About Poynting vector in axially symmetric stationary spacetimes
We dispose of some objections raised by Manko et al. \cite{Manko} on a recently published paper on the role of Poynting vector in the ocurrence of vorticity in electrovaccum spacetimes \cite{Herrera}.
gr-qc0605062.tex
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\begin{document}

\title [About Poynting vector in axially symmetric stationary 
spacetimes]{\textbf {About Poynting vector in axially symmetric stationary 
spacetimes }}


\author {
                Leonardo A. Pach\'{o}n$^{1}$
                \footnote[1]{e-mail: leaupaco@laft.org}
                and
                Jorge A. Rueda$^{2,3}$
                \footnote[2]{e-mail: jrueda@ula.ve}
                }
\address{
         $^{1}$ Departamento de F\'isica, Universidad Nacional de Colombia, Santa F\'e de Bogot\'a D. C., 
                Colombia.\\
         $^{2}$ Escuela de F\'{i}sica, Universidad Industrial de Santander, Bucaramanga, Colombia.\\
         $^{3}$ Centro de F\'isica Te\'orica, Universidad de Los Andes, M\'erida, Venezuela.
         }
\begin{abstract}
We dispose of some objections raised  by Manko \emph{et 
al.} \cite{Manko} on a recently published paper on the role of Poynting vector in the ocurrence of vorticity in electrovaccum spacetimes \cite{Herrera}.
\end{abstract}

In order to confirm the Bonnor's hyphothesis about the role of the electromagnetic 
energy flux as the responsible for  the vorticity in the surrounding of non--rotating sources of 
some gravitational fields \cite{Bon}, Herrera \emph{et al.} \cite{Herrera} recently presented 
a general study on the vorticity  in axially 
symmetric stationary electrovacuum spacetimes, considering the influence of, both, the 
mass rotations and electromagnetic fields.

As was pointed out in \cite{Manko}, the authors of \cite{Herrera} define the electromagnetic 
Ernst potential as $\Phi(\rho,z)=\phi + i \psi$ and the electromagnetic 4-potential as 
$A_{\mu}=(\phi,0,A,0)$ forgetting to change the sign of the  time component of $A_{\mu}$. 
This misprint is translated to the definition of  the Poynting vector, 
\footnote{The missing  4 in the denominator of $S{^\phi}$ in \cite{Herrera} is a typographic misprint without any relevance.}
which should read 
\begin{equation}\label{poyntingVector}
S{^\phi}= \frac{f^{3/2}}{4\pi \rho^2\,e^{2\gamma}}\left(\omega \nabla
\phi \cdot \nabla \phi - \nabla\phi\cdot \nabla A\right)\, .
\end{equation}
instead of 
\begin{equation}\label{poyntingVector}
S{^\phi}= \frac{f^{3/2}}{4\pi \rho^2\,e^{2\gamma}}\left(\omega \nabla
\phi \cdot \nabla \phi + \nabla\phi\cdot \nabla A\right)\, .
\end{equation}

The above mentioned  fact, the wrong sign in the definition of the electromagnetic four potential, 
is the leiv motiv of the paper by Manko \emph{et al.} \cite{Manko}.

All this having been said, the following comments are in order:
\begin{itemize}

\item  All the physical conclusions in \cite{Herrera} are  correct, and remain the same independently on the misprint mentioned before.

\item The comment in  \cite{Manko} ``....we observe that in \cite{Herrera} the electrostatic limit 
of Manko's solution was accomplished ...... for getting the factor $\I qb...$'' , is irrelevant, and might even be misleading for a  non attentive reader.
Indeed,  equation (39) in \cite{Herrera} was obtained as follows: the $\Omega$ potential was quoted from  \cite{Ruiz} and then the limit 
for nor arbitrary cuadripolar deformation ($k\rightarrow 0$) and for rigid rotations ($b \rightarrow 0$) was taken. 
\end{itemize}

\ack

The authors wish to thank  Professor Luis Herrera for useful comments and for checking the redaction of this note.

\section*{References}
\begin{thebibliography}{99}
%%%%%%%%%%%%%%%%%%%%%%


\bibitem{Herrera} Herrera L, Gonz\'alez G A, Pach\'on L A and Rueda J A
\J{2006}{\CQG}{23}{2395}

\bibitem{Manko} Manko V S, Rodchenko D E , Sadovnikov B I, Sod-Hoffs J {\it S gr--qc/0604091}

\bibitem{Bon} Bonnor W B \J{1991}{\PLA}{158}{23} 

\bibitem{Ernst} Ernst F J \J{1968}{\PR}{168}{1415}

\bibitem{Ruiz} Manko V S,  Martin J and  Ru\'iz E  \J {1995}{\JMP}{36}{3063}

\end{thebibliography}

 
\end{document}


gr-qc0605062.extracted_bib
\begin{thebibliography}{99}
%%%%%%%%%%%%%%%%%%%%%%


\bibitem{Herrera} Herrera L, Gonz\'alez G A, Pach\'on L A and Rueda J A
\J{2006}{\CQG}{23}{2395}

\bibitem{Manko} Manko V S, Rodchenko D E , Sadovnikov B I, Sod-Hoffs J {\it S gr--qc/0604091}

\bibitem{Bon} Bonnor W B \J{1991}{\PLA}{158}{23} 

\bibitem{Ernst} Ernst F J \J{1968}{\PR}{168}{1415}

\bibitem{Ruiz} Manko V S,  Martin J and  Ru\'iz E  \J {1995}{\JMP}{36}{3063}

\end{thebibliography}