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 ofTheoretical 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 is available at IOP
PACS: 03.30.+p, 45.50.−j (all)
DOI: 10.1070/PU2003v046n10ABEH001661
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

:   ,   ,    « c/31/2  c/21/2  » 173 1131–1136 (2003); DOI: 10.3367/UFNr.0173.200310e.1131

References (12) ↓ Cited by (4) Similar articles (20)

  1. Ashby N, Allen D W Radio Science 14 649 (1979)
  2. Guinot B Metrologia 34 261 (1997)
  3. Schwarzschild K Sitzungsber. Deutsch. Akad. Wissenschaft Berlin Kl. Math. Phys. Tech. 189 (1916)
  4. Weinberg S Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York: Wiley, 1972) [Translated into Russian (Moscow: Mir, 1975)]
  5. Landau L D, Lifshitz E M Teoriya Polya (Classical Theory of Fields, Moscow: Fizmatlit, 2001) [Translated into English (Oxford: Pegramon Press, 1983)]
  6. Misner C W, Thorne K S, Wheeler J A Gravitation (San Francisco: W.H. Freeman, 1973) [Translated into Russian (Moscow: Mir, 1977)]
  7. Lightman A, Press W, Price R, Teukolsky S Problems Book in Relativity and Gravitation (Princeton, NJ: Princeton Univ. Press, 1975) [Translated into Russian (Moscow: Mir, 1979)]
  8. Schwarzschild K Sitzungsber. Deutsch. Akad. Wissenschaft Berlin Kl. Math. Phys. Tech. 424 (1916)
  9. Carmeli M Lett. Nuovo Cimento 3 379 (1972)
  10. Carmeli M Classical Fields: General Relativity and Gauge Theory (New York: J. Wiley, 1982)
  11. Blinnikov S I, Okun L B, Vysotsky M I, gr-qc/0111103; in Proc. of the Workshops "What Comes Beyond the Standard Model 2000, 2001" Vol. 1 Festschrift Dedicated to the 60th Birthday of Holger Bech Nielsen (Bled Workshops in Physics, Vol. 2, No 2, Eds N M Borštnik, C D Froggatt, D Lukman, Ljubljana: DMFA–Založništvo, 2001) p. 115; hep-ph/0212221
  12. Kobzarev I Yu, Okun L B, Pomeranchuk I Ya Yad. Fiz. 3 1154 (1966) [Sov. J. Nucl. Phys. 3 837 (1966)]

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: Editorial office contacts About the journal Terms and conditions