Artículo
Aspects of electrostatics in BTZ geometries
Fecha de publicación:
10/2015
Editorial:
American Physical Society
Revista:
Physical Review D
ISSN:
0556-2821
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In the present paper the electrostatics of charges in nonrotating BTZ black hole and wormhole spacetimes is studied. Our attention is focused on the self-force of a point charge in the geometry, for which a regularization prescription based on the Haddamard Green function is employed. The differences between the self-force in both cases is a theoretical experiment for distinguishing both geometries, which otherwise are locally indistinguishable. This idea was applied before to four and higher-dimensional black holes by the present and other authors. However, the particularities of the BTZ geometry makes the analysis considerable more complicated than those. First, the BTZ spacetimes are not asymptotically flat but instead asymptotically AdS. In addition, the relative distance d ( r , r + 1 ) between two particles located at a radius r and r + 1 in the geometry tends to zero when r → ∞ . This behavior, which is radically different in a flat geometry, changes the analysis of the asymptotic conditions for the electrostatic field. The other problem is that there exist several regularization methods other than the one we are employing, and there does not exist a proof in three dimensions that they are equivalent. However, we focus on the Haddamard method and obtain an expression for the hypothetical self-force in series, and the resulting expansion is convergent to the real solution. We suspect that the convergence is not uniform, and furthermore there are no summation formulas at our disposal. It appears, for points that are far away from the black hole the calculation of the Haddamard self-force requires higher-order summation. These subtleties are carefully analyzed in the paper, and it is shown that they lead to severe problems when calculating the Haddamard self-force for asymptotic points in the geometry.
Palabras clave:
Black Hole
,
Wormhole
,
Einstein-Maxwell
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Identificadores
Colecciones
Articulos(IFIBA)
Articulos de INST.DE FISICA DE BUENOS AIRES
Articulos de INST.DE FISICA DE BUENOS AIRES
Citación
Herrera, Yago; Hurovich, Valeria Laura; Santillán, Osvaldo Pablo; Simeone, Claudio Mauricio; Aspects of electrostatics in BTZ geometries; American Physical Society; Physical Review D; 92; 8; 10-2015; 8504201-8504233
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