Geodesic
Static limit and Penrose effect in rotating reference frames
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 223-233 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that effects similar to those for a rotating black hole arise for an observer using a uniformly rotating reference frame in a flat space–time: a surface appears such that no body can be stationary beyond this surface, while the particle energy can be either zero or negative. Beyond this surface, which is similar to the static limit for a rotating black hole, an effect similar to the Penrose effect is possible. We consider the example where one of the fragments of a particle that has decayed into two particles beyond the static limit flies into the rotating reference frame inside the static limit and has an energy greater than the original particle energy. We obtain constraints on the relative velocity of the decay products during the Penrose process in the rotating reference frame. We consider the problem of defining energy in a noninertial reference frame. For a uniformly rotating reference frame, we consider the states of particles with minimum energy and show the relation of this quantity to the radiation frequency shift of the rotating body due to the transverse Doppler effect.
Keywords: rotating reference frame, negative-energy particle, Penrose effect. 
@article{TMF_2019_200_2_a3,
     author = {A. A. Grib and Yu. V. Pavlov},
     title = {Static limit and {Penrose} effect in rotating reference frames},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {223--233},
     year = {2019},
     volume = {200},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a3/}
}
TY  - JOUR
AU  - A. A. Grib
AU  - Yu. V. Pavlov
TI  - Static limit and Penrose effect in rotating reference frames
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 223
EP  - 233
VL  - 200
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a3/
LA  - ru
ID  - TMF_2019_200_2_a3
ER  - 
%0 Journal Article
%A A. A. Grib
%A Yu. V. Pavlov
%T Static limit and Penrose effect in rotating reference frames
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 223-233
%V 200
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a3/
%G ru
%F TMF_2019_200_2_a3
A. A. Grib; Yu. V. Pavlov. Static limit and Penrose effect in rotating reference frames. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 223-233. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a3/

[1] P. Ehrenfest, “Gleichförmige Rotation starrer Körper und Relativitätstheorie”, Phys. Z., 10 (1909), 918 ; П. Эренфест, “Равномерное вращательное движение твердых тел и теория относительности”, Относительность. Кванты. Статистика. Сборник статей, Наука, М., 1972, 37–39 | DOI

[2] G. Rizzi, M. L. Ruggiero (eds.), Relativity in Rotating Frames. Relativistic Physics in Rotating Reference Frames, Fundamental Theories of Physics book series, 135, Kluwer, Boston, 2004 | DOI

[3] A. A. Grib, Yu. V. Pavlov, “Comparison of particle properties in Kerr metric and in rotating coordinates”, Gen. Rel. Grav., 49:6 (2017), 78, 20 pp., arXiv: 1609.04202 | DOI | MR

[4] Ch. Mizner, K. Torn, Dzh. Uiler, Gravitatsiya, Mir, M., 1977 | MR

[5] R. Penrose, “Gravitational collapse: the role of general relativity”, Rivista Nuovo Cimento, Num. Spec. I, 1969, 252–276 | MR

[6] W. G. Unruh, “Notes on black-hole evaporation”, Phys. Rev. D., 14:4 (1976), 870–892 | DOI

[7] L. D. Landau, E. M. Lifshits, Teoriya polya, Nauka, M., 1988 | MR

[8] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, GIFML, M., 1961 | MR

[9] A. Einshtein, L. Infeld, Evolyutsiya fiziki. Razvitie idei ot pervonachalnykh ponyatii do teorii otnositelnosti i kvantov, Nauka, M., 1965 | Zbl

[10] A. A. Fridman, Mir kak prostranstvo i vremya, Nauka, M., 1965

[11] M. Born, Einshteinovskaya teoriya otnositelnosti, Mir, M., 1972

[12] R. A. Syunyaev (red.), Fizika kosmosa. Malenkaya entsiklopediya, Sovetskaya entsiklopediya, M., 1986

[13] R. H. Boyer, R. W. Lindquist, “Maximal analytic extension of the Kerr metric”, J. Math. Phys., 8:2 (1967), 265–281 | DOI | MR | Zbl

[14] S. Chandrasekar, Matematicheskaya teoriya chernykh dyr, Mir, M., 1986 | MR

[15] A. Laitman, V. Press, R. Prais, S. Tyukolski, Sbornik zadach po teorii otnositelnosti i gravitatsii, Mir, M., 1979 | MR

[16] L. D. Landau, E. M. Lifshits, Mekhanika, Nauka, M., 1988 | MR

[17] A. Vilenkin, “Quantum field theory at finite temperature in a rotating system”, Phys. Rev. D, 21:18 (1980), 2260–2269 | DOI

[18] J. R. Letaw, J. D. Pfautseh, “Quantized scalar field in rotating coordinates”, Phys. Rev. D, 22:6 (1980), 1345–1351 | DOI | MR

[19] G. Duffy, A. C. Ottewill, “Rotating quantum thermal distribution”, Phys. Rev. D, 67:4 (2003), 044002, 5 pp. | DOI

[20] W. Kündig, “Measurement of the transverse Doppler effect in an accelerated system”, Phys. Rev., 129:6 (1963), 2371–2375 | DOI

[21] J. M. Bardeen, W. H. Press, S. A. Teukolsky, “Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation”, Astrophys. J., 178 (1972), 347–369 | DOI