Abstract
The formation of a naked singularity in f (R) global monopole spacetime is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r = 0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity formed in f (R) global monopole spacetime remains quantum mechanically singular when it is probed with quantum fields having different spin structures. Pitelli and Letelier (Phys. Rev. D 80 (2009) 104035) had shown that for quantum scalar (spin 0) probes the general relativistic global monopole singularity remains intact. For specific modes electromagnetic (spin 1) and Dirac field (spin 1/2) probes, however, we show that the global monopole spacetime behaves quantum mechanically regular. The admissibility of this singularity is also incorporated within the Gubser’s singularity conjecture.
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References
G. Ellis and B. Schmidt, Singular space-times, Gen. Rel. Grav. 8 (1977) 915 [INSPIRE].
P. Bell and P. Szekeres, Interacting electromagnetic shock waves in general relativity, Gen. Rel. Grav. 5 (1974) 275 [INSPIRE].
G.T. Horowitz, Spacetime in string theory, New J. Phys. 7 (2005) 201 [gr-qc/0410049] [INSPIRE].
M. Natsuume, The singularity problem in string theory, gr-qc/0108059 [INSPIRE].
A. Ashtekar, Singularity resolution in loop quantum cosmology: a brief overview, J. Phys. Conf. Ser. 189 (2009) 012003 [arXiv:0812.4703] [INSPIRE].
J. Polchinski, String theory, Cambridge University Press, Cambridge U.K. (1998).
A. Giveon, B. Kol, A. Ori and A. Sever, On the resolution of the timelike singularities in Reissner-Nordström and negative mass Schwarzschild, JHEP 08 (2004) 014 [hep-th/0401209] [INSPIRE].
R.M. Wald, Dynamics in nonglobally hyperbolic, static space-times, J. Math. Phys. 21 (1980) 2082.
G.T. Horowitz and D. Marolf, Quantum probes of space-time singularities, Phys. Rev. D 52 (1995) 5670 [gr-qc/9504028] [INSPIRE].
A. Ishibashi and A. Hosoya, Who’s afraid of naked singularities? Probing timelike singularities with finite energy waves, Phys. Rev. D 60 (1999) 104028 [gr-qc/9907009] [INSPIRE].
D. Konkowski and T. Helliwell, Quantum singularity of quasiregular space-times, Gen. Rel. Grav. 33 (2001) 1131 [INSPIRE].
T. Helliwell, D. Konkowski and V. Arndt, Quantum singularity in quasiregular space-times, as indicated by Klein-Gordon, Maxwell and Dirac fields, Gen. Rel. Grav. 35 (2003) 79 [INSPIRE].
D. Konkowski, T. Helliwell and C. Wieland, Quantum singularity of Levi-Civita space-times, Class. Quant. Grav. 21 (2004) 265 [gr-qc/0401009] [INSPIRE].
D.A. Konkowski, C. Reese, T.M. Helliwell and C. Wieland, Classical and quantum singularities of Levi-Civita spacetimes with and without a cosmological constant, in Procedings of the Workshop on the Dynamics and Thermodynamics of Black holes and Naked Singularities, L. Fatibene, M. Francaviglia, R. Giambo and G. Megli eds., Milan Italy (2004) [Conf. Proc. C 0405132 (2004) 247] [gr-qc/0410114] [INSPIRE].
D. Konkowski and T. Helliwell, Quantum singularities in static and conformally static space-times, Int. J. Mod. Phys. A 26 (2011) 3878 [Int. J. Mod. Phys. Conf. Ser. 3 (2011) 364] [arXiv:1112.5488] [INSPIRE].
T. Helliwell and D. Konkowski, Quantum singularities in spherically symmetric, conformally static spacetimes, Phys. Rev. D 87 (2013) 104041 [arXiv:1302.3970] [INSPIRE].
P.M. Pitelli and P.S. Letelier, Quantum singularities in spacetimes with spherical and cylindrical topological defects, J. Math. Phys. 48 (2007) 092501 [arXiv:0708.2052] [INSPIRE].
J.P.M. Pitelli and P.S. Letelier, Quantum singularities in the BTZ spacetime, Phys. Rev. D 77 (2008) 124030 [arXiv:0805.3926] [INSPIRE].
J.P.M. Pitelli and P.S. Letelier, Quantum singularities around a global monopole, Phys. Rev. D 80 (2009) 104035 [arXiv:0911.2626] [INSPIRE].
P.S. Letelier and J.P.M. Pitelli, n-dimensional FLRW quantum cosmology, Phys. Rev. D 82 (2010) 104046 [arXiv:1010.3054] [INSPIRE].
O. Unver and O. Gurtug, Quantum singularities in (2 + 1) dimensional matter coupled black hole spacetimes, Phys. Rev. D 82 (2010) 084016 [arXiv:1004.2572] [INSPIRE].
S.H. Mazharimousavi, O. Gurtug and M. Halilsoy, Generating static, spherically symmetric black-holes in third order Lovelock gravity, Int. J. Mod. Phys. D 18 (2009) 2061 [arXiv:0809.3649] [INSPIRE].
S.H. Mazharimousavi, M. Halilsoy, I. Sakalli and O. Gurtug, Dilatonic interpolation between Reissner-Nordström and Bertotti-Robinson spacetimes with physical consequences, Class. Quant. Grav. 27 (2010) 105005 [arXiv:0908.3113] [INSPIRE].
S.H. Mazharimousavi, O. Gurtug, M. Halilsoy and O. Unver, 2 + 1 dimensional magnetically charged solutions in Einstein-power-Maxwell theory, Phys. Rev. D 84 (2011) 124021 [arXiv:1103.5646] [INSPIRE].
T. Tahamtan and O. Gurtug, Quantum singularities in a model of f (R) gravity, Eur. Phys. J. C 72 (2012) 2091 [arXiv:1205.5125] [INSPIRE].
T. Carames, E. Bezerra de Mello and M. Guimaraes, Gravitational field of a global monopole in a modified gravity, Int. J. Mod. Phys. Conf. Ser. 3 (2011) 446 [arXiv:1106.4033] [INSPIRE].
M. Barriola and A. Vilenkin, Gravitational field of a global monopole, Phys. Rev. Lett. 63 (1989) 341 [INSPIRE].
J. Man and H. Cheng, The thermodynamic quantities of a black hole with an f (R) global monopole, Phys. Rev. D 87 (2013) 044002 [arXiv:1301.2739] [INSPIRE].
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
M. Reed and B. Simon, Functional analysis, Academic Press, New York U.S.A. (1980).
M. Reed and B. Simon, Fourier analysis and self-adjointness, Academic Press, New York U.S.A. (1975).
R.D. Richtmyer, Principles of advanced mathematical physics, Springer, New York U.S.A. (1978).
S. Chandrasekhar, The mathematical theory of black holes, Oxford University Press, Oxford U.K. (1992).
I. Seggev, Dynamics in stationary, nonglobally hyperbolic space-times, Class. Quant. Grav. 21 (2004) 2651 [gr-qc/0310016] [INSPIRE].
H.D. Kim, A criterion for admissible singularities in brane world, Phys. Rev. D 63 (2001) 124001 [hep-th/0012091] [INSPIRE].
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Gurtug, O., Halilsoy, M. & Mazharimousavi, S.H. Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime. J. High Energ. Phys. 2014, 178 (2014). https://doi.org/10.1007/JHEP01(2014)178
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DOI: https://doi.org/10.1007/JHEP01(2014)178