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

Bahram Mashhoon

doi:10.3390/universe7020039

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

Universe2021, 7(2), 39;https://doi.org/10.3390/universe7020039

Version Notes

Order Reprints

In writing out the tidal equation for X in my recent paper [], 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.

\begin{matrix} \frac{d^{2} X}{d T^{2}} & + (A - 2 E X) (1 - 2 {\dot{X}}^{2}) + A^{2} X (1 + 2 {\dot{X}}^{2}) \\ - \frac{2}{3} E [X ({\dot{Y}}^{2} + {\dot{Z}}^{2}) + 2 \dot{X} (Y \dot{Y} + Z \dot{Z})] + 2 H (1 - {\dot{X}}^{2}) (Y \dot{Z} - Z \dot{Y}) = 0, \end{matrix}

(1)

\begin{matrix} \frac{d^{2} X}{d T^{2}} & + (A - 2 E X) (1 - 2 {\dot{X}}^{2}) + A^{2} X (1 + 2 {\dot{X}}^{2}) \\ - \frac{2}{3} E \dot{Y} (X \dot{Y} + 2 Y \dot{X}) = 0, \end{matrix}

(2)

X_{S} = \frac{3 A}{7 E - 3 A^{2}} = 3 \frac{{[r^{3} (r - 2 M)]}^{1 / 2}}{7 r - 17 M}, r \neq 17 M / 7,

(3)

X_{S} = \frac{3}{7} r (1 + \frac{10}{7} \frac{M}{r} + \dots),

(4)

\frac{d^{2} P}{d η^{2}} - \frac{4}{3} E η \frac{d P}{d η} - 2 \frac{A}{X_{S}} P - \frac{4}{3} E X_{S} \frac{d Q}{d η} = 0,

(5)

\frac{d^{2} Q}{d η^{2}} - 4 E η \frac{d Q}{d η} + 4 A^{2} X_{S} \frac{d P}{d η} = 0,

(6)

w_{1} = \frac{16}{3} E, w_{2} = \frac{16}{3} E^{2}, w_{3} = 2 E [\frac{3 r - 7 M}{r - 2 M} - 24 \frac{M^{2}}{{(7 r - 17 M)}^{2}}],

(7)

w_{4} = \frac{8}{3} E^{2} (\frac{7 r - 17 M}{r - 2 M}), E = \frac{M}{r^{3}},

(8)

q_{1} = - 2 E \frac{{[r^{3} (r - 2 M)]}^{1 / 2}}{7 r - 17 M}, q_{2} = \frac{1}{2} w_{3} - E (\frac{3 r - 7 M}{r - 2 M}) = - 24 E \frac{M^{2}}{{(7 r - 17 M)}^{2}}

(9)

and

q_{3} = w_{1} + w_{3} - \frac{2}{3} E (\frac{11 r - 25 M}{r - 2 M}), q_{4} = \frac{1}{2} w_{5} - \frac{1}{3} w_{3} E (\frac{13 r - 29 M}{r - 2 M}) .

(10)

Conflicts of Interest

The author declares no conflict of interest.

Reference

Mashhoon, B. Critical tidal currents in general relativity. Universe 2020, 6, 104. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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

Conflicts of Interest

Reference

Article Metrics

Citations

Article Access Statistics