Publisher Erratum: Eur. Phys. J. C (2023) 83:608 https://doi.org/10.1140/epjc/s10052-023-11705-6

In the original article, several corrections had not been implemented.

The sentence “The scattering angle \(\chi ^{\text {eff}}\) for an EOB system can be found from the dynamics of a test particle’s orbits around a black hole, [...].” has been changed to “The scattering angle \(\chi ^{\text {eff}}\) for an EOB system can be found from the dynamics of a test particle scattered by a black hole, [...].”.

Equation (22) has been updated to:

$$\begin{aligned} \chi ^{\text {eff}}= & {} \frac{R_{11}}{\sqrt{R_{00}}}\frac{G}{J_0}+ \frac{ \pi (2 R_{22} - R_{11} R_{31} + R_{00}(\frac{3}{4} R_{31}^2-R_{42}))}{4} \Big (\frac{G}{J_0}\Big )^2\nonumber \\{} & {} +\frac{1}{12 R_{00}^{3/2}} \Big \{-R_{11}^3 - 6 R_{00} R_{11}^2 R_{31} + 12 R_{00} R_{11} \Big [R_{22} \nonumber \\{} & {} + 2 R_{00} (R_{31}^2 - R_{42})\Big ] - 8 R_{00}^2 \Big [3 R_{22} R_{31} - 3 R_{33} \nonumber \\{} & {} +2 R_{00} (R_{31}^3 - 2 R_{31} R_{42} + R_{53})\Big ]\Big \}\Big (\frac{G}{J_0}\Big )^3\nonumber \\{} & {} + \frac{3\pi }{1024}\Big \{128 R_{22}^2+48 R_{11}^2 \left( 5 R_{31}^2-4 R_{42}\right) \nonumber \\{} & {} -96 R_{22} \left( 4 R_{11} R_{31}-5 R_{00} R_{31}^2+4 R_{00} R_{42}\right) \nonumber \\{} & {} +16 R_{11} \left( 16 R_{33}+R_{00}\left( -35 R_{31}^3+60 R_{31} R_{42}-24 R_{53}\right) \right) \nonumber \\{} & {} +R_{00} \Big [-384 R_{31} R_{33}+256 R_{44}+3 R_{00} \Big (105 R_{31}^4 \nonumber \\{} & {} -280 R_{31}^2 R_{42}+80 R_{42}^2+160 R_{31} R_{53}-64 R_{64}\Big )\Big ]\Big \} \Big (\frac{G}{J_0}\Big )^4.\nonumber \\ \end{aligned}$$
(22)

The original article has been corrected.