## G C McVittie - some of his papers

Below we list a few of McVittie's papers together with some brief comments by reviewers extracted from longer reviews, or McVittie's own comments in the paper itself:

*The cosmical constant and the structure of the universe*(1939).

H P Robertson writes: The author re-determines the radius of the closed Friedmann universe on following Einstein's suggestion of allowing the cosmological constant to vanish, and finds that this would require a high density of matter.*Axiomatic treatment of kinematical relativity*(1942).

A H Taub writes: The fundamental results of E A Milne's kinematical relativity are derived from nine axioms. All but the last of these deal with the assignment of coordinates and definitions of velocity and acceleration. These are axioms used by Milne. The author uses these to obtain results which Milne and his coworkers had obtained as properties of sets of "equivalent" observers. The ninth axiom defines equivalent observers. It is argued that kinematical relativity cannot be applied to a physical theory without the addition of a further axiom which would enable one to identify a theoretical observer with a terrestrial one.*The regraduation of clocks in spherically symmetric space-times of general relativity*(1945).

Arthur Walker writes: This paper gives a preliminary examination of the question as to whether general relativity admits clock regraduations other than trivial coordinate transformations, a question which has been suggested by recent kinematical theories of relativity. This examination is restricted to spherically symmetric space-times ...*The equations governing the motion of a perfect-gas atmosphere*(1948).

B Haurwitz writes: In most investigations of dynamic meteorology the earth's surface is regarded as a rotating disc tangential to the actual earth. For many meteorological studies this drastic simplification is unsatisfactory because of the magnitude of the atmospheric perturbations. The introduction of the customary spherical polar coordinates with the origin at the earth's center is also not considered suitable because the origin is thus far removed from the region in which the motion is to be studied. Therefore a new system of hydrodynamic equations is developed ...*A systematic treatment of moving axes in hydrodynamics*(1949).

J L Synge writes: The author employs the technique of tensor calculus to transform the equations of classical hydrodynamics to moving curvilinear coordinates. ... He discusses in this way the expansion and vorticity of a fluid, the equations of motion and of continuity, and heat transfer. He gives also two examples which refer to the motion of a gas on a spherical rotating earth.*Two-dimensional fluid motion referred to a network of orthogonal curves*(1949).

J L Synge writes: The author's method of transforming the equations of hydrodynamics [see the preceding review] is applied to the case of motion parallel to a surface; two coordinates are orthogonal coordinates in this surface and the third coordinate is orthogonal to it. The equations of motion and continuity are worked out in detail and applied to Meyer's equation in aerodynamics and to the gradient wind in dynamic meteorology.*Cosmological Theory*(First Edition 1937, Second Edition 1949).

H P Robertson writes: The first three of the five chapters present a rapid survey of our knowledge of extra-galactic nebulae, of the tensor calculus and of the principles of the general theory of relativity. These are applied in the fourth chapter to the problem of the expanding universe; McVittie's treatment of Hubble's data leads to a hyperbolic universe in which the rate of expansion is being retarded, in contrast with the small closed universe deduced by Hubble and Tolman. The booklet concludes with a brief account of E A Milne's kinematical theory of the universe.*Coordinate systems in dynamic meteorology*(1951).

J L Synge writes: This paper is concerned with the transformation of the equations of hydrodynamics to various curvilinear coordinate systems convenient for meteorology, the earth (without rotation) being regarded as a Newtonian frame of reference.*A model universe admitting the interchangeability of stress and mass*(1952).

McVittie writes: The possibility of the existence of negative stress in the general relativity treatment of a perfect fluid is used to construct a model universe which is in a 'gravitationally steady state'. Without employing Newtonian analogies, it is shown that stress and mass are mutually convertible into one another in this model, and it is suggested that this process corresponds to the creation of matter postulated in recent cosmological investigations. Using, as the sole empirical datum, the magnitude of the local rate of change of red-shift with distance, plausible assumptions lead to a numerical value of the cosmical constant, to a small value of the density of matter in space and to an unobservably small rate of conversion of stress into mass. The model has an infinitely long contracting phase, followed by an expanding phase which has been proceeding for at least 9. 10^{9}years.*Relativistic and Newtonian cosmology*(1954).

H P Robertson writes: The author's purpose is to show how, and to what extent, Newtonian cosmological models are derivable from those of the general theory of relativity.*General relativity and cosmology*(1956).

G Y Rainich writes: In the introduction the author stresses the inevitability of taking, implicitly or explicitly, a definite philosophical position in discussing questions of general relativity and does it rather explicitly. He forgoes then an elaborate inductive derivation of the basic equations, using instead analogy with the Newtonian theory.*Cosmology and the interpretation of astronomical data*(1962).

McVittie writes: This paper deals with three problems in cosmology, namely, the applicability of uniform model universes to the observed universe, the present status of the expansion question, and the distribution in space of extragalactic Class II (faint) radio sources.*Spherical symmetry and mass-energy in general relativity***I**(1970).

Cahill and McVittie (the authors) write: The mass-energy of spherically symmetric distributions of material is studied according to general relativity.*Spherical symmetry and mass-energy in general relativity***II**(1970).

Cahill and McVittie (the authors) write: A solution of Einstein's field equations for the motion of a spherically symmetric distribution of perfect fluid is investigated in an isotropic comoving coordinate system.*A point-particle model universe*(1982).

Newman and McVittie (the authors) write: The observable cosmos is modeled as a set of point particles, representing the galaxies, which perturb a dust-filled, Robertson-Walker space-time.