RSS feeds
ÐóññêèéEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2003

 / 

October

←  →

Methodological notes


Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity

, ,
Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the outside motion there exists a critical value of coordinate velocity c/sqrt{3}: particles with v < vc are accelerated by the field like Newtonian apples, and particles with v > vc are decelerated like photons. Particles moving inside a body with constant density have no critical velocity; they are always accelerated. We consider also the motion of a ball inside a tower, when it is thrown from the top (bottom) of the tower and after elastically bouncing at the bottom (top) comes back to the original point. The total time of flight is the same in these two cases if the initial proper velocity v0 is equal to c/sqrt{2}.

Fulltext pdf (187 KB)
Fulltext is also available at DOI: 10.1070/PU2003v046n10ABEH001661
PACS: 03.30.+p, 45.50.−j (all)
DOI: 10.1070/PU2003v046n10ABEH001661
URL: https://ufn.ru/en/articles/2003/10/d/
000188974100004
Citation: Blinnikov S I, Okun L B, Vysotskii M I "Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity" Phys. Usp. 46 1099–1103 (2003)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Áëèííèêîâ Ñ È, Âûñîöêèé Ì È, Îêóíü Ë Á «Ñêîðîñòè c/31/2 è c/21/2 â îáùåé òåîðèè îòíîñèòåëüíîñòè» ÓÔÍ 173 1131–1136 (2003); DOI: 10.3367/UFNr.0173.200310e.1131

References (12) Cited by (5) Similar articles (20) ↓

  1. V.I. Ritus “On the difference between Wigner’s and Møller’s approaches to the description of Thomas precession” Phys. Usp. 50 95–101 (2007)
  2. V.I. Ritus “Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry” Phys. Usp. 51 709–721 (2008)
  3. P.B. Ivanov “On relativistic motion of a pair of particles having opposite signs of masses” Phys. Usp. 55 1232–1238 (2012)
  4. G.B. Malykin “Application of the modified Duguay method for measuring the Lorentz contraction of a moving body length” Phys. Usp. 64 1058–1062 (2021)
  5. G.B. Malykin “The Sagnac effect: correct and incorrect explanations” Phys. Usp. 43 1229 (2000)
  6. Yu.I. Hovsepyan “Some notes on the relativistic Doppler effect” Phys. Usp. 41 941–944 (1998)
  7. M.I. Krivoruchenko “Rotation of the swing plane of Foucault’s pendulum and Thomas spin precession: two sides of one coin” Phys. Usp. 52 821–829 (2009)
  8. X.-B. Huang “A rigorous minimum-assumption derivation of the Lorentz transformation” Phys. Usp. 54 529–532 (2011)
  9. V.I. Ritus “Lagrange equations of motion of particles and photons in the Schwarzschild field” Phys. Usp. 58 1118–1123 (2015)
  10. V.I. Ritus “Generalization of the k coefficient method in relativity to an arbitrary angle between the velocity of an observer (source) and the direction of the light ray from (to) a faraway source (observer) at rest” Phys. Usp. 63 601–610 (2020)
  11. G.B. Malykin “The relation of Thomas precession to Ishlinskii’s theorem as applied to the rotating image of a relativistically moving body” Phys. Usp. 42 505–509 (1999)
  12. A.A. Logunov “The theory of the classical gravitational field” Phys. Usp. 38 179–193 (1995)
  13. V.A. Aleshkevich “On special relativity teaching using modern experimental data” Phys. Usp. 55 1214–1231 (2012)
  14. G.B. Malykin “Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?” Phys. Usp. 57 714–720 (2014)
  15. V.L. Ginzburg, V.P. Frolov “Vacuum in a homogeneous gravitational field and excitation of a uniformly accelerated detector” Sov. Phys. Usp. 30 1073–1095 (1987)
  16. S.I. Syrovatskii “On the problem of the ’retardation’ of the relativistic contraction of moving bodies” Sov. Phys. Usp. 19 273–274 (1976)
  17. A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects” Phys. Usp. 47 797–820 (2004)
  18. V.P. Makarov, A.A. Rukhadze “Force acting on a substance in an electromagnetic field” Phys. Usp. 52 937–943 (2009)
  19. G.B. Malykin “Para-Lorentz transformations” Phys. Usp. 52 263–266 (2009)
  20. V.B. Morozov “On the question of the electromagnetic momentum of a charged body” Phys. Usp. 54 371–374 (2011)

The list is formed automatically.
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions