# Particles with Negative Energies in Nonrelativistic and Relativistic Cases

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Negative Energies and the Penrose Effect in Nonrelativistic Case

## 2. Negative Energies in Rotating Coordinates

## 3. Negative Energies and Static Limit in Expanding Universe

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Landau, L.D.; Lifshitz, E.M. Mechanics; Pergamon Press: Oxford, UK, 1976. [Google Scholar]
- Penrose, R. Gravitational collapse: The role of general relativity. Rivista Nuovo Cimento I
**1969**, Num. Spec., 252–276. Available online: http://adsabs.harvard.edu/abs/1969NCimR...1..252P (accessed on 15 March 2020). - Penrose, R.; Floyd, R.M. Extraction of rotational energy from a black hole. Nat. Phys. Sci.
**1971**, 229, 177–179. [Google Scholar] [CrossRef] - Oberth, H. Wege zur Raumschiffahrt; R. Oldenbourg Verlag: Munich-Berlin, Germany, 1929; [Engl. transl.: Oberth, H. Ways to Spaceflight; NASA: TT F-622, 1970]. [Google Scholar]
- Syunyaev, R.A. (Ed.) Physics of the Cosmos: Little Encyclopedia; Soviet Encyclopedia: Moscow, Russia, 1986. (In Russian) [Google Scholar]
- Grib, A.A.; Pavlov, Y.V. Comparison of particle properties in Kerr metric and in rotating coordinates. Gen. Relativ. Gravit.
**2017**, 49, 78. [Google Scholar] [CrossRef] [Green Version] - Grib, A.A.; Pavlov, Y.V. Static limit and Penrose effect in rotating reference frames. Theor. Math. Phys.
**2019**, 200, 1117–1125. [Google Scholar] [CrossRef] [Green Version] - Boyer, R.H.; Lindquist, R.W. Maximal analytic extension of the Kerr metric. J. Math. Phys.
**1967**, 8, 265–281. [Google Scholar] [CrossRef] - Landau, L.D.; Lifshitz, E.M. The Classical Theory of Fields; Pergamon Press: Oxford, UK, 1983. [Google Scholar]
- Ellis, G.F.R.; Rothman, T. Lost horizons. Am. J. Phys.
**1993**, 61, 883–893. [Google Scholar] [CrossRef] - Grib, A.A. Early Expanding Universe and Elementary Particles; Friedmann Lab. Publ.: St. Petersburg, Russia, 1995. [Google Scholar]
- Grib, A.A.; Pavlov, Y.V. Particle properties outside of the static limit in cosmology. Int. J. Mod. Phys. A
**2020**, 35, 2040044. [Google Scholar] [CrossRef] [Green Version] - Grib, A.A.; Pavlov, Y.V. Particles with negative energies in black holes. Int. J. Mod. Phys. D
**2011**, 20, 675–684. [Google Scholar] [CrossRef] [Green Version]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Grib, A.A.; Pavlov, Y.V.
Particles with Negative Energies in Nonrelativistic and Relativistic Cases. *Symmetry* **2020**, *12*, 528.
https://doi.org/10.3390/sym12040528

**AMA Style**

Grib AA, Pavlov YV.
Particles with Negative Energies in Nonrelativistic and Relativistic Cases. *Symmetry*. 2020; 12(4):528.
https://doi.org/10.3390/sym12040528

**Chicago/Turabian Style**

Grib, Andrey A., and Yuri V. Pavlov.
2020. "Particles with Negative Energies in Nonrelativistic and Relativistic Cases" *Symmetry* 12, no. 4: 528.
https://doi.org/10.3390/sym12040528