Arthur Eddington

How to use this course

Arthur Eddington is remembered by the public for one photograph of an eclipse and by astrophysicists for a whole discipline. He showed how to compute the inside of a star from the outside, recognized that radiation pressure holds massive stars up, and proposed in 1920 that stars shine by turning hydrogen into helium. He was also the leading English interpreter of Einstein’s general relativity and, late in life, the author of a speculative theory of the constants of nature that few accepted.

His career also contains a famous error. From 1935 until his death he rejected the upper mass limit for white dwarfs found by Subrahmanyan Chandrasekhar. Lesson 10 treats that dispute in detail, with the physics on both sides. The companion course on Chandrasekhar tells the same story from the other side, with the same facts.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. SI units are used except in relativity, where \(G=c=1\) is stated when used.

Timeline

Kendal and Weston, 1882–1898

Arthur Stanley Eddington was born on 28 December 1882 in Kendal, Westmorland, in the north-west of England. Both parents came from Quaker families. His father, Arthur Henry Eddington, was headmaster of the Quaker school in Kendal. He died in the typhoid epidemic of 1884, when his son was not yet two. Sarah Ann Eddington moved with her two children to Weston-super-Mare in Somerset, where they lived on modest means. His mother and sister called him Stanley.

He was taught at home, then at a preparatory school, and from 1893 at Brynmelyn School in Weston. His teachers saw a strong mathematician, and in 1898, at fifteen, he won a scholarship to Owens College in Manchester.

The Quaker faith of his family shaped his whole life. It gave him his pacifism, his internationalism and a habit of quiet, inward religion that he later defended in public lectures. It also brought him, in 1918, close to prison.

Manchester and Cambridge, 1898–1906

At Owens College, Eddington spent a general first year and then specialized in physics. He lived at Dalton Hall, a Quaker hall of residence, where the Quaker mathematician J. W. Graham influenced him. In 1902 he took a BSc in physics with first-class honours and won a scholarship to Trinity College, Cambridge.

Cambridge mathematics was then organized around the Mathematical Tripos, a ranked examination whose top candidate was the Senior Wrangler. Eddington took Part I in 1904, after only two years, and came first. No second-year student had done this before. He took his MA in 1905 and worked briefly in the Cavendish Laboratory before turning to astronomy.

Choosing astronomy

In January 1906 he was nominated chief assistant to the Astronomer Royal at the Royal Observatory, Greenwich, and moved there the next month. The post gave him practical training in observation, instrument work and the reduction of data. It also started his first research programme, on the motions of stars.

Greenwich, the Plumian chair and the war, 1906–1918

At Greenwich Eddington analysed the proper motions of stars. Jacobus Kapteyn had found that stars near the Sun move in two preferred streams, and Eddington gave the statistical analysis of this result. His essay on stellar proper motions won the Smith’s Prize in 1907 and with it a fellowship at Trinity. His first book, Stellar Movements and the Structure of the Universe (1914), summarized the field.

George Darwin, Plumian Professor at Cambridge, died in December 1912. Eddington was elected to the chair early in 1913, at the age of 30. After Robert Ball’s death he also became director of the Cambridge Observatory in 1914, and he lived at the Observatory for the rest of his life with his sister. He was elected a Fellow of the Royal Society in May 1914.

Conscientious objection

When conscription came in 1916, Cambridge obtained his exemption on the grounds that his work was of national importance. In 1918 the Ministry of National Service appealed. At the June hearing Eddington declared himself a conscientious objector on religious grounds, and offered instead to serve with the Friends’ Ambulance Unit or as a farm labourer. The Astronomer Royal, Frank Dyson, intervened with a statement about a planned eclipse expedition. The tribunal granted a twelve-month exemption on condition that he continue his astronomical work. The war ended before it expired.

Einstein’s theory reaches England

As secretary of the Royal Astronomical Society during the war, Eddington received papers from the Dutch astronomer Willem de Sitter describing Albert Einstein’s general relativity, completed in November 1915. Communication with Germany was cut, and few English astronomers could follow the mathematics. Eddington could. His Report on the Relativity Theory of Gravitation (1918), written for the Physical Society, was the first full account in English. For a Quaker internationalist, testing a German theory with a British expedition just after the war also had a meaning beyond physics.

Radiative equilibrium and the standard model

For the general reader. No one can see inside a star. Eddington showed that one can still calculate it. If a star is a ball of hot gas held up by its own pressure, and if heat leaks outward as light, then a few equations fix its interior almost completely. His model of 1916–1926 gave central temperatures of millions of degrees and showed that the pressure of light itself matters in massive stars.

The equations

For a spherical star in equilibrium, with mass \(m(r)\) inside radius \(r\), density \(\rho\) and pressure \(P\),

Karl Schwarzschild had shown in 1906 that the outer layers of the Sun carry energy by radiation. Eddington made radiation the main transport mechanism throughout the star. In the diffusion approximation the radiation pressure \(P_r=\tfrac13 aT^4\) satisfies

where \(\kappa\) is the opacity (cross-section per unit mass) and \(L(r)\) the luminosity crossing radius \(r\). The total pressure is gas plus radiation, \(P=P_g+P_r\), with \(P_g=\rho kT/(\mu m_H)\) for mean molecular weight \(\mu\).

The standard model

Divide the two pressure gradients: \(dP_r/dP=\kappa L(r)/(4\pi c G m(r))\). Eddington assumed that \(\kappa L(r)/m(r)\) is roughly constant through the star. Then \(P_r/P\) is constant. Write \(P_g=\beta P\) and \(P_r=(1-\beta)P\) with \(\beta\) constant.

Derivation. Eliminate \(T\) between \(\beta P=\rho kT/(\mu m_H)\) and \((1-\beta)P=aT^4/3\). From the first, \(T=\beta P\mu m_H/(\rho k)\). Substituting, \((1-\beta)P=\frac a3\big(\beta P\mu m_H/(\rho k)\big)^4\), so \(P^3=\frac{3}{a}\frac{(1-\beta)}{\beta^4}\big(\frac{k}{\mu m_H}\big)^4\rho^4\). For a polytrope \(P=K\rho^{1+1/n}\), the Lane–Emden equation \(\frac{1}{\xi^2}\frac{d}{d\xi}\big(\xi^2\frac{d\theta}{d\xi}\big)=-\theta^n\) has its first zero at \(\xi_1=6.897\) for \(n=3\), and the mass is independent of the central density: \(M=4\pi(K/\pi G)^{3/2}\,\omega_3\) with \(\omega_3=-\xi_1^2\theta'(\xi_1)\). This independence is what makes \(\beta\) a function of \(M\) and \(\mu\) alone.

The quartic says that radiation pressure is negligible for small stars and grows steadily with mass. For \(\mu\approx0.6\) it supplies about 10% of the pressure near 20 solar masses and half near 140. Eddington saw in the growing role of radiation a natural reason why very massive stars are rare.

Mass, luminosity and the Eddington limit

For the general reader. In 1924 Eddington showed that a star’s brightness depends mainly on its mass. Double the mass and the star shines roughly ten times brighter. The same reasoning gives a maximum brightness for any object of a given mass, beyond which light pushes matter away faster than gravity can hold it. That ceiling, the Eddington luminosity, governs quasars and X-ray binaries today.

Luminosity of the standard model

Near the surface, where \(L(r)=L\) and \(m(r)=M\), the ratio of pressure gradients gives \(dP_r/dP=\kappa L/(4\pi cGM)\). In the standard model \(dP_r/dP=1-\beta\). Hence

Eddington’s 1924 paper compared this with stars of known mass in binary systems and found good agreement across a wide range, including dwarfs as well as giants. The result surprised him. He had expected dense dwarf stars to deviate from ideal-gas behaviour. The agreement showed that stellar matter stays an ideal gas at very high density, because the atoms are ionized and the free electrons and nuclei are tiny. Modern main-sequence stars follow roughly \(L\propto M^{3.5}\) in the solar range, the exponent depending on the opacity law.

The Eddington luminosity

Consider fully ionized hydrogen. Radiation of flux \(F=L/(4\pi r^2)\) pushes on each electron with force \(\sigma_T F/c\), where \(\sigma_T\) is the Thomson cross-section, and the electron drags its proton along by electrostatic attraction. Gravity pulls the proton with force \(GMm_p/r^2\). Both forces fall off as \(1/r^2\), so their ratio is the same at every radius.

The standard-model formula already contains the limit: \(L=(4\pi cGM/\kappa)(1-\beta)\) cannot exceed \(4\pi cGM/\kappa\), reached as \(\beta\to0\). For electron scattering \(\kappa=\sigma_T/m_p\), and the two expressions coincide.

Subatomic energy: the 1920 fusion proposal

For the general reader. In 1920 nobody knew what made the Sun shine. Gravity could supply energy for only tens of millions of years, far less than the age of the Earth. Speaking at Cardiff, Eddington pointed to a laboratory measurement: a helium atom weighs slightly less than four hydrogen atoms. If stars build helium from hydrogen, the missing mass becomes energy, enough for billions of years. The idea was right, two decades before anyone knew how the reaction worked.

The timescale problem

Hermann von Helmholtz and Lord Kelvin proposed that the Sun shines by slow contraction. The energy available is of order \(GM^2/R\), which lasts a time

Geologists and biologists needed far longer. Eddington also had a direct astronomical argument: the period of the Cepheid δ Cephei had stayed constant to a precision that contraction could not allow (Lesson 07).

The Cardiff address

On 24 August 1920 Eddington addressed the mathematics and physics section of the British Association in Cardiff, under the title “The Internal Constitution of the Stars”. Francis Aston had just measured atomic masses precisely with his mass spectrograph. Eddington used the result that helium is lighter than four hydrogen atoms by about 0.8% (the modern value is 0.7%). By Einstein’s \(E=mc^2\), a star containing a few per cent of hydrogen could shine for billions of years by forming helium. He added that if stars use subatomic energy “to maintain their great furnaces”, humans might one day learn to control it.

The main objection was that stellar temperatures of \(10^7\) K seemed far too low for protons to overcome their electric repulsion. Eddington’s reply became famous: the critics should “go and find a hotter place”. The answer came from quantum tunnelling, worked out by George Gamow in 1928 and applied to stars by Robert Atkinson and Fritz Houtermans in 1929. Hans Bethe identified the proton–proton chain and the CNO cycle in 1938–39. Eddington himself, through the 1920s, also entertained the complete annihilation of protons and electrons as an energy source, an idea that did not survive.

Pulsating stars

For the general reader. Cepheid variable stars brighten and dim with clockwork regularity, and their periods reveal their luminosities, which makes them distance markers across the galaxy. In 1916 many astronomers explained them as eclipsing pairs. Eddington, following an idea of Harlow Shapley, treated each Cepheid as a single star that breathes in and out, and asked what keeps the oscillation going.

A one-zone model

Let a thin outer shell of mass \(m\) sit at radius \(R\) above a core of mass \(M\), supported by gas pressure \(P\) acting on area \(4\pi R^2\). Then \(m\ddot R=-GMm/R^2+4\pi R^2P\). In equilibrium \(4\pi R_0^2P_0=GMm/R_0^2\). Under adiabatic compression of the interior, \(P\propto\rho^{\Gamma_1}\propto R^{-3\Gamma_1}\).

Derivation. Put \(R=R_0(1+x)\). To first order, \(-GM/R^2\approx -(GM/R_0^2)(1-2x)\) and \(4\pi R^2P/m\approx (GM/R_0^2)(1+2x-3\Gamma_1x)\). Hence \(R_0\ddot x=-(GM/R_0^2)(3\Gamma_1-4)x\). August Ritter had found the period–density law in 1879; Eddington gave it a full treatment for a star in radiative equilibrium in 1917–18.

What keeps it going

An adiabatic oscillation neither gains nor loses energy, while real stars lose heat and should damp. Eddington argued in The Internal Constitution of the Stars that some layer must act like a valve: it must trap heat when compressed and release it when expanded, as in a heat engine. If opacity rose on compression, radiation would be dammed up at maximum compression and released during expansion, doing positive work. In ordinary stellar matter opacity falls on compression, so Eddington could not find the layer. In the 1950s Sergei Zhevakin, and then John Cox and others, located it in the zone where helium is partly ionized. Eddington’s valve, now called the κ-mechanism, is the accepted explanation of Cepheid pulsation.

Relativity and the 1919 eclipse

For the general reader. Einstein predicted that the Sun’s gravity bends passing starlight by 1.75 seconds of arc, twice the amount a Newtonian calculation gives. Stars near the Sun can be seen only during a total eclipse. In 1919 two British expeditions photographed the eclipse of 29 May from Brazil and from the island of Príncipe off West Africa. Their announcement on 6 November made Einstein world-famous overnight.

The prediction

The factor 2 comes from space curvature. In isotropic coordinates the weak-field metric is \(ds^2=-(1-2\Phi')c^2dt^2+(1+2\gamma\Phi')d\vec x^2\) with \(\Phi'=GM/(c^2r)\). The time part alone gives the Newtonian value; the space part, with \(\gamma=1\) in general relativity, adds an equal amount. Eddington, in The Mathematical Theory of Relativity (1923), wrote the Schwarzschild solution with undetermined coefficients in the expansion of the metric so that each test measures one of them. His parameters, later extended by Howard Robertson and others, became the parametrized post-Newtonian formalism used in all modern tests. The deflection is \(\tfrac{1+\gamma}{2}\times1.75''\).

The expeditions

Frank Dyson planned two expeditions. Andrew Crommelin and Charles Davidson went to Sobral in Brazil; Eddington and Edwin Cottingham went to Príncipe. Clouds covered Príncipe for most of totality, and only a few plates showed usable stars. The 1920 report of Dyson, Eddington and Davidson gave

• Sobral, 4-inch lens: \(1.98''\pm0.16''\);
• Príncipe: \(1.61''\pm0.30''\);
• Sobral astrographic: about \(0.93''\), set aside because the images were blurred, attributed at the time to heating of the mirror.

Critics later argued that Eddington discarded the astrographic plates to favour Einstein. Historians who have studied the records, notably Daniel Kennefick, conclude that the decision was reasonable and was taken by Dyson’s team at Greenwich. A 1979 remeasurement of the Sobral plates with modern equipment supported the original conclusion. Later radio measurements confirm \(\gamma=1\) to better than one part in ten thousand.

Eddington–Finkelstein coordinates

In 1924 Eddington compared Alfred North Whitehead’s theory of gravity with Einstein’s and, in passing, wrote the Schwarzschild metric in a new time coordinate. David Finkelstein rediscovered the transformation in 1958 and recognized what it meant: the surface \(r=2GM/c^2\) is not a true singularity. With \(G=c=1\), set \(v=t+r_*\), where \(r_*=r+2M\ln|r/2M-1|\). Then

which is regular at \(r=2M\).

The unstable static universe

For the general reader. Einstein’s first cosmological model of 1917 was a static universe held in balance by a cosmological constant. In 1930 Eddington showed that the balance is unstable, like a pencil standing on its point. He then learned that his former student Georges Lemaître had already found expanding solutions in 1927, and he made sure the world read them.

For a homogeneous, isotropic universe of pressureless matter with scale factor \(a(t)\), spatial curvature \(k\) and cosmological constant \(\Lambda\) (units \(c=1\)),

Proof. Static means \(\ddot a=0\), so \(\Lambda=4\pi G\rho_E\). Put \(a=a_E(1+\epsilon)\). Then \(\rho=\rho_E(1-3\epsilon)\) to first order, and

So \(\epsilon\propto e^{\pm\sqrt{\Lambda}\,t}\), and the growing mode takes over. An expansion lowers the density, weakens gravity relative to \(\Lambda\), and speeds the expansion further.

Lemaître

Georges Lemaître, a Belgian priest and physicist, had spent the academic year 1923–24 in Cambridge working with Eddington. In 1927 he published, in a little-read Belgian journal, a model expanding from the Einstein state, together with a relation between distance and recession velocity. Early in 1930 Lemaître reminded Eddington of the paper. Eddington drew attention to it in print and arranged for an English translation in the Monthly Notices (1931). The model that starts arbitrarily close to the static state in the infinite past and expands toward de Sitter space is the Eddington–Lemaître universe. Eddington preferred it to a beginning in time, which he found philosophically repugnant. His popular book The Expanding Universe (1933) brought these ideas to a wide public.

White dwarfs and relativistic degeneracy

For the general reader. White dwarfs pack the mass of the Sun into a ball the size of the Earth. Eddington noticed in 1926 that such a star posed a puzzle about how it could ever cool. Quantum physics solved the puzzle and then raised a bigger one: Chandrasekhar showed that a white dwarf heavier than about 1.4 Suns cannot exist. Eddington, the leading authority on stars, rejected that conclusion in public from 1935 until his death. He was wrong, and the episode is now part of the history of black holes.

Sirius B and Eddington’s paradox

Walter Adams’s spectra of Sirius B (1915) showed a hot star with a small radius and hence a mean density tens of thousands of times that of water. Eddington accepted the density and suggested a test: such a compact star should show a measurable gravitational redshift. Adams reported one in 1925, though modern measurements show the true shift is several times larger than his value.

In 1926, in The Internal Constitution of the Stars, Eddington posed a paradox. Matter this dense would need energy to re-expand into normal atoms when it cooled. A cold white dwarf would have to be in a state with less energy than ordinary matter, which seemed impossible, so the star could never cool down. Later that year Ralph H. Fowler resolved the problem using the new Fermi–Dirac statistics. At high density the electrons fill the lowest momentum states up to the Fermi momentum \(p_F\), and they exert pressure even at zero temperature.

The limiting mass

A polytrope \(P=K\rho^{1+1/n}\) has mass–radius relation \(M\propto R^{(3-n)/(1-n)}\). In the non-relativistic regime \(n=3/2\), so \(R\propto M^{-1/3}\): heavier white dwarfs are smaller and denser. As the density rises the electrons become relativistic and \(n\to3\). For \(n=3\) the mass no longer depends on the radius. Edmund Stoner and Wilhelm Anderson found mass limits in 1929–30 with uniform-density models. Subrahmanyan Chandrasekhar derived the limit in 1930 on his voyage from India to England, published it in 1931, and in 1934–35 computed exact models with the full relativistic equation of state (Lev Landau also found the limit independently in 1932). The limit is

about \(1.4M_\odot\) for \(\mu_e=2\) (the usually quoted value is \(1.44M_\odot\)). A cold star heavier than this cannot be supported by electron degeneracy and must contract further.

11 January 1935

Eddington had examined Chandrasekhar’s thesis in 1933 with Milne, and at Trinity he followed the younger man’s work with interest, hoping it would help settle his own dispute with Milne over stellar models. On 11 January 1935 Chandrasekhar presented his exact models at the Royal Astronomical Society in London. Eddington spoke immediately afterwards, on a paper whose contents he had not disclosed to Chandrasekhar in advance. He did not dispute the mathematics. He argued that the relativistic formula for degenerate pressure was itself wrong, because in his view it combined special relativity with a non-relativistic quantum theory in an illegitimate way. In his corrected physics the law \(P\propto\rho^{5/3}\) would hold at all densities, so every star could settle down as a stable white dwarf. He concluded that there should be “a law of Nature to prevent a star from behaving in this absurd way” (The Observatory, 1935). Edward Arthur Milne also opposed Chandrasekhar’s conclusions.

Eddington repeated his criticism at the International Astronomical Union in Paris in July 1935 and at Harvard in 1936, and published it in the Monthly Notices (1935) and the Proceedings of the Royal Society (1935). In private, Niels Bohr, Léon Rosenfeld and Wolfgang Pauli told Chandrasekhar that Eddington’s argument had no basis, but they declined to enter the controversy in print. Christian Møller and Chandrasekhar (1935), Rudolf Peierls (1936), and finally Paul Dirac, Peierls and Maurice Pryce (1942) published rebuttals of Eddington’s physics. Eddington held his position to the end, restating it in 1940. Most textbooks followed Chandrasekhar and mentioned Eddington’s view only in footnotes.

The dispute did not end their personal relations. They remained on friendly terms and corresponded until Eddington’s death. Chandrasekhar admired Eddington throughout his life and in 1982 gave the centenary lectures published as Eddington: The Most Distinguished Astrophysicist of His Time (1983). The physics is settled. White dwarfs above the limit do not exist. Stars whose cores exceed it collapse into neutron stars or black holes, and white dwarfs pushed over it by accretion explode as type Ia supernovae.

Philosopher, popularizer and Fundamental Theory, 1920–1944

After 1919 Eddington was the most famous scientist in Britain after Einstein himself. At the joint meeting of the Royal Society and the Royal Astronomical Society on 6 November 1919, Ludwik Silberstein reportedly told him that he must be one of only three people who understood relativity. Eddington hesitated, then said he was trying to think who the third might be.

He wrote a series of books for general readers: Space, Time and Gravitation (1920), Stars and Atoms (1927), The Nature of the Physical World (1928), The Expanding Universe (1933), New Pathways in Science (1935) and The Philosophy of Physical Science (1939). The Nature of the Physical World, from his Gifford Lectures in Edinburgh in 1927, opens with his two tables: the solid one he writes on and the scientific one, mostly empty space crossed by electric charges. The same book popularized the phrase “arrow of time” for the one-way direction given by increasing entropy. He gave the Swarthmore Lecture to the Quakers in 1929, argued that physics leaves room for religious experience without proving anything about it, and chaired the National Peace Council from 1941 to 1943.

Fundamental Theory

From the late 1920s Eddington tried to derive the dimensionless constants of physics from pure reasoning. He argued first that the inverse fine-structure constant \(1/\alpha\) must equal 136 exactly, and when measurements came closer to 137, he argued for 137. He also claimed that the number of protons in the universe is exactly \(N=136\times2^{256}\approx1.57\times10^{79}\), now called the Eddington number. The work appeared in Relativity Theory of Protons and Electrons (1936) and in Fundamental Theory, which Edmund Whittaker prepared after his death and published in 1946. Most physicists considered it numerology. Historians have noted that Eddington believed his rejection of relativistic degeneracy was tied to this programme, which helps explain how firmly he held it.

Honours and offices

He received the Gold Medal of the Royal Astronomical Society, the Bruce Medal and the Henry Draper Medal (all 1924), the Royal Medal of the Royal Society (1928), a knighthood (1930) and the Order of Merit (1938). He was President of the Royal Astronomical Society (1921–23), of the Physical Society (1930–32) and of the International Astronomical Union (1938–44).

Death and legacy

Eddington never married. He lived at the Cambridge Observatory with his sister, cycled long distances and kept careful records of his rides. In 1944 he fell ill with cancer. He died on 22 November 1944 at the Evelyn Nursing Home in Cambridge, aged 61, and was buried in his mother’s grave. He was still President of the International Astronomical Union.

Legacy

• Stellar structure: his radiative models, the standard model and the mass–luminosity relation founded theoretical astrophysics. The Internal Constitution of the Stars (1926) remained the reference for a generation.
• Stellar energy: the 1920 proposal that stars convert hydrogen to helium was confirmed by Bethe and others in 1938–39.
• Radiation pressure: the Eddington luminosity is a basic quantity in the study of accreting black holes, quasars and the most massive stars.
• Relativity: the 1919 eclipse result, his textbook, his parametrized metric and the Eddington–Finkelstein coordinates.
• Cosmology: the instability of the static universe and the promotion of Lemaître’s expanding model.
• Error: his rejection of the Chandrasekhar limit, held from 1935 to 1944, is the best-known example of a great authority resisting a correct result in astrophysics. Chandrasekhar shared the 1983 Nobel Prize in Physics for work on the structure and evolution of stars.

The Royal Astronomical Society awards the Eddington Medal for theoretical astrophysics, first given in 1953.

Connections

People linked to Arthur Eddington across this collection. A name without a link has no page here yet. See Arthur Eddington in the network of all 337 lives →

Students

• Georges Lemaître 1923-1924
• Hermann Bondi
• Leslie Comrie

Influenced by

• Albert Einstein
• Jacobus Kapteyn
• Karl Schwarzschild

Influenced

• Hans Bethe

Colleagues and collaborators

• Jean Perrin
• Frank Dyson 1906-1920
• Ralph H. Fowler
• Willem de Sitter

Rivals

• James Jeans
• Subrahmanyan Chandrasekhar 1935-1944
• Edward Arthur Milne

Also mentioned in this life

• Niels Bohr
• John Dalton
• Paul Dirac
• Enrico Fermi
• George Gamow
• Hermann von Helmholtz
• William Thomson, Lord Kelvin
• Wolfgang Pauli

Fields

• astrophysics 6 lives
• general relativity 4 lives
• cosmology 7 lives

On CoursesHub

• General Relativity
• Cosmology

Sources and further reading

Biography

1. Arthur Stanley Eddington, MacTutor History of Mathematics.
2. Arthur Eddington, Wikipedia (with extensive references).
3. The Chandrasekhar–Eddington dispute, MacTutor.
4. H. C. Plummer, Arthur Stanley Eddington 1882–1944, Obituary Notices of Fellows of the Royal Society 5 (1945).
5. A. V. Douglas, The Life of Arthur Stanley Eddington, Nelson, 1956.
6. S. Chandrasekhar, Eddington: The Most Distinguished Astrophysicist of His Time, Cambridge University Press, 1983.
7. M. Stanley, Practical Mystic: Religion, Science, and A. S. Eddington, University of Chicago Press, 2007.
8. A. I. Miller, Empire of the Stars, Houghton Mifflin, 2005.

Physics

1. A. S. Eddington, The internal constitution of the stars, The Observatory 43 (1920) 341–358.
2. F. W. Dyson, A. S. Eddington, C. Davidson, A determination of the deflection of light by the Sun’s gravitational field, Phil. Trans. R. Soc. A 220 (1920) 291–333.
3. A. S. Eddington, The Mathematical Theory of Relativity, Cambridge University Press, 1923.
4. A. S. Eddington, On the relation between the masses and luminosities of the stars, MNRAS 84 (1924) 308–332.
5. A. S. Eddington, A comparison of Whitehead’s and Einstein’s formulæ, Nature 113 (1924) 192.
6. A. S. Eddington, The Internal Constitution of the Stars, Cambridge University Press, 1926.
7. R. H. Fowler, On dense matter, MNRAS 87 (1926) 114–122.
8. A. S. Eddington, On the instability of Einstein’s spherical world, MNRAS 90 (1930) 668–678.
9. A. S. Eddington, On “relativistic degeneracy”, MNRAS 95 (1935) 194–206.
10. R. E. Peierls, Note on the derivation of the equation of state for a degenerate relativistic gas, MNRAS 96 (1936) 780–784.
11. Chandrasekhar limit, Wikipedia (history and primary references).
12. A century of light-bending measurements, arXiv:2002.01179.
13. Eddington–Finkelstein coordinates, Wikipedia.
14. D. Kennefick, No Shadow of a Doubt: The 1919 Eclipse That Confirmed Einstein’s Theory of Relativity, Princeton University Press, 2019.