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Correction

Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104

by
Bahram Mashhoon
1,2
1
Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA
2
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531 Tehran, Iran
Universe 2021, 7(2), 39; https://doi.org/10.3390/universe7020039
Submission received: 4 January 2021 / Accepted: 18 January 2021 / Published: 5 February 2021
In writing out the tidal equation for X in my recent paper [1], an inadvertent sign error led to two errant numerical coefficients in Equation (15) that propagated to Section 4. The main results and conclusions of my paper remain unchanged. All of the affected formulas are corrected below. The list consists of Equations (15), (35), (38), (40), (43), (44), (46), (47), (61), and (62), respectively.
d 2 X d T 2 + ( A 2 E X ) ( 1 2 X ˙ 2 ) + A 2 X ( 1 + 2 X ˙ 2 ) 2 3 E [ X ( Y ˙ 2 + Z ˙ 2 ) + 2 X ˙ ( Y Y ˙ + Z Z ˙ ) ] + 2 H ( 1 X ˙ 2 ) ( Y Z ˙ Z Y ˙ ) = 0 ,
d 2 X d T 2 + ( A 2 E X ) ( 1 2 X ˙ 2 ) + A 2 X ( 1 + 2 X ˙ 2 ) 2 3 E Y ˙ ( X Y ˙ + 2 Y X ˙ ) = 0 ,
X S = 3 A 7 E 3 A 2 = 3 [ r 3 ( r 2 M ) ] 1 / 2 7 r 17 M , r 17 M / 7 ,
X S = 3 7 r 1 + 10 7 M r + ,
d 2 P d η 2 4 3 E η d P d η 2 A X S P 4 3 E X S d Q d η = 0 ,
d 2 Q d η 2 4 E η d Q d η + 4 A 2 X S d P d η = 0 ,
w 1 = 16 3 E , w 2 = 16 3 E 2 , w 3 = 2 E 3 r 7 M r 2 M 24 M 2 ( 7 r 17 M ) 2 ,
w 4 = 8 3 E 2 7 r 17 M r 2 M , E = M r 3 ,
q 1 = 2 E [ r 3 ( r 2 M ) ] 1 / 2 7 r 17 M , q 2 = 1 2 w 3 E 3 r 7 M r 2 M = 24 E M 2 ( 7 r 17 M ) 2
and
q 3 = w 1 + w 3 2 3 E 11 r 25 M r 2 M , q 4 = 1 2 w 5 1 3 w 3 E 13 r 29 M r 2 M .

Conflicts of Interest

The author declares no conflict of interest.

Reference

  1. Mashhoon, B. Critical tidal currents in general relativity. Universe 2020, 6, 104. [Google Scholar] [CrossRef]
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MDPI and ACS Style

Mashhoon, B. Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104. Universe 2021, 7, 39. https://doi.org/10.3390/universe7020039

AMA Style

Mashhoon B. Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104. Universe. 2021; 7(2):39. https://doi.org/10.3390/universe7020039

Chicago/Turabian Style

Mashhoon, Bahram. 2021. "Correction: Mashhoon, B. Critical Tidal Currents in General Relativity. Universe 2020, 6, 104" Universe 7, no. 2: 39. https://doi.org/10.3390/universe7020039

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