卡尔·史瓦西Karl Schwarzschild

卡尔·史瓦西的父母是Henrietta Sabel和Moses Martin Schwarzschild。这个家庭是犹太人，史瓦西的父亲是法兰克福商业界的一位富裕成员。Dieke在[1]中写道：-

从他母亲，一个活泼、温暖的人，史瓦西无疑继承了他快乐、外向的个性；从他父亲，继承了持续努力工作的能力。

史瓦西 是他父母六个孩子中最大的，有四个弟弟和一个妹妹。他也是一个更大的亲戚大家庭的一员，这些人有教养，兴趣主要在艺术和音乐上。然而，他并不是从直系或旁系家庭中获得对科学的热爱的，因为他成为家族中第一位科学家。

他在法兰克福的一所犹太小学上学，直到十一岁，然后他进入了那里的文理中学。正是在这个阶段，他对天文学产生了兴趣，并节省零花钱为自己购买材料，如透镜，以便制作望远镜。史瓦西的父亲与J 保罗·爱泼斯坦教授关系友好，后者是Philanthropin学院的教授，并拥有自己的私人天文台。他们的友谊源于对音乐的共同兴趣。爱泼斯坦教授有一个儿子，Paul 保罗·爱泼斯坦，比史瓦西大两岁，两个男孩成为了好朋友。他们共同对天文学感兴趣，史瓦西学会了如何使用望远镜，还从他的朋友Paul 保罗·爱泼斯坦那里学到了一些高等数学。

在很大程度上，正是他通过与保罗·爱泼斯坦的友谊所学到的东西，使史瓦西在十六岁时掌握了天体力学。这种掌握如此之深，以至于他在这个年龄还在法兰克福中学时，就写了他的前两篇关于双星轨道理论的论文。这些论文于1890年发表在Astronomische Nachrichten上。

史瓦西在1891-93两年间于斯特拉斯堡大学学习，期间学到了大量实用天文学知识，随后在慕尼黑大学获得博士学位。他的学位论文是关于将儒勒·昂利·庞加莱的旋转体稳定构型理论应用于卫星的潮汐变形以及皮埃尔·西蒙·拉普拉斯的太阳系起源，由Hugo von Seeliger指导。史瓦西从Seeliger的教学中获得了极大的启发，这影响了他的一生。

获得博士学位后，史瓦西 被任命为维也纳郊区奥塔克林的冯·库夫纳天文台的助理。他于1896年10月上任，任职至1899年6月。在天文台期间，他研究利用照相底片确定恒星视亮度的方法[4]：-

……一项长期持续的研究，既需要细节上的精益求精，也需要构思上的卓越才华。

他于1899年6月离开冯·库夫纳天文台，成为慕尼黑大学的Privatdozent，并提交了关于测量恒星星等的工作作为他的教授资格论文（Habilitation）学位论文Beiträge zur photographischen Photometrie der Gestirne Ⓣ（对恒星照相测光的贡献）。这项工作使他做出了几项重要发现。首先，他看到他测量的照相星等与已列表的目视星等不同。他意识到差异是由于恒星颜色不同造成的。他从冯·库夫纳天文台选择367颗恒星进行测量，其中包括两颗变星。用他的照相方法测得的星等变化范围远大于目视星等的变化范围。他正确地认识到，这是由于变星在其周期中表面温度的变化。

在1900年于海德堡举行的德国天文学会会议上，史瓦西讨论了空间是非欧几里得的可能性。同年，他发表了一篇论文，给出空间曲率半径的下限为2500光年。他还研究了太阳的辐射压，并假设彗尾由能很好反射光的球形粒子组成，计算了彗尾中粒子的大小。他知道辐射压必须克服引力，也知道粒子不散射光。这使他推断出粒子的直径必须在0.07到1.5微米之间。

从1901年到1909年，他是哥廷根大学的非常任教授，同时也是那里天文台的台长。在哥廷根，他与菲利克斯·克莱因、大卫·希尔伯特和赫尔曼·闵可夫斯基合作。不到一年，他就被提升为常任教授。亚瑟·爱丁顿在[4]中写道：-

对于一位在数学和物理所有分支都有广泛兴趣的人来说，这样的环境一定非常适宜……

史瓦西在哥廷根期间发表了关于电动力学和几何光学的论文。他在哥廷根天文台工作期间进行了大规模的恒星亮度巡天，出版了Aktinometrie Ⓣ（《辐射测量学》）（第一部分于1910年，第二部分于1912年）。1906年，他研究了能量通过辐射在恒星中的传输，并发表了一篇关于太阳大气辐射平衡的重要论文。1909年10月22日，他与Else Posenbach结婚，她是哥廷根一位外科教授的女儿。他们有三个孩子：Agathe、Martin（生于1912年5月31日，后来成为普林斯顿大学天文学教授）和Alfred。

结婚后，在1909年底，史瓦西离开哥廷根，就任波茨坦天体物理天文台台长。这是德国天文学家所能获得的最负盛名的职位，他非常成功地担任了这一职务。他有机会研究1910年波茨坦探险队前往特内里费拍摄的爱德蒙·哈雷彗星回归的照片。他还在光谱学方面做出了重大贡献，这成为他此时非常感兴趣的一个主题。

1913年，史瓦西当选为柏林科学院院士。在他的入院演讲中，他很好地表明了自己对科学的态度（例如参见[4]）：——

数学、物理学、化学、天文学，齐步前进。无论哪个落后，都会被拖拽着跟上。无论哪个加速前进，都会帮助其他学科。天文学与整个精确科学圈子之间有着最紧密的团结。……从这个方面来看，我可以认为我的兴趣从未局限于月球之外的事物，而是沿着从那里延伸到我们月下知识的线索前行；我常常对天空不忠。这是一种对普遍性的冲动，它被我的老师Seeliger无意中强化，后来又受到Felix 菲利克斯·克莱因和哥廷根整个科学圈子的滋养。那里的座右铭是：数学、物理学和天文学构成一门知识，就像希腊文化一样，只有作为一个完美的整体才能被理解。

1914年8月战争爆发时，史瓦西自愿服兵役。他曾在比利时服役，负责一个气象站；在法国被分配到炮兵部队，负责计算导弹弹道；之后又去了俄罗斯。

在俄国期间，他写了两篇关于阿尔伯特·爱因斯坦相对论的论文和一篇关于马克斯·普朗克的quantum theory的论文。那篇量子理论论文解释了斯塔克效应，即氢光谱线在电场中分裂（分裂量正比于场强），可以从量子理论的假设得到证明。几乎同时，慕尼黑的一位P 爱泼斯坦独立地证明了这一点。

史瓦西的相对论论文给出了阿尔伯特·爱因斯坦广义引力方程的第一个精确解，使人们理解了点质量附近空间的几何结构。他把第一篇论文寄给了阿尔伯特·爱因斯坦，后者回复道：——

我没想到人们能以如此简单的方式表述这个问题的精确解。

这两篇论文中提出的工作为后来对黑洞的研究奠定了基础，表明质量足够大的物体其逃逸速度将超过光速，因而无法被看见。然而，史瓦西本人明确表示，他认为这一理论解在物理上没有意义，因此非常清楚地表明他并不相信黑洞的物理实在性。

他在俄国期间患上了一种叫做天疱疮的疾病，这是一种罕见的自身免疫性皮肤水疱病。患此病的人，其免疫系统将皮肤细胞误认为外来物并攻击它们，导致疼痛的水疱。在史瓦西的时代，尚无已知的治疗方法，1916年3月他因病被送回家，两个月后去世。

亚瑟·爱丁顿在[4]中写道：-

他对知识的广泛贡献使人将他与儒勒·昂利·庞加莱相提并论；但史瓦西的志趣更为实际，他对仪器方法的设计与分析的成功同样感到欣喜。……他的乐趣在于不受限制地漫游于知识的牧场，并且像游击队长一样，他的攻击落在最意想不到的地方。

史瓦西在42岁、正值成就巅峰时去世，因此他一生中获得的荣誉相对较少也就不足为奇了。然而，他于1905年当选为哥廷根科学学会会员，1909年6月11日当选为皇家天文学会 of London会士，1913年当选为德国科学院会士。他也获得了身后的荣誉，特别是一座天文台，于1960年在陶滕堡建立，作为德国科学院的附属研究所，以他的名字命名。献词中将他描述为：-

……过去一百年间最伟大的德国天文学家。

德国统一后，该研究所于1992年重建，并更名为“陶滕堡史瓦西图林根州立天文台”。德国天文学会于1959年设立了一个以他命名的特别讲座，并设立了史瓦西奖章。第一位获得者是Martin Schwarzschild，他的儿子。

Karl Schwarzschild's parents were Henrietta Sabel and Moses Martin Schwarzschild. The family was Jewish, with Karl's father being a well-off member of the business community in Frankfurt. Dieke writes in [1]:-

From his mother, a vivacious, warm person, Schwarzschild undoubtedly inherited his happy, outgoing personality; from his father, a capacity for sustained hard work.

Karl was the oldest of his parents six children, having four younger brothers and one sister. He was part of a larger extended family of relatives, too, who were cultured people with interests mainly in art and music. He did not, however, get his love of science from his immediate or extended family since he became the first member of his family to become a scientist.

He attended a Jewish primary school in Frankfurt up to the age of eleven, then he entered the Gymnasium there. It was at this stage that he became interested in astronomy and saved his pocket money to buy himself materials such as lens from which he could construct a telescope. Karl's father was friendly with Professor J Epstein, who was professor at the Philanthropin Academy and had his own private observatory. Their friendship arose through a common interest in music. Professor Epstein has a son, Paul Epstein, who was two years older than Karl and the two boys became good friends. They shared an interest in astronomy, and Karl learnt how to use a telescope and also learnt some advanced mathematics from his friend Paul Epstein.

It was in large part what he learnt through his friendship with Epstein which led to Schwarzschild mastering celestial mechanics by the age of sixteen. Such was this mastery that he wrote his first two papers on the theory of orbits of double stars at this age while still at the Frankfurt Gymnasium. The papers were published in Astronomische Nachrichten in 1890.

Schwarzschild studied at the University of Strasbourg during the two years 1891-93 where he learnt a great deal of practical astronomy, then at the University of Munich where he obtained his doctorate. His dissertation, on an application of Poincaré's theory of stable configurations of rotating bodies to tidal deformation of moons and to Laplace's origin of the solar system, was supervised by Hugo von Seeliger. Schwarzschild found great inspiration from Seeliger's teaching which influenced him throughout his life.

After the award of his doctorate, Schwarzschild was appointed as an assistant at the Von Kuffner Observatory in Ottakring which is a suburb of Vienna. He took up his appointment in October 1896 and held it until June 1899. While at the Observatory he worked on ways to determine the apparent brightness of stars using photographic plates [4]:-

... a long and sustained investigation, which required much perfection of detail as well as brilliance of conception.

He left the Von Kuffner Observatory in June 1899 and became a Privatdozent at the University of Munich, having submitted his work on measuring stellar magnitudes as his habilitation thesis Beiträge zur photographischen Photometrie der Gestirne Ⓣ. This work led him to make several important discoveries. First he saw that the photographic magnitudes which he measured differed from the visual magnitudes which had been tabulated. He realised that the difference was due to different colours of the stars. Choosing 367 stars to measure from the Von Kuffner Observatory, he included two variable stars. The range of magnitude change as measured by his photographic methods was much greater than the range of change in visual magnitude. He realised, correctly, that this was due to changes in surface temperature of the variable star through its cycle.

At a meeting of the German Astronomical Society in Heidelberg in 1900 Schwarzschild discussed the possibility that space was non-Euclidean. In the same year he published a paper giving a lower limit for the radius of curvature of space as 2500 light years. He also worked on radiation pressure from the sun and, with the assumption that the tails of comets consisted of spherical particles which reflected light well, he calculated the size of the particles in the tails. He knew that radiation pressure had to overcome gravitation, and he also knew that the particles did not scatter light. This allowed him to deduce that the diameters of the particles had to be between 0.07 and 1.5 microns.

From 1901 until 1909 he was extraordinary professor at Göttingen and also director of the Observatory there. In Göttingen he collaborated with Klein, Hilbert and Minkowski. In less than a year he had been promoted to Ordinary Professor. Eddington writes in [4]:-

To a man of his wide interests in all branches of mathematics and physics the surroundings must have been very congenial ...

Schwarzschild published on electrodynamics and geometrical optics during his time at Göttingen. He carried out a large survey of stellar magnitudes while at the Göttingen Observatory, publishing Aktinometrie Ⓣ (the first part in 1910, the second in 1912). In 1906 he studied the transport of energy through a star by radiation and published an important paper on radiative equilibrium of the atmosphere of the sun. He married Else Posenbach, the daughter of a professor of surgery at Göttingen, on 22 October 1909. They had three children, Agathe, Martin who was born on 31 May 1912 and went on to became a professor of astronomy at Princeton, and Alfred.

After his marriage, near the end of 1909, Schwarzschild left Göttingen to take up an appointment as director of the Astrophysical Observatory in Potsdam. This was the most prestigious post available for an astronomer in Germany and he filled the position with great success. He had the opportunity to study photographs of the return of Halley's comet in 1910 taken by a Potsdam expedition to Tenerife. He also made major contributions to spectroscopy which became a topic of great interest to him around this time.

In 1913 Schwarzschild was elected to the Berlin Academy. In his admission speech he gave a good indication of his attitude towards science (see for example [4]):-

Mathematics, physics, chemistry, astronomy, march in one front. Whichever lags behind is drawn after. Whichever hastens ahead helps on the others. The closest solidarity between astronomy and the whole circle of exact science. ... from this aspect I may count it well that my interest has never been limited to the things beyond the moon, but has followed the threads which spin themselves from there to our sublunar knowledge; I have often been untrue to the heavens. That is an impulse to the universal which was strengthened unwittingly by my teacher Seeliger, and afterwards was further nourished by Felix Klein and the whole scientific circle at Göttingen. There the motto runs that mathematics, physics, and astronomy constitute one knowledge, which, like the Greek culture, is only comprehended as a perfect whole.

On the outbreak of war in August 1914 Schwarzschild volunteered for military service. He served in Belgium where he was put in charge of a weather station, France where he was assigned to an artillery unit and given the task of calculating missile trajectories, and then Russia.

While in Russia he wrote two papers on Einstein's relativity theory and one on Planck's quantum theory. The quantum theory paper explained that the Stark effect, namely the splitting of the spectral lines of hydrogen by an electric field (the amount being proportional to the field strength), could be proved from the postulates of quantum theory. This was proved independently by a P Epstein from Munich at almost the same time.

Schwarzschild's relativity papers give the first exact solution of Einstein's general gravitational equations, giving an understanding of the geometry of space near a point mass. He sent the first paper to Einstein who replied:-

I had not expected that one could formulate the exact solution of the problem in such a simple way.

The work presented in these two papers formed the basis for a later study of black holes, showing that bodies of sufficiently large mass would have an escape velocity exceeding the speed of light and so could not be seen. However, Schwarzschild himself makes clear that he believes that the theoretical solution is physically meaningless, so making it very clear that he did not believe in the physical reality of black holes.

He contracted an illness while in Russia called pemphigus, which is a rare autimmune blistering disease of the skin. For people with this disease the immune system mistakes the cells in the skin as foreign and attacks them causing painful blisters. In Schwarzschild's time there was no known treatment and, after being invalided home in March 1916, he died two months later.

Eddington writes in [4]:-

The wide range of his contributions to knowledge suggests a comparison with Poincaré; but Schwarzschild's bent was more practical, and he delighted as much in the design of instrumental methods as in the triumphs of analysis. ... his joy was to range unrestricted over the pastures of knowledge, and, like a guerrilla leader, his attacks fell where they were least expected.

Since Schwarzschild died at age 42 at the height of his achievements, it is not too surprising that he received relatively few honours in his lifetime. He was, however, elected to the Scientific Society of Göttingen in 1905, the Royal Astronomical Society of London on 11 June 1909, and the German Academy of Sciences in 1913. He did receive posthumous honours too, in particular an observatory, founded in 1960 in Tautenburg as an affiliated Institute of the German Academy of Sciences, was named after him. The dedication described him as:-

... the greatest German astronomer of the last hundred years.

After the reunification of Germany, the Institute was refounded in 1992 and renamed "Thüringer Landessternwarte 'Karl Schwarzschild' Tautenburg". The German Astronomical Society established a special lectureship in his honour in 1959 and a Karl Schwarzschild Medal. The first recipient was Martin Schwarzschild, his son.