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\title{Reply on Comment on ``Gravitating Magnetic Monopole in the Global Monopole Spacetime''}
\author{E. R. Bezerra de Mello \thanks{E-mail: emello@fisica.ufpb.br}
\address{Departamento de F\'{\i}sica-CCEN\\
Universidade Federal da Para\'{\i}ba\\
58.059-970, J. Pessoa, PB\\
C. Postal 5.008, Brazil}\\
\parbox{14 cm}{\medskip\rm\indent
In this Reply we present some argument in favor of the stability of the topological 
defect composed by global and magnetic monopoles.}}
\maketitle

In a recent paper A. Ach\'ucarro and J. Urrestill \cite{AU} have pointed
the stability problem for composite, global and magnetic monopoles, presented 
in a previous publication \cite{JUE}. In the former it is claimed that this 
topological defect is not classically stable against axially symmetric angular 
deformation. By this deformation an extra tension is created at the north-pole 
which drags the core of the global monopole upwards {\it with no cost of energy}. 
Once the cores are separated they are repelled by an induced self-interaction 
\footnote{The stability problem of the global monopole against angular perturbation
has been observed  by A. S. Goldhaber \cite{G}, and also by the authors in 
\cite{AU1}.}. However, in the composite defect system this analysis 
must take into account the induced self-energy more carefully. In \cite{EC} it was 
calculated the formal expression to the electrostatic self-energy associated with a 
test charged particle in the pointlike global monopole spacetime. It was observed 
that it is positive, and by numerical evaluation can be seen that the induced
electrostatic strength increases for larger values of the parameter $\Delta$
\footnote{Although in \cite{AU} the authors said that the 
effect of the core has been considered, this is not true. In \cite{EC} the metric 
tensor considered was associated with the global monopole with no internal 
structure.}. Considering the effect of the core of the global monopole, the 
calculation of the self-energy becomes much more complicated; however we can infer 
that this self-energy goes to zero for very small separation between the charged
particle and the core of the monopole, peaks around the distance of the order 
of the monopole's size and decreases approximately with $1/r$ for larger value of 
separation. Assuming that this effect is presented to magnetic charged particle
as the authors also admit, to separate the cores of the global and
magnetic monopoles needs some amount of energy to overcome the barrier 
\footnote{An estimation for the peak of the magnetostatic self-energy can be 
provided considering the expression for self-energy given in \cite{EC} and that the 
monopole's size is of order $\eta^{-1}\lambda^{-1/2}$ \cite{BV}.}. So the question 
about the classical stability condition of the composite defect against axially 
symmetric perturbation must take into account this fact.

Another point raised by  Ach\'ucarro and Urrestilla is about the profile of 
the Higgs field. In fact for the model analysed in \cite{JUE} there are 
three mass parameters to scale the radial distance. In our numerical analysis we 
adopted the mass of the boson vector: $x=e\eta r$. This choice of mass
scale seemed convenient for us to analyse the behavior of the fields varying the 
self-coupling $\lambda$, keeping the electric coupling $e$ fixed.

\noindent
{\bf Acknowledgment}\\
\noindent
This work was partially supported by CNPq.
 
 
\begin{thebibliography}{100}
\bibitem{AU} A. Ach\'ucarro and J. Urrestilla, pre-print, hep-th/0212148. 
\bibitem{JUE} J. Spinelly, U. de Freitas and E. R. Bezerra de Mello, Phys. Rev. D {\bf 66}, 024018 (2002).
\bibitem{G} A. S. Goldhaber, Phys. Rev. Lett. {\bf 63}, 2158 (1989).
\bibitem{AU1}  A. Ach\'ucarro and J. Urrestilla, Phys. Rev. Lett. {\bf 85},
3091 (2000).
\bibitem{EC} E. R. Bezerra de Mello and C. Furtado, Phys. Rev. D {\bf 56},
1345 (1997).
\bibitem{BV} M. Barriola and A. Vilenkin, Phys. Rev. Lett. {\bf 63}, 341 
(1989).
\end{thebibliography}



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