which has puzzled scientists for decades.Another aspect is the role of black holes in the evolution of galaxies. Understanding how black holes interact with the surrounding matter and influence the formation and growth of galaxies could provide crucial insights into the structure and dynamics of the universe.In conclusion, the study of black holes is not only about uncovering the mysteries of these cosmic giants but also about advancing our knowledge of the fundamental laws of nature and the universe as a whole.。
空间曲率驱动原理The concept of space curvature driving principle is a fundamental idea in physics that suggests the curvature of space influences the motion of objects. It is a key aspect of the general theory of relativity proposed by Albert Einstein. 空间曲率驱动原理是物理学中的基本概念，它表明空间的曲率影响物体的运动。
这是爱因斯坦提出的广义相对论的关键方面。
In the context of general relativity, the curvature of space-time is determined by the distribution of mass and energy. According to the theory, massive objects like stars and planets cause space-time to bend around them, creating what we perceive as the force of gravity. 据广义相对论的理论，空间时间的曲率由质量和能量的分布决定。
根据这一理论，像恒星和行星这样的大质量物体使空间时间围绕它们弯曲，形成我们所感知到的引力。
The concept of space curvature driving principle has been verified through various experiments and observations. One of the most notable examples is the bending of light around massive objects, known as gravitational lensing. 过去通过各种实验和观测已经验证了空间曲率驱动原理。
英语单词迅速背诵方法英语单词迅速背诵方法［学习方法］幽默英语单词速记1.背口诀记单词旅游去趟France (法国)巴黎舞厅dance (跳舞)正在大步advance (前进)忽见美女glance (匆匆一看)脚下失去balance (平衡)踩高根鞋抓住了chance (机会)(假装失足，找机会接近。
)2.识音标，记单词France n.法国,法兰西。
dance n.跳舞,舞蹈a social dance(交谊舞),舞会,舞曲,舞步，舞蹈艺术，跳跃；v.跳舞,舞蹈,雀跃，飘扬，摇曳。
advance n.前进,进步，提升,上涨，预付款；v.前进,提前,促进，提升，发展，上涨，预付；adj.前面的,预先的，前进的；[习语] on the advance(在上涨)，in advance(预先,事先)。
glance v.扫视,匆匆一看，闪耀,擦过；n.一瞥,眼光,匆匆一看,闪光,掠过; [习语] give a glance at(对...匆匆一看,一瞥)。
balance n.秤,天平,平衡,收支差额,余额；v.平衡,称,权衡,对比,结算；[习语] on balance(总的来说)，in the balance(命运未定，不确定)。
chance n.机会,可能性,偶然性,运气；v.碰巧,偶然发生,冒...的险；adj.偶然的，意外的；[习语] by chance(偶然,意外地)，take a chance(冒一冒险,碰碰运气)。
3.邻里邻外dance---在dance后加r变为：dancer n.舞女,舞蹈少女advance---把advance里的ce换为age变为：advantage n.优势,有利条件,利益glance---去掉glance里的e换为ing变为：glancing adj.粗略的balance---在balance前加un变为：unbalance v.使心情紊乱n.失去平衡chance---在chance后加ful变为：chanceful多变的,多事的4.佳句背诵All are not merry that dance lightly轻歌曼舞未必快乐。
现在改变过去——物理学家惠勒延迟选择实验约翰·惠勒（1911年7月9日——2008年4月13日），美国物理开拓时期的科学家，普林斯顿大学教授，从事原子核结构、粒子理论、广义相对论及宇宙学等研究。
他27岁就与丹麦的波耳发展出核分裂理论；后与学生理查·费曼（1965年诺贝尔物理奖得主）改写电磁理论，并提出时光回溯移动的构想。
惠勒的研究为20世纪下半叶物理学的发展勾勒出了方向。
唯一一个表述“意识决定物质”的物理学实验：惠勒延迟实验在人间：本文将用当代最前沿物理学实验，证明：我们当下的所思所想、所作所为，足以影响已经发生的事情。
（对于常人，只要这件事情还没有被你自己发现记忆）（接下来，如何去影响呢？这便是宇宙的核心秘密---唯心所现、唯识所变。
）当代美国物理学家惠勒的延迟选择实验，不断地被一次次实验所证明。
它带来的结论是一切自然科学革命式的颠覆。
至少，孩子们从小学到大学的物理课上，最后一章可以不停留在“相对论、量子力学”啦，就连霍金的时间简史，也将成为物理学的记忆了~~~o(∩_∩)o...不过令人奇怪和遗憾的是，这个30年前的实验，中国物理学家们似乎视而不见喔~~~ 还有那可怜的唯物主义，大哲学家、大思想家们，恐怕又要重新认识世界啦~~~ 真的想看看这些大物理学家，如果能够认真研读一下佛经，结果会是如何。
只可惜他们边地受生，与佛无缘，也是我们世界共同的业力啊~~~ 约翰·阿奇博尔德·惠勒（John Archibald Wheeler，1911年7月9日—2008年4月13日）美国著名的物理学家、物理学思想家和物理学教育家。
1911年7月9日出生在美国的佛罗里达州，惠勒生前是美国自然科学院院士和文理科学院院士，曾任美国物理学会主席。
关于时间，爱因斯坦创立相对论时也有一个著名的结论，“过去、现在、将来的区别，只是一种幻觉，不管人们怎么坚持这种区别也没有用”。
不过，相对论强调的是我们对时间的幻觉，而量子力学的结论更加普遍，那就是一切实相都是幻觉。
以下是90个超新星纪元的词语以及它们的译文：1.超新星纪元- Supernova Age2.星际物质- Interstellar Matter3.星云- Nebula4.恒星- Star5.黑洞- Black Hole6.脉冲星- Pulsar7.星系- Galaxy8.旋臂- Spiral Arm9.恒星系- Stellar System10.双星- Binary Star11.星团- Star Cluster12.星云团- Nebula Cluster13.星际空间- Interstellar Space14.星尘- Stardust15.星系团- Galaxy Cluster16.超星系团- Supercluster17.宇宙射线- Cosmic Ray18.反物质- Antimatter19.高能射线- High-energy Radiation20.量子力学- Quantum Mechanics21.引力波- Gravitational Wave22.宇宙微波背景辐射- Cosmic Microwave Background Radiation23.暗物质- Dark Matter24.暗能量- Dark Energy25.星系核- Galaxy Core26.黑洞吞噬- Black Hole Accretion27.恒星演化- Stellar Evolution28.核合成- Nucleosynthesis29.星系碰撞- Galaxy Collision30.恒星爆炸- Stellar Explosion31.引力透镜- Gravitational Lensing32.宇宙网- Cosmic Web33.反物质粒子- Antimatter Particles34.高纬宇宙模型- High-dimensional Cosmic Model35.宇宙常数- Cosmological Constant36.宇宙密度- Cosmic Density37.宇宙膨胀- Cosmic Expansion38.宇宙学红移- Cosmological Redshift39.大爆炸理论- Big Bang Theory40.弦理论- String Theory41.相对论- Relativity42.量子力学- Quantum Mechanics43.弦理论- String Theory44.卡鲁扎-克莱因理论- Kaluza-Klein Theory45.高维时空- Higher-dimensional Spacetime46.虚时间- Virtual Time47.宇宙微波背景辐射- Cosmic Microwave Background Radiation48.标准宇宙模型- Standard Cosmological Model49.星系团- Galaxy Cluster50.超星系团- Supercluster51.丝状结构- Filamentary Structure52.大尺度结构- Large-scale Structure53.哈勃常数- Hubble Constant54.引力波- Gravitational Wave55.黑洞信息悖论- Black Hole Information Paradox56.夸克星- Quark Star57.反物质星- Antimatter Star58.原子核- Atomic Nucleus59.量子纠缠- Quantum Entanglement60.高温高压状态方程- High-temperature and high-pressure equation ofstate61.星系演化- Galaxy Evolution62.星系动力学- Galaxy Dynamics63.星际物质循环- Interstellar Matter Cycle64.恒星形成- Star Formation65.分子云- Molecular Cloud66.星际空间气体- Interstellar Gas67.星际尘埃- Interstellar Dust68.星系核活动- Active Galactic Nucleus69.射电星系- Radio Galaxy70.光学星系- Optical Galaxy71.X射线星系- X-ray Galaxy72.恒星团- Star Cluster73.双星系统- Binary Star System74.变星- Variable Star75.新星- Nova76.超新星- Supernova77.中子星- Neutron Star78.脉冲星- Pulsar79.黑洞候选体- Black Hole Candidate80.高光度蓝变星- High-luminosity Blue Variable Star81.超巨星- Supergiant Star82.红巨星- Red Giant Star83.黄矮星- Yellow Dwarf Star84.白矮星- White Dwarf Star85.恒星演化模型- Stellar Evolution Model86.星际物质分布- Interstellar Matter Distribution87.分子光谱学- Molecular Spectroscopy88.高能天体物理学- High-energy Astrophysics89.天体化学- Astrochemistry90.宇宙射线物理学- Cosmic Ray Physics。
a r X i v :1012.1670v 3 [g r -q c ] 19 F eb 2011Strong gravitational lensing in a noncommutative black-hole spacetimeChikun Ding,∗Shuai Kang,and Chang-Yong ChenDepartment of Physics and Information Engineering,Hunan Institute of Humanities Science and Technology,Loudi,Hunan 417000,P.R.ChinaSongbai Chen †and Jiliang Jing ‡Institute of Physics and Department of Physics,Hunan Normal University,Changsha,Hunan 410081,P.R.China Key Laboratory of Low Dimensional Quantum Structures and Quantum Control (Hunan Normal University),Ministry of Education,P.R.China.AbstractNoncommutative 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 non-commutative 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 ob-servables for strong gravitational paring to the Reissner-Norstr¨o m black hole,we find that the influences of the spacetime noncommutative parameter is similar to those of the charge,just these influences are much smaller.This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstr¨o m black hole,and may probe the spacetime noncommutative constant ϑ[1]by the astronomical instruments in the future.PACS numbers:04.70.-s,95.30.Sf,97.60.LfI.INTRODUCTIONThe theoretical discovery of radiating black holes disclosed thefirst window on the mysteries of quantum gravity.Though after thirty years of intensive research,the full quantum gravity is still unknown.However there are two candidates for quantum gravity,which are the string theory and the loop quantum gravity.By the string/black hole correspondence principle[2],stringy effects cannot be neglected in the late stage of a black hole.In the string theory,coordinates of the target spacetime become noncommutating operators on a D-brane as[3][ˆxµ,ˆxν]=iϑµν,(1.1) whereϑµνis a real,anti-symmetric and constant tensor which determines the fundamental cell discretization of spacetime much in the same way as the Planck constant discretizes the phase space,[ˆx i,ˆp j]=i δij. Motivated by string theory arguments,noncommutative spacetime has been reconsidered again and is believed to afford a starting point to quantum gravity.Noncommutative spacetime is not a new conception,and coordinate noncommutativity also appears in anotherfields,such as in quantum Hall effect[4],cosmology[5],the model of a very slowly moving charged particle on a constant magneticfield[6],the Chern-Simon’s theory[7],and so on.The idea of noncommutative spacetime dates back to Snyder[8]who used the noncommutative structure of spacetime to introduce a small length scale cut-offinfield theory without breaking Lorentz invariance and Yang[9]who extended Snyder’s work to quantize spacetime in1947before the renormalization theory.Noncommutative geometry[10]is a branch of mathematics that has many applications in physics,a good review of the noncommutative spacetime is in[11,12].The fundamental notion of the noncommutative geometry is that the picture of spacetime as a manifold of points breaks down at distance scales of the order of the Planck length:Spacetime events cannot be localized with an accuracy given by Planck length[12]as well as particles do in the quantum phase space.So that the points on the classical commutative manifold should then be replaced by states on a noncommutative algebra and the point-like object is replaced by a smeared object[13]to cure the singularity problems at the terminal stage of black hole evaporation[14].The approach to noncommutative quantumfield theory follows two paths:one is based on the Weyl-Wigner-Moyal*-product and the other on coordinate coherent state formalism[13].In a recent paper,following the coherent state approach,it has been shown that Lorentz invariance and unitary,which are controversial questions raised in the*-product approach[15],can be achieved by assumingϑµν=ϑdiag(ǫ1,...,ǫD/2),(1.2) whereϑ[1]is a constant which has the dimension of length2,D is the dimension of spacetime[16]and,there isn’t any UV/IR mixing.Inspire by these results,various black hole solutions of noncommutative spacetime have been found[17];thermodynamic properties of the noncommutative black hole were studied in[18];the evaporation of the noncommutative black hole was studied in[19];quantized entropy was studied in[20],and so on.It is interesting that the noncommutative spacetime coordinates introduce a new fundamental natural length √scalebe described by this metric and then obtain the numerical results for the observational gravitational lensing parameters defined in Sec.II.Then,we make a comparison between the properties of gravitational lensing in the noncommutative Schwarzschild and Reissner-Norstr¨o m metrics.In Sec.IV,we present a summary.II.DEFLECTION ANGLE IN THE NONCOMMUTATIVE SCHW ARZSCHILD BLACK HOLESPACETIMEThe line element of the noncommutative Schwarzschild black hole reads[14]ds2=−f(r)dt2+dr2r√ϑ→∞.And Eq.(2.1)leads to the mass distribution m(r)=2Mγ 3/2,r2/4ϑ /√ϑ,the event horizons are given byr±=4Mπγ 3/2,r2±/4ϑ ,(2.4)which behaviors as that of Reissner-Norstr¨o m black hole.The line element(2.1)describes the geometry of a noncommutative black hole and should give us useful insights about possible spacetime noncommutative effects on strong gravitational lensing.As in[27,28,30],we set2M=1and rewrite the metric(2.1)asds2=−A(r)dt2+B(r)dr2+C(r) dθ2+sin2θdφ2 ,(2.5) withA(r)=f(r),B(r)=1/f(r),C(r)=r2.(2.6) The deflection angle for the photon coming from infinite can be expressed asα(r0)=I(r0)−π,(2.7)where r 0is the closest approach distance and I (r 0)is [27,28]I(r 0)=2∞r 0C (r )A (r 0)C (r )=A ′(r )2−r 3psπϑe−r 2ps√2,r 2psϑ.ϑ0.2540.2420.230r ps 1.494051.497211.49890√0.2180.2060.1940.1821.499621.499891.499981.50000ϑ→0,it can recovers that in the commutative Schwarzschild black hole spacetime whichr ps =1.5.Fig.1shows that the relation between the photon sphere radius and the spacetime noncommutative parameter ϑis very coincident to the functionr ps =1.5−7.8×107√ϑ∈(0,19−32q 2)/4,which implies that there exist some distinct effects of the noncommutative parameterϑon gravitational lensing in the strong field limit.FIG.1:Thefigure is for the radius of the photon sphere in the noncommutative Schwarzschild black hole spacetime √with differentϑ17.Following the method developed by Bozza[30,37],we define a variabler0z=1−A(r)B(r)C(r0)wherep(r0)=2−3√2,r202ϑ√4ϑ,q(r0)=3√2,r204ϑ√4ϑ 2+r20u ps−1+¯b+O(u−u ps),(2.19) where¯a=R(0,r ps)q(r ps)= 1−r4psπϑe−r2ps2,¯b=−π+bR +¯a log4q2(r ps) 2A(r ps)−r2ps A′′(r ps)A3(r ps),b R=I R(r ps),p′(r ps)=dpϑas in[30].Because the values of various low derivative of integrand ofI R(r ps)atϑ→0is zero,we can getb R=2log[6(2−√ϑ).(2.21) Then we can obtain the¯a,¯b and u ps,and describe them in Fig(2).Figures(2)tell us that with the increase ofϑthe coefficient¯a increase,the¯b slowly increases atfirst,then decrease quickly when it arrives at a peak, and the minimum impact parameter u ps decreases,which is similar to that in the Reissner-Norstr¨o m black hole metric.However,as shown in Fig.(2),in the noncommutative Schwarzschild black hole,¯a increases more slowly,both of¯b and u ps decrease more slowly.In a word,comparing to the Reissner-Nordstrom black hole,the influences of the spacetime noncommutative parameter on the strong gravitational lensing is similar to those of the charge,merely they are much smaller.On the other side,in principle we can distinguish a noncommutative Schwarzschild black hole from the Reissner-Nordstrom black hole and,may be probe the value of the spacetime noncommutative constant by using strongfield gravitational lensing.0.100.120.140.160.180.200.220.241.0001.0011.0021.0031.0041.005a0.100.120.140.160.180.200.220.240.400280.400260.400240.400220.40020b0.100.120.140.160.180.200.220.242.597942.597962.597982.598002.598022.598042.59806u p sq a0.100.150.200.250.300.350.400.4040.4020.4000.3980.396qbqu p sFIG.2:Variation of the coefficients of the strong field limit ¯a ,¯b and the minimum impact parameter u ps with the spacetime noncommutative parameter√ϑ.Considering the source,lens and observer are highly aligned,the lens equation in strong gravitational lensing can be written as [39]β=θ−D LSbetween the source and the lens,θis the angular separation between the image and the lens,∆αn=α−2nπis the offset of deflection angle and n is an integer.The position of the n-th relativistic image can be approximated asu ps e n(β−θ0n)D OSθn=θ0n+¯a,(2.24)θ0n are the image positions corresponding toα=2nπ.The magnification of n-th relativistic image is given byu2ps e n(1+e n)D OSµn=∞n=2µn.(2.28) For highly aligned source,lens and observer geometry,these observable can be simplified ass=θ∞e¯b−2π¯a.(2.29) The strong deflection limit coefficients¯a,¯b and the minimum impact parameter u ps can be obtain through measuring s,R andθ∞.Then,comparing their values with those predicted by the theoretical models,we can identify the nature of the black hole lens.III.NUMERICAL ESTIMATION OF OBSER V ATIONAL GRA VITATIONAL LENSINGPARAMETERSIn this section,supposing that the gravitational field of the supermassive black hole at the galactic center of Milk Way can be described by the noncommutative Schwarzschild black hole metric,we estimate the numerical values for the coefficients and observables of the strong gravitational lensing,and then we study the effect of the spacetime noncommutative parameter ϑon the gravitational lensing.The mass of the central object of our Galaxy is estimated to be 2.8×106M ⊙and its distance is around 8.5kpc.For different ϑ,the numerical value of the minimum impact parameter u ps ,the angular position of the asymptotic relativistic images θ∞,the angular separation s and the relative magnification of the outermost relativistic image with the other relativistic images r m are listed in the table (II).It is easy to obtain thatTABLE II:Numerical estimation for main observables and the strong field limit coefficients for black hole at the center of our galaxy,which is supposed to be described by the noncommutative Schwarzschild black hole metric.R s is Schwarzschild radius.r m =2.5log R .ϑs (µarcsecs)u ps /R S¯b16.8706.82191.0000.160.021092.59808−0.4002316.86996.821701.000030.200.021162.59807−0.4001916.86936.800521.003140.240.023042.59752−0.4005816.85506.547741.041870.100.120.140.160.180.200.220.2416.869016.869216.869416.869616.8698Θ0.100.120.140.160.180.200.220.246.7856.7906.7956.8006.8056.8106.8156.820r m0.100.120.140.160.180.200.220.240.02110.02120.02130.02140.02150.02160.02170.0218 s0.100.150.200.250.300.350.4014.515.015.516.016.5qΘ0.100.150.200.250.300.350.406.06.26.46.66.8qr m0.100.150.200.250.300.350.400.0250.0300.035qsFIG.4:Strong gravitational lensing by the Galactic center black hole.Variation of the values of the angular positionθ∞,the relative magnitudes r m and the angular separation s with parameter√the table(II),we alsofind that as the parameterϑincreases,the minimum impact parameter u ps,the angular position of the relativistic imagesθ∞and the relative magnitudes r m decrease,but the angular separation s increases.From Fig.(4),wefind that in the noncommutative Schwarzschild black hole with the increase of parameter ϑ,the angular positionθ∞and magnitudes r m decreases more slowly,angular separation s increases more slowly than those in the Reissner-Norstr¨o m black hole spacetime.This means that the bending angle is smaller and the relative magnification of the outermost relativistic image with the other relativistic images is bigger in the noncommutative Schwarzschild black hole spacetime.In order to identify the nature of these two compact objects lensing,it is necessary for us to measure angular separation s and the relative magnification r m in the astronomical observations.Tables(II)tell us that the resolution of the extremely faint image is∼0.03µarc sec,which is too small.However,with the development of technology,the effects of the spacetime noncommutative constantϑon gravitational lensing may be detected in the future.IV.SUMMARYNoncommutative geometry may be a starting point to a quantum gravity.Spacetime noncommutative constant would be a new fundamental natural constant which can affect the classical gravitational effect such as gravitational lensing.Studying the strong gravitational lensing can help us to probe the spacetime noncommutative constant and the noncommutative gravity.In this paper we have investigated strongfield lensing in the noncommutative Schwarzschild black hole spacetime to study the influence of the spacetime noncommutative parameter on the strong gravitational lensing.The model was applied to the supermassive black hole in the Galactic center.Our results show that with the increase of the parameterϑthe minimum impact parameter u ps,the angular position of the relativistic imagesθ∞and the relative magnitudes r m decrease,and the angular separation s paring to the Reissner-Norstr¨o m black hole,wefind that the angular positionθ∞and magnitude r m decrease 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