New Equation and Energy-Tensor of a Gravitational Field
Open accessAbstract
A new equation for a gravitational field is proposed by following the line of arguments in the current theory of gauge fields. A linear approximation of this field equation which is the fourth order differential equation of the metric field gµν shows that it describes two kinds of particles with finite masses in addition to the familiar massless gravitons. An application to a static case shows that the static potential consists of three parts, 1) Newtonian potential, 2) a repulsive potential with a finite range and 3) an attractive potential with another finite force-range. A very interesting result is obtained from the above-mentioned potential. Namely, it seems quite probable that a point-source can be free from the Schwarzschild singularity, provided that the mass of the source is less than some critical value. The energy-“tensor” of the gravitational field is also investigated. It is shown that the total energy can always be transformed into an integral over a large closed surface owing to the invariant property of the Lagrangian. This feature makes it easy to compute the energy of an isolated system, the magnitude of which coincides with the value derived from the conventional theory of relativity.
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Cites
Invariant Theoretical Interpretation of Interaction
Utiyama, R. (1956) · Physical Review · doi:10.1103/physrev.101.1597 · Cited by 1,524 · see citing works
Self-citationRenormalization of a Classical Gravitational Field Interacting with Quantized Matter Fields
Utiyama, R., & DeWitt, B. S. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724264 · Cited by 492 · see citing works
Self-citationGeneral Relativity and Gravitation
Francaviglia, M., Longhi, G., Lusanna, L., & Sorace, E. (1997) · General Relativity and Gravitation · doi:10.1142/9789814531108 · Cited by 347 · see citing works
On a New Equation for a Gravitational Field
Utiyama, R. (1984) · Progress of Theoretical Physics · doi:10.1143/ptp.71.1116 · Cited by 1 · see citing works
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Research works printed but not linked: 4
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Aoki, S. (2025) · Modern Physics Letters A · doi:10.1142/s0217732325502086 · Cited by 2 · see citing works
Energies and a gravitational charge for massive particles in general relativity
Aoki, S., Onogi, T., & Yamaoka, T. (2024) · International Journal of Modern Physics A · doi:10.1142/s0217751x24500490 · Cited by 1 · see citing works
- Authors
- Utiyama, R.
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1984-07
- Volume
- 72
- Issue
- 1
- Pages
- 83-97
- ISSN
- 0033-068X (ISSN-L)
- 1347-4081
- OpenAlex
- W1977239023
- Cited by
- 10
- References
- 4
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2022: 2 · 2012: 1
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Progress of Theoretical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Einstein field equations, linearized gravity, massive graviton, Newtonian potential, repulsive potential, Schwarzschild singularity, energy conservation (physics)
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