Abstract
In this paper, we consider both Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation) analogs of the energy-momentum definition of Møller in order to explicitly evaluate the energy distribution (due to matter and fields including gravity) associated with a general black hole model which includes several well-known black holes. To calculate the special cases of energy distribution, here we consider eight different types of black hole models such as anti-de Sitter Cmetric with spherical topology, charged regular black hole, conformal scalar dyon black hole, dyadosphere of a charged black hole, regular black hole, charged topological black hole, charged massless black hole with a scalar field, and the Schwarzschild-de Sitter space-time. Our teleparallel gravitational result is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in teleparallel equivalent of general relativity but also in any teleparallel model. This paper also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is the powerful concept to calculate energy distribution in a given space-time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aguirregabiria, J. M., Chamorro, A., and Virbhadra, K. S. (1996). General Relativity and Gravitation 28, 1393.
Albrow, M. G. (1973). Nature 241, 56.
Aydogdu, O. (2005). gr-qc/0509047.
Aydogdu, O. and Salti, M. (2005). Astrophysics and Space Science 299, 227.
Aydogdu, O., Salti, M., and Korunur, M. (2005). Acta Physica Slovenica 55, 537.
Ayon-Beato, E. and Garcia, A. (1999). Physics Letters B 464, 25.
Banerjee, N. and Sen, S. (1997). Pramana-Journal of Physics 49, 609.
Bardeen, J. (1968). Proceedings of the GR5, Tiflis, USSR.
Bergmann, P. G. and Thomson, R. (1953). Physical Review 89, 400.
Borde, A. (1994). Physical Review D 50, 3692.
Borde, A. (1997). Physical Review D 50, 7615.
Chamorro, A. and Virbhadra, K. S. (1995). Pramana-Journal of Physics 45, 181.
Chamorro, A. and Virbhadra, K. S. (1996). International Journal of Modern Physics D 5, 251.
Cooperstock, F. I. (1994). General Relativity and Gravitation 26, 323.
Cooperstock, F. I. and Israelit, M. (1995). Foundations of Physics 25, 631.
Cooperstock, F. I. and Richardson, S. A. (1992). In Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, held 16–18 May, 1991 at University of Winnipeg. Kunstatter, G., Vincent, D. E., and Williams, J. G., eds., World Scientific, Singapore, p. 110.
de Andrade, V. V. and Pereira, J. G. (1997). Physical Review D 56, 4689.
De Lorenci, V. A., Figueredo, N., Fliche, H. H., and Novello, M. (2000). Physics Letters B 482, 134.
Dias, O. J. C. and Lemos, J. P. S. (2003). Physical Review D 67, 064001.
Einstein, A. (1915). Sitzungsber. Preus. Akad. Wiss. Berlin (Math. Phys.) 778 (1915), Addendum-ibid. 799 (1915).
Hayashi, K. and Shirafuji, T. (1978). Physical Review D 19, 3524.
Hayashi, K. and Shirafuji, T. (1980a). Progress in Theoretical Physics 64, 866.
Hayashi, K. and Shirafuji, T. (1980b). Progress in Theoretical Physics 65, 525.
Hehl, F. W., Nitsch, J., and von der Heyde, P. (1980). In General Relativity and Gravitation, Held, A., ed., Plenum, New York, p. 329.
Johri, V. B., Kalligas, D., Singh, G. P. and Everitt, C. W. F. (1995). General Relativity and Gravitation 27, 323.
Landau, L. D. and Lifshitz, E. M. (1987). The Classical Theory of Fields 4th edition, Pergamon Press, Oxford.
Lessner, G. (1990). General Relativity and Gravitation 28, 527.
Lessner, G. (1996). General Relativity and Gravitation 28, 527.
Møller, C. (1958). Annales de Physique (NY) 4, 347.
Møller, C. (1961) Mat. Fys. Medd. K. Vidensk. Selsk. 1, 10.
Møller, C. (1961). Annales de Physique (NY) 12, 118.
Møller, C. (1978). Mat. Fys. Medd. K. Vidensk. Selsk. 39, 13.
Martinez, C. and Staforelli, J. P. (2005). hep-th/0512022.
Meyer, H. (1982). General Relativity and Gravitation 14, 531.
Mikhail, F. I., Wanas, M. I., Hindawi, A., and Lashin, E. I. (1993). International Journal of Theoretical Physics 32, 1627.
Nashed, G. G. L. (2002). Physical Review D 66, 064015.
Papapetrou, A. (1948). Proceedings of the Royal Irish Academy A 52, 11.
Plebanski, J. A. and Demianski, M. (1976). Annals of Physics (NY) 98, 98.
Preparata, G., Ruffini, R. and Wue, S.-S. (1998). A and A L87, 338.
Qadir, A. and Sharif, M. (1992). Physics Letters A 167, 331.
Radinschi, I. (2000). Modern Physics Letters A 15, 2171.
Radinschi, I. (2001). Modern Physics Letters A 20, 673.
Robertson, H. P. (1932). Annals of Mathematics (Princeton) 33, 496.
Rosen, N. (1994). General Relativity and Gravitation 26, 319.
Rosen, N. and Virbhadra, K. S. (1993). General Relativity and Gravitation 25, 429.
Ruffini, R. (1998). Yamada Conference ob Black Holes and High Energy Astrophysics, Salto, H., ed., University Academic Press, Tokyo.
Ruffini, R., Bianco, C. L., Xue, S.-S., Chardonnet, P., and Fraschetti, F. (2003). International Journal of Modern Physics D 12, 173.
Saez, D. (1983). Physical Review D 27, 2839.
Salti, M. (2005a). Astrophysics and Space Science 299, 159.
Salti, M. (2005b). Modern Physics Letters A 20, 2175.
Salti, M. (2005c). Acta Physica Slovenica 55, 563.
Salti, M. (2005d). Nuovo Cimento B 120, 53.
Salti, M. and Aydogdu, O. (2005). gr-qc/0511030.
Salti, M. and Havare, A. (2005). International Journal of Modern Physics A 20, 2169.
Shankaranarayanan, S. (2003). Physical Review D 67, 084026.
Sharif, M. (2004). Nuovo Cimento B 19, 463.
TCI Software Research (1998). Scientific Workplace 3.0.
Tolman, R. C. (1934). Relativity, Thermodynamics and Cosmology, Oxford University Pres, London, p. 227.
Tryon, E. P. (1973). Nature 246, 396.
Vagenas, E. C. (2003a). International Journal of Modern Physics A 18, 5781.
Vagenas, E. C. (2003b). International Journal of Modern Physics A 18, 5949.
Vagenas, E. C. (2004). Modern Physics Letters A 19, 213.
Vagenas, E. C. (2005).International Journal of Modern Physics D 14, 573.
Vagenas, E. C. (2006). gr-qc/0602107.
Vargas, T. (2004). General Relativity and Gravitation 36, 1255.
Virbhadra, K. S. (1990a). Physical Review D 41, 1086.
Virbhadra, K. S. (1990b). Physical Review D 42, 2919.
Virbhadra, K. S. (1995). Pramana-Journal of Physics 45, 215.
Virbhadra, K. S. (1999) Physical Review D 60, 104041.
Virbhadra, K. S. and Parikh, J. C. (1994). Physics Letters B331, 302.
Weinberg, S. (1972). Gravitation and Cosmology: Principle and Applications of General Theory of Relativity, John Wiley and Sons, Inc., New York.
Weitzenböck, R. (1923). Invariantten theorie, Noordhoff, Gronningen.
Wolfram Research (2003). Mathematica 5.0.
Xulu, S. S. (2000a). International Journal of Modern Physics A 15, 4849–4856.
Xulu, S. S. (2000b). International Journal of Theoretical Physics 30, 1153–1161.
Xulu, S. S. (2003). Preprint gr-qc/0304081.
Yang, C. and Radinschi, I. (2003). Chinese Journal of Physics 41, 326 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saltı, M., Aydogdu, O. On the Møller Energy Associated with Black Holes. Int J Theor Phys 45, 2437–2452 (2006). https://doi.org/10.1007/s10773-006-9212-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9212-2