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We analyze the induced self-energy and self-force on a scalar point-like charged test particle placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the threedimensional Green function associated with this physical system. We explicitly show that for points outside the monopole's core the scalar self-energy presents two distinct contributions. The first one is induced by the non-trivial topology of the global monopole considered as a point-like defect and the second is a correction induced by the non-vanishing inner structure attributed to it. For points inside the monopole, the self-energy also present a similar structure, where now the first contribution depends on the geometry of the spacetime inside. As illustrations of the general procedure adopted, two specific models, namely flower-pot and the ballpoint-pen, are considered for the region inside. For these two different situations, we were able to obtain exact expressions for the self-energies and self-forces in the regions outside and inside the global monopole.Although the geometric properties of the spacetime outside the monopole are very well understood, there are no explicit expressions for the components of the metric tensor in the region inside. 1 As a consequence of this fact, many interesting investigations of physical effects associated with global monopole consider this object as a point-like defect. Adopting this simple model, calculations of vacuum polarization effects associated with bosonic [6] and fermionic quantum fields [7], in four-dimensional global monopole spacetime, present divergence on the monopole's core. Moreover, considering higher-dimensional spacetime, vacuum polarization effects associated with bosonic [8] and fermionic [9] quantum fields, also present divergences on the monopole's core.A very well known phenomenon that occur with an electric charged test particle placed at rest in a curved spacetime, is that it may become subjected to an electrostatic self-interactions. The origin of this induced self-interaction resides on the non-local structure of the field caused by the spacetime curvature and/or non-trivial topology. This phenomenon has been analyzed in an idealized cosmic string spacetime by Linet [10] and Smith [11], independently, and also in the spacetime of a global monopole considered as a point-like defect in [12]. In these analysis, the corresponding self-forces are repulsive and depend on the square of electric charge; moreover they present divergences on the respective defects' core. A possible way to circumvent the divergence problem is to consider these defects as having a non-vanishing radius, and attributing for the region inside a structure. For the cosmic string, two different models have been adopted to describe the geometry inside it: the ballpoint-pen model proposed independently by Gott and Hiscock [13], replaces the conical singularity at the string axis by a constant curvature spacetime in...

In this work we analise the electrostatic self-energy and self-force on a point-like electric charged particle induced by a global monopole spacetime considering a inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points inside and outside the monopole's core the self-energy presents two distinct contributions. The first is induced by the geometry associated with the spacetime under consideration, and the second one is a correction due to the non-vanishing inner structure attributed to it. Considering specifically the ballpoint-pen model for the region inside, we were able to obtain exact expressions for the self-energies in the regions outside and inside the monopole's core.

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In this paper we correct previous result obtained in published paper.In the analysis of electrostatic self-energy on a point-like electric-charged particle induced by a global monopole space-time considering the ballpoint pen model for the region inside, 1 we found, among several other interesting results, that near the boundary this self-energy presents logarithmic divergent results in both regions, i.e. for r ≤ r 0 and r ≥ r 0 , where r 0 is the radius of monopole. However, in recent paper Ref. 2, we have observed that these conclusions are not correct. In fact, in the analysis for large value of l, of the coefficients inside the summations of Eqs. (44) and (56) of Ref. 1, we have missed out extra terms in both expressions. These extra terms exactly cancel the 1/l behavior previously obtained, giving as correct expressions, coefficients proportional to 1/l 2 , which provide finite results for r = r 0 .So, we conclude that there is no logarithmic divergent contribution on the induced self-energy in the ballpoint pen model. The rest of our results, especially the most important one related with the behavior of self-energy near the monopole's center, and also the behavior of selfenergy for large distances from the monopole, remain correct.

Uma explicaçãoOs presentes estudos respondem a indagações relativas a um pleito judicial específico: a ação proposta por dezenas de sindicatos rurais de Mato Grosso perante a Monsanto, questionando a cobrança -que entendem indevida -relativa a certas patentes pertinentes à tecnologia Roundup Ready.Assim, não se leva em conta a série de temas suscitados na outra massa litigiosa ajuizada pelos agricultores do sul brasileiro. A carência da discussão desses temas não se deve entender como nos alheando da discussão travada nos tribunais do Rio Grande do Sul. Das habilitações que se entende ter para dar o presente estudoConvidado a enunciar meu entendimento sobre a matéria da Ação Coletiva 82-2012, correndo perante a Justiça de Mato Grosso, sinto-me habilitado a fazê-lo. Uma vez superadas as questões de fato de que patentes são relevantes para prover a hipótese de incidência da obrigação de pagar royalties, todas as questões subsequentes do pagamento são estritamente matéria de direito. E é com esse ramo do Direito Industrial com que tenho tido a oportunidade de laborar desde que, a 15 de agosto de 1979, passei a exercer a função de Assessor do Presidente do INPI, para ser posteriormente Procurador Geral daquela autarquia, e Assessor Especial do Ministro da Indústria e Comércio.Ao deixar a advocacia na União, em 1988, para integrar o serviço jurídico de outra entidade federada, continuei ininterruptamente a advogar no âmbito da Propriedade Intelectual, ou seja, já há 33 anos. No âmbito acadêmico, sou há muitos anos professor de direito de patentes nos cursos de pós-graduação na PUC-Rio, aliás o único curso regular da matéria nas universidades brasileiras.