Geodesic
Can the energy of particles be negative in the absence of external fields?
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 504-518 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the question of conditions for the existence of negative-energy states of particles in the absence of external fields in inertial and noninertial frames of reference. We show that in the nonrelativistic case in noninertial reference frames, there always exist domains where the energy of particles is negative. We also show that in the relativistic case, the existence of negative-energy states of point particles does not lead to violations of the energy dominance condition. We consider conditions for the appearance of negative and zero energies of particles in the Milne universe and Rindler space–time.
Keywords: negative energies, Penrose effect, noninertial reference frame. 
@article{TMF_2023_216_3_a9,
     author = {A. A. Grib and Yu. V. Pavlov},
     title = {Can the energy of particles be negative in the absence of external fields?},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {504--518},
     year = {2023},
     volume = {216},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a9/}
}
TY  - JOUR
AU  - A. A. Grib
AU  - Yu. V. Pavlov
TI  - Can the energy of particles be negative in the absence of external fields?
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 504
EP  - 518
VL  - 216
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a9/
LA  - ru
ID  - TMF_2023_216_3_a9
ER  - 
%0 Journal Article
%A A. A. Grib
%A Yu. V. Pavlov
%T Can the energy of particles be negative in the absence of external fields?
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 504-518
%V 216
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a9/
%G ru
%F TMF_2023_216_3_a9
A. A. Grib; Yu. V. Pavlov. Can the energy of particles be negative in the absence of external fields?. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 504-518. http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a9/

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

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

[3] D. Christodoulou, R. Ruffini, “Reversible transformations of a charged black hole”, Phys. Rev. D, 4:12 (1971), 3552–3555 | DOI

[4] A. A. Grib, S. G. Mamaev, V. M. Mostepanenko, Vakuumnye kvantovye effekty v silnykh polyakh, Energoatomizdat, M., 1988

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

[6] 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. | DOI | MR

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

[8] A. A. Grib, Yu. V. Pavlov, “Predel statichnosti i effekt Penrouza vo vraschayuscheisya sisteme koordinat”, TMF, 200:2 (2019), 223–233 | DOI | DOI | DOI | MR

[9] S. W. Hawking, “Particle creation by black holes”, Commun. Math. Phys., 43:3 (1975), 199–220 | DOI | MR

[10] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. II, Teoriya polya, Nauka, M., 1988 | MR | Zbl

[11] D. A. Kirzhnits, V. N. Sazonov, “Sverkhsvetovye dvizheniya i spetsialnaya teoriya otnositelnosti”, Einshteinovskii sbornik 1973, ed. V. L. Ginzburg, Nauka, M., 1974, 84–111 | MR

[12] G. Feinberg, “Possibility of faster-than-light particles”, Phys. Rev., 159:5 (1967), 1089–1105 | DOI

[13] A. Yu. Andreev, D. A. Kirzhnits, “Takhiony i neustoichivost fizicheskikh sistem”, UFN, 166:10 (1996), 1135–1140 | DOI | DOI

[14] N. N. Bogolyubov, D. V. Shirkov, Kvantovye polya, Fizmatlit, M., 2005 | MR | Zbl

[15] A. A. Grib, Yu. V. Pavlov, “K voprosu o fazovykh perekhodakh v okrestnosti chernykh dyr”, Pisma v ZhETF, 116:8 (2022), 493–499

[16] R. C. Tolman, The Theory of the Relativity of Motion, University of California Press, Berkeley, CA, 1917

[17] O. M. P. Bilaniuk, V. K. Deshpande, E. C. G. Sudarshan, “ ‘Meta’ relativity”, Amer. J. Phys., 30:10 (1962), 718–723 | DOI | MR

[18] E. C. G. Stueckelberg, “Remarque à propos de la création de paires de particules en théorie de relativité”, Helv. Phys. Acta., 14 (1941), 588–594 | MR

[19] R. P. Feynman, “The theory of positrons”, Phys. Rev., 76:6 (1949), 749–759 | DOI

[20] E. Recami, R. Mignani, “Classical theory of tachyons (special relativity extended to superluminal frames and objects)”, Riv. Nuovo Cim. (1971–1977), 4:2, 209–290 | DOI

[21] A. A. Grib, “Vozmozhno li dvizhenie nazad vo vremeni?”, Priroda, 1974, no. 4, 24–32

[22] M. Dzhemmer, Ponyatie massy v klassicheskoi i sovremennoi fizike, Progress, M., 1967

[23] H. Bondi, “Negative mass in general relativity”, Rev. Mod. Phys., 29:3 (1957), 423–428 | DOI | MR

[24] Ya. P. Terletskii, Paradoksy teorii otnositelnosti, Nauka, M., 1966 | MR | MR

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

[26] W. B. Bonnor, “Negative mass in general relativety”, Gen. Rel. Grav., 21:11 (1989), 1143–1157 | DOI | MR

[27] A. A. Shatskii, I. D. Novikov, N. S. Kardashev, “Zadacha Keplera i stolknoveniya dlya tel s otritsatelnymi massami”, UFN, 181:4 (2011), 399–403 | DOI

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

[29] I. D. Novikov, V. P. Frolov, Fizika chernykh dyr, Nauka, M., 1986 | DOI

[30] R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics”, Phys. Rev. Lett., 11:5 (1963), 237–238 | DOI | MR

[31] P. Ehrenfest, “Gleichförmige Rotation starrer Körper und Relativitätstheorie”, Phys. Z., 10:23 (1909), 918–920 | DOI

[32] S. Veinberg, Gravitatsiya i kosmologiya. Printsipy i prilozheniya obschei teorii otnositelnosti, Mir, M., 1975

[33] E. A. Milne, Relativity, Gravitation and World-Structure, Clarendon Press, Oxford, 1935

[34] Ya. B. Zeldovich, I. D. Novikov, Stroenie i evolyutsiya Vselennoi, Nauka, M., 1975

[35] G. F. R. Ellis, T. Rothman, “Lost horizons”, Amer. J. Phys., 61:10 (1993), 883–893 | DOI | MR

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

[37] N. Birrell, P. Devis, Kvantovannye polya v iskrivlennom prostranstve-vremeni, Mir, M., 1984 | MR

[38] W. Rindler, “Kruskal space and the uniformly accelerated frame”, Amer. J. Phys., 34:12 (1966), 1174–1178 | DOI

[39] A. A. Grib, Yu. V. Pavlov, “Particles with negative energies in black holes”, Internat. J. Modern Phys. D, 20:5 (2011), 675–684 | DOI | MR