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 < v_c are accelerated by the field like Newtonian apples, and particles with v > v_c 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}.

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 TY JOUR TI Critical velocities c/sqrt{3} and c/sqrt{2} in the general theory of relativity AU Blinnikov, S. I. AU Okun, L. B. AU Vysotskii, M. I. PB Physics-Uspekhi PY 2003 JO Physics-Uspekhi JF Physics-Uspekhi JA Phys. Usp. VL 46 IS 10 SP 1099-1103 UR https://ufn.ru/en/articles/2003/10/d/ ER https://doi.org/10.1070/PU2003v046n10ABEH001661 Оригинал: Блинников С И, Высоцкий М И, Окунь Л Б «Скорости c/31/2 и c/21/2 в общей теории относительности» УФН 173 1131–1136 (2003); DOI: 10.3367/UFNr.0173.200310e.1131