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

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.

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

(1)

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

(2)

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

(3)

$$X_{\mathrm{S}}=\frac{3}{7}r\left(1+\frac{10}{7}\frac{M}{r}+\cdots \right),$$

(4)

$$\frac{d^{2}P}{d{\eta }^2}-\frac{4}{3}E\eta \frac{dP}{d\eta }-2\frac{A}{X_{\mathrm{S}}}P-\frac{4}{3}E{X}_{\mathrm{S}}\frac{dQ}{d\eta }=0,$$

(5)

$$\frac{d^{2}Q}{d{\eta }^2}-4E\eta \frac{dQ}{d\eta }+4A^2{X}_{\mathrm{S}}\frac{dP}{d\eta }=0,$$

(6)

$$w_1=\frac{16}{3}E,w_2=\frac{16}{3}{E}^2,w_3=2E\left[\frac{3r-7M}{r-2M}-24\frac{M^2}{{(7r-17M)}^2}\right],$$

(7)

$$w_4=\frac{8}{3}{E}^2\left(\frac{7r-17M}{r-2M}\right),E=\frac{M}{r^3},$$

(8)

$$q_1=-2E\frac{{\left[r^3(r-2M)\right]}^{1/2}}{7r-17M},q_2=\frac{1}{2}{w}_3-E\left(\frac{3r-7M}{r-2M}\right)=-24E\frac{M^2}{{(7r-17M)}^2}$$

(9)

and

$$q_3=w_1+w_3-\frac{2}{3}E\left(\frac{11r-25M}{r-2M}\right),q_4=\frac{1}{2}{w}_5-\frac{1}{3}{w}_{3}E\left(\frac{13r-29M}{r-2M}\right).$$

(10)