Modified Gravity and Cosmology

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the ${U}_{4}$ theory arises as a local gauge theory for the Poincar\'e group in space-time. The deviations of the ${U}_{4}$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

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General Relativity with Spin and Torsion: Foundations and Prospects

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

Superstring theoryをめぐって(放談室)

Rotating, charged, and uniformly accelerating mass in general relativity

Within the spinorial version of the Cartan structure formulas with the built‐in (complex) Einstein vacuum equations some closed semi‐Einsteinian substructures are isolated and discussed. Then the idea of semigraviton is introduced, and its relationship to Penrose’s nonlinear graviton is described.

On the separation of Einsteinian substructures

Complex V4’s are investigated where ΓȦḂ =0 and therefore a fortiori equations Gab=0 are fulfilled. A general theory of spaces of this type is outlined and examples of nontrivial solutions of all degenerate algebraic types are provided.

Some solutions of complex Einstein equations

1. How the theory of relativity came into being (a brief historical sketch) Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries 3. Tensors, tensor densities 4. Covariant derivatives 5. Parallel transport and geodesic lines 6. Curvature of a manifold: flat manifolds 7. Riemannian geometry 8. Symmetries of Rieman spaces, invariance of tensors 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs 10. The spatially homogeneous Bianchi-type spacetimes 11. The Petrov classification by the spinor method Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory 14. Spherically symmetric gravitational field of isolated objects 15. Relativistic hydrodynamics and thermodynamics 16. Relativistic cosmology I: general geometry 17. Relativistic cosmology II: the Robertson-Walker geometry 18. Relativistic cosmology III: the Lemaitre-Tolman geometry 19. Relativistic cosmology IV: generalisations of L-T and related geometries 20. The Kerr solution 21. Subjects omitted in this book References.

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An Introduction to General Relativity and Cosmology

The scattering of plane electromagnetic waves by the gravitational field of an isolated physical system is studied. On the level of the geometrical optics approximation the general theory of light rays is formulated. In particular, the generalized formula for the Einstein deflection of light rays is obtained. On the level of the vectorial optics the problem of polarization is examined in detail. The formula obtained, describing a rotation of the plane of polarization due to the presence of the gravitational field, admits a direct geometrical interpretation. The theory is applied to the rotating body and a system of point masses. The physical results established concerning the asymptotic behavior of the electromagnetic waves are independent of the coordinate system used in the computations.

Jerzy F. Plebański

Papers

Rotating, charged, and uniformly accelerating mass in general relativity

On the separation of Einsteinian substructures

Some solutions of complex Einstein equations

An Introduction to General Relativity and Cosmology

Electromagnetic Waves in Gravitational Fields