# Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

@article{Grishchuk1984ExactTO, title={Exact theory of the (Einstein) gravitational field in an arbitrary background space-time}, author={Leonid P. Grishchuk and Alexander N. Petrov and Alla D. Popova}, journal={Communications in Mathematical Physics}, year={1984}, volume={94}, pages={379-396} }

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The…

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## References

SHOWING 1-10 OF 24 REFERENCES

### Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics

- Physics
- 1968

A formalism is developed for obtaining approximate gravitational wave solutions to the vacuum Einstein equations of general relativity in situations where the gravitational fields of interest are…

### Gravitational Radiation in the Limit of High Frequency

- Physics
- 1967

I r-~ ·. This dissertation deals with a technique for obtaining approximate radiative solutions to the Eiri.stein equa,tions of general relativity in situations where the gravitational fields of…

### Quantum mechanics of the gravitational field

- Mathematics
- 1982

An approach to the quantum theory of gravitation is developed by analogy with the quantum mechanics of the simplest generally covariant system: the relativistic point particle. The central object in…

### Photons and gravitons in perturbation theory: Derivation of maxwell's and einstein's equations

- Physics
- 1965

The S matrix for photon and graviton processes is studied in perturbation theory, under the restriction that the only creation and annihilation operators for massless particles of spin j allowed in…

### Classical theory of fields

- Physics, Geology
- 1952

The principle of relativity Relativistic mechanics Electromagnetic fields Electromagnetic waves The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a…

### Foundations for a Theory of Gravitation Theories

- Physics
- 1973

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold.…

### Gravitational radiation in Robertson-Walker backgrounds

- Physics
- 1983

The radiative perturbations studied by Chang and Janis in the Newman-Penrose formalism are shown to be a proper subset of those treated in the approach pioneered by Lifshitz. A scheme is developed…