Republication of: New mechanics of material systems

This is an English translation of the first of two papers by Myron Mathisson, first published in German in 1931 and 1937, in which he presented the correct formulation of equations of motion of spinning bodies in general relativity (today known as the Mathisson–Papapetrou equations). The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note and Mathisson’s brief biography, both written by Andrzej Trautman.     

Republication of: The physical reality of some normal spaces of Bianchi

This is an English translation of the first of two papers by Tullio Levi-Civita, first published in 1917 and 1919. The papers are remarkable as being among the earliest in which exact solutions of Einstein’s equations were derived. Of the two solutions presented, the first (republished as this Golden Oldie) is better known today as the Bertotti-Robinson solution, and the second one (republished as an accompanying Golden Oldie) is the gravitational field of an infinite cylinder. The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Malcolm MacCallum, and by a brief biography of the author, compiled from internet sources by Andrzej Krasiński.     

Republication of: Einsteinian <Emphasis Type="Italic">ds</Emphasis><Superscript>2</Superscript> in Newtonian fields. IX: The analog of the logarithmic potential

This is an English translation of the second of two papers by Tullio Levi-Civita, first published in 1917 and 1919. The papers are remarkable as being among the earliest in which exact solutions of Einstein’s equations were derived. Of the two solutions presented, the first (republished as an accompanying Golden Oldie) is better known today as the Bertotti-Robinson solution, and the second one (republished as this Golden Oldie) is the gravitational field of an infinite cylinder. The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Malcolm MacCallum, and by a brief biography of the author, compiled from internet sources by Andrzej Krasiński.     

Republication of: 3. On the theory of gravitation

This is the English translation of the first of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917–1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein’s equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.     

Republication of: New solutions to Einstein’s equations of gravitation. B. Explicit determination of static,axially symmetric fields. By Rudolf Bach. With a supplement on the static two-body problem. By H. Weyl.

This is the English translation of the third of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917–1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein’s equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.     

Republication of: 5. Comment on the axially symmetric solutions to Einstein’s equations of gravitation

This is the English translation of the second of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917–1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein’s equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.     

Republication of: On the formal analogy between the basic electromagnetic equations and Einstein’s gravity equations in first approximation

This is an English translation of a paper by Hans Thirring, first published in German in 1918, which contains the first and correct presentation of the basic equations of gravitomagnetism in linear order. The paper has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Herbert Pfister, and Thirring’s brief biography compiled by Andrzej Krasinski from internet sources     

Republication of: On the initial value problem of the equations of gravitation

This is an English translation of a paper by Karl Stellmacher, first published in German in 1938, in which he presented the first, correct and successful, formulation of the initial value problem for Einstein’s equations in vacuum and with a dust source. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich and Stellmacher’s brief biography written by Hubert Goenner.     

Republication of: Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.     

Dynamics of extended bodies with spin-induced quadrupole in Kerr spacetime: generic orbits

We discuss motions of extended bodies in Kerr spacetime by using Mathisson–Papapetrou–Dixon equations. We firstly solve the conditions for circular orbits, and calculate the orbital frequency shift due to the mass quadrupoles. The results show that we need not consider the spin-induced quadrupoles in extreme-mass-ratio inspirals for space-based gravitational wave detectors. We quantitatively investigate the temporal variation of rotational velocity of the extended body due to the coupling of quadrupole and background gravitational field. For generic orbits, we numerically integrate the Mathisson–Papapetrou–Dixon equations for evolving the motion of an extended body orbiting a Kerr black hole. By comparing with the monopole–dipole approximation, we reveal the influences of quadrupole moments of extended bodies on the orbital motion and chaotic dynamics of extreme-mass-ratio systems. We do not find any chaotic orbits for the extended bodies with physical spins and spin-induced quadrupoles. Possible implications for gravitational wave detection and pulsar timing observation are outlined.     

Republication of: A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae

This is an English translation of a paper by Georges Lemaître, first published in French in 1927, in which the author, having re-discovered and generalised the Friedmann models, for the first time related them to the then-already-available observations of expansion of the Universe. The translation published in 1931 in MNRAS was not perfectly faithful to the original text—it was updated. As it turned out very recently, the updates were done by Lemaître himself, but the discrepancies between the two texts caused a temporary stir among historians. Our translation follows the 1927 version exactly. The paper has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Jean-Pierre Luminet that, among other things, lists and explains the differences between the 1927 and 1931 versions.     

Republication of: The beginning of the world from the point of view of quantum theory

This is a reprinting of a very short note by Georges Lemaitre, first published in Nature in 1931, in which he envisages the Universe evolving out of a single atom by quantum processes. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Jean-Pierre Luminet.     

Republication of: Quantum theory of weak gravitational fields

This is an English translation of a paper by Matvei Bronstein, first published in German in 1936 in a long-extinct Soviet journal, in which he presented the first attempt at quantizing a weak (linearized) gravitational field, rather modern in its approach. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Stanley Deser and Alexei Starobinsky, and Bronstein’s brief biography written by Stanley Deser.     

Republication of: Large number coincidences and the anthropic principle in cosmology

This is a reprinting of the paper by Brandon Carter, first published in a little-known volume of conference proceedings in 1974, that moved the anthropic principle from the realm of philosophical speculations to the subject of theoretical physics. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis.     

Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole

The scattering of spinning test particles by a Schwarzschild black hole is studied. The motion is described according to the Mathisson–Papapetrou–Dixon model for extended bodies in a given gravitational background field. The equatorial plane is taken as the orbital plane, the spin vector being orthogonal to it with constant magnitude. The equations of motion are solved analytically in closed form to first-order in spin and the solution is used to compute corrections to the standard geodesic scattering angle as well as capture cross section by the black hole.     

Republication of: Relativistic cosmology

This is a reprinting of the paper by Howard Percy Robertson, first published in 1933 in Rev. Mod. Phys., that is a very authoritative summary of relativistic cosmology at the stage at which it was up to 1933. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis, and by Robertson’s biography, compiled by Andrzej Krasinski from printed sources.     

Republication of: On the gravitational stability of the expanding universe

This is the republished English edition of a paper by E. Lifshitz, first published in 1946, in which the author investigates the gravitational stability of the non–stationary isotropic models of the universe. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George F. R. Ellis, and by a brief biography of Evgenii Mikhailovich Lifshitz, written by Andrzej Krasiński.     

Republication of: Observations in cosmology

This is a reprinting of a paper by Jerome Kristian and Rainer K. Sachs, first published in 1966, in which they proposed a power-series scheme for reading out various parameters of the Universe directly from observations in a model-independent way. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis and by a brief biography of J. Kristian, compiled by A. Krasiński from internet sources.     

Nonequatorial circular orbits of spinning particles in the Schwarzschild–de Sitter background

In this paper analytical solutions of the Mathisson–Papapetrou equations that describe nonequatorial circular orbits of a spinning particle in the Schwarzschild–de Sitter background are studied, and the role of the cosmological constant is emphasized. It is shown that generally speaking a highly relativistic velocity of the particle is a necessary condition of motion along this type of orbits, with an exception of orbits locating close to the position of the static equilibrium, where low velocities are possible as well. Depending on the correlation between the spin orientation of the particle and its orbital velocity some of the possible nonequatorial circular orbits exist due to the repulsive action on the particle caused by the spin–gravity coupling and the others are caused by the attractive action. Here values of the energy of the particle on the corresponding orbits are also analyzed.