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

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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}.

 Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 03.30.+p, 45.50.−j (all)
DOI: 10.1070/PU2003v046n10ABEH001661
URL: https://ufn.ru/en/articles/2003/10/d/
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)
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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

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