Gravitomagnetism and angular momenta of black–holes
Marcelo Samuel Berman
Instituto Albert Einstein, Curitiba, PR, Brazil
Marcelo Samuel Berman: Instituto Albert Einstein, Av. Candido Hartmann, 575, No. 17, 80730–440, Curitiba–PR, Brazil (msberman@institutoalberteinstein.org).
Received 2006 September 27 ]]> Accepted 2007 April 12
Resumen
Revisamos las fórmulas del contenido energético de los hoyos negros de Kerr–Newman, para los cuales la parte de energía gravitomagnética entra en escena (Berman 2004, 2006a,b). Después, obtenemos las fórmulas de los momentos angulares, incluyendo el efecto gravitomagnético. Se establecen tres teoremas: (1) Ningún hoyo negro tiene su energía confinada en su interior; (2) Los hoyos negros en rotación no poseen su momento angular confinado; (3) La densidad de energía de un hoyo negro no está confinada interiormente. La diferencia entre nuestros resultados y los previamente publicados por Virbhadra (1990a,b,c), y Aguirregabiria et al. (1996), se desprende de la ausencia de energía auto–gravitacional en el cálculo efectuado por aquellos autores. Esta ausencia se nota directamente en el cálculo de la energía de un hoyo negro estático.
Abstract
We review the energy contents formulae of Kerr–Newman black–holes, where gravitomagnetic energy term comes into play (Berman 2004, 2006a,b). Then, we obtain the angular momenta formulae, which include the gravitomagnetic effect. Three theorems can be enunciated: (1) No black–hole has its energy confined to its interior; (2) Rotating black–holes do not have confined angular momenta; (3) The energy density of a black–hole is not confined to its interior. The difference between our calculation and previous ones by Virbhadra (1990a,b,c), and Aguirregabiria et al. (1996), lies in the fact that we include a term responsible for the self–gravitational energy, while the cited authors discarded such effect, which appears in the static black hole energy calculation.
Key Words: Black hole physics—gravitation—magnetic fields
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]]>Acknowledgement
The author was saved from unclear passages by an anonymous referee, whom I thank. I am grateful as well to my intellectual mentors, Fernando de Mello Gomide and M. M. Som. I thank Paula, Albert, and Geni for encouragement and also Marcelo Guimaráes, Nelson Suga, Mauro Tonasse, Antonio Teixeira and Herman J. M. Cuesta.
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