Abstract
We rigorously prove that for compact charged general relativistic objects there is a lower bound for the mass–radius ratio. This result follows from the same Buchdahl type inequality for charged objects, which has been extensively used for the proof of the existence of an upper bound for the mass–radius ratio. The effect of the vacuum energy (a cosmological constant) on the minimum mass is also taken into account. Several bounds on the total charge, mass and the vacuum energy for compact charged objects are obtained from the study of the Ricci scalar invariants. The total energy (including the gravitational one) and the stability of the objects with minimum mass–radius ratio is also considered, leading to a representation of the mass and radius of the charged objects with minimum mass–radius ratio in terms of the charge and vacuum energy only.
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References
Chodos A., Jaffe R.L., Johnson K., Thorn C.B. and Weisskopf V.F. (1974). Phys. Rev. D9: 3471
Chodos A., Jaffe R.L., Johnson K. and Thorn C.B. (1974). Phys. Rev. D10: 2599
DeGrand T., Jaffe R.L., Johnson K. and Kiskis J. (1975). Phys. Rev. D12: 2060
Hosoka A. and Toki H. (1996). Phys. Rep. 277: 65
Buballa M. (2005). Phys. Rep. 407: 205
Poncede Leon J. (2004). Gen. Rel. Grav. 36: 1453
Tiwari R.N., Rao J.R. and Kanakamedala R.R. (1984). Phys. Rev. D30: 489
Lopez C.A. (1984). Phys. Rev. D30: 313
Gautreau R. (1985). Phys. Rev. D 31: 1860
Gron O. (1985). Phys. Rev. D31: 2129
Tiwari R.N., Rao J.R. and Kanakamedala R.R. (1986). Phys. Rev. D 34: 1205
Bonnor W.B. and Cooperstock F.I. (1989). Phys. Lett. A 139: 442
Herrera L. and Verela V. (1994). Phys. Lett. A 189: 11
Tiwari N. and Ray S. (1997). Gen. Rel. Grav. 29: 683
Ray S., Espindola A.L., Malheiro M., Lemos J.P.S. and Zanchin V.T. (2003). Phys. Rev. D 68: 084004
Ghezzi C.R. (2005). Phys. Rev. D 72: 104017
Whinnett A.W. and Torres D.F. (1999). Phys. Rev. D 60: 104050
Yoshinoya H. and Mann R.B. (2006). Phys. Rev. D 74: 044003
Booth I.S. and Mann R.B. (1999). Phys. Rev. D 60: 124009
Riess A.G. (1998). Astron. J. 116: 109
Perlmutter S. (1999). Astrophys. J. 517: 565
de Bernardis P. (2000). Nature 404: 995
Hanany S. (2000). Astrophys. J. 545: L5
Peebles P.J.E. and Ratra B. (2003). Rev. Mod. Phys. 75: 559
Padmanabhan T. (2003). Phys. Rep. 380: 235
Nojiri S. and Odintsov S.D. (2003). Phys. Lett. B 562: 147
Nojiri S. and Odintsov S.D. (2003). Phys. Lett. B 571: 1
Nojiri S. and Odintsov S.D. (2004). Phys. Rev. D 70: 103522
Buchdahl H.A. (1959). Phys. Rev. 116: 1027
Mak M.K., Harko T. and Dobson P.N. (2000). Mod. Phys. Lett. A 15: 2153
Böhmer C.G. (2004). Gen. Rel. Grav. 36: 1039
Böhmer C.G. (2005). Ukr. J. Phys. 50: 1219
Balaguera-Antolínez A., Böhmer C.G. and Nowakowski M. (2005). Int. J. Mod. Phys. D 14: 1507
Böhmer C.G. and Harko T. (2006). Class. Quantum Grav. 23: 6479
Mak M.K., Harko T. and Dobson P.N. (2001). Europhys. Lett. 55: 310
Straumann N. (1984). General Relativity and Relativistic Astrophysics. Springer, Berlin
Böhmer C.G. and Harko T. (2005). Phys. Lett. B 630: 73
Landau L.D. and Lifshitz E.M. (1975). The Classical Theory of Fields. Pergamon Press, Oxford
Beckenstein J.D. (1971). Phys. Rev. D4: 2185
Katz J., Lynden-Bell D. and Israel W. (1988). Class. Quantum Grav. 5: 971
Gron O. and Johannesen S. (1992). Astrophys. Space Sci. 19: 411
Einstein A. (1923). The Principle of Relativity: Einstein and Others. Dover, New York
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Böhmer, C.G., Harko, T. Minimum mass–radius ratio for charged gravitational objects. Gen Relativ Gravit 39, 757–775 (2007). https://doi.org/10.1007/s10714-007-0417-3
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DOI: https://doi.org/10.1007/s10714-007-0417-3