Abstract
A study is made of the vacuum expectation values for the energy-momentum tensor of a massive scalar field that satisfy a Robin mixed boundary condition on a spherical surface with a background gravitational field from a D+1-dimensional global monopole. Expressions are derived for the Wightman function, vacuum expectation of the square of the field, vacuum energy density, and the radial and azimuthal pressures inside the spherical surface. The regularization procedure involves using the generalized Abel-Plana formula for series in terms of the zeroes of cylindrical functions. This formula makes it possible to separate the part owing to the gravitational field of a global monopole without boundaries from the vacuum expectation and to represent the parts induced by the boundary in the form of exponentially converging integrals which are especially convenient for numerical calculations. The asymptotic behavior of the vacuum averages is studied at the center of the sphere and near its surface. It is shown that for small values of the parameter describing the solid-angle deficit in the geometry of a global monopole, the vacuum stresses induced by the boundary are highly anisotropic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge Univ. Press, Cambridge (1994).
A. M. Polyakov, Pis'ma zh. eksperim. i teor. fiz. 20, 430 (1974); G. t'Hooft, Nucl. Phys. B79, 276 (1974).
T. W. B. Kibble, J. Phys. A9, 1387 (1976).
D. D. Sokolov and A. A. Starobinskii, Dokl. AN SSSR 234, 1043 (1977).
M. Barriola and A. Vilenkin, Phys. Rev. Lett. 63, 341 (1989).
W. A. Hiscock, Class. Quantum Gravity 7, L235 (1990).
F. D. Mazzitelli and C. O. Lousto, Phys. Rev. D43, 468 (1991).
E. R. Bezerra de Mello, V. B. Bezerra, and N. R. Khusnutdinov, Phys. Rev. D60, 063506 (1999).
E. R. Bezerra de Mello, J. Math. Phys. 43, 1018 (2002).
M. Bordag, K. Kirsten, and S. Dowker, Commun. Math. Phys. 182, 371 (1996).
E. R. Bezerra de Mello, V. B. Bezerra, and N. R. Khusnutdinov, J. Math. Phys. 42, 562 (2001).
V. M. Mostepanenko and N. N. Trunov, The Casimir Effect and Its Applications, Clarendon, Oxford (1997).
G. Plunien, B. Muller, and W. Greiner, Phys. Rep. 134, 87 (1986).
M. Bordag, U. Mohidden, and V. M. Mostepanenko, Phys. Rep. 353, 1 (2001).
A. A. Saaryan, Izv. AN Arm. SSR, Matematika 22, 166 (1987); Candidate's Dissertation, Erevan (1987).
A. A. Saharian, The Generalized Abel-Plana Formula. Applications to Bessel Functions and Casimir Effect, Report1 IC/2000/14; hep-th/0002239.
N. Birrell and P. Davis, Quantized Fields in Curved Space-time [Russian translation], Mir, Moscow (1984).
A. Erdelyi, et al., Higher Transcendental Functions, vol. 2, McGraw Hill, New York (1953).
L. Sh. Grigoryan and A. A. Saaryan, DAN Arm. SSR 83, 28 (1986); Izv. AN Arm. SSR, Fizika 22, 3 (1987).
A. A. Saharian, Phys. Rev. D63, 125007 (2001).
A. A. Saaryan, Izv. AN Arm. SSR, Fizika 23, 130 (1988).
A. Romeo and A. A. Saharian, Phys. Rev. D63, 105019 (2001).
A. Rezaeian and A. A. Saharian, Class. Quantum Gravity 19, 3625 (2002).
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions [Russian translation], Nauka, Moscow (1979).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions [in Russian], Nauka, Moscow (1983).
A. Romeo and A. A. Saharian, J. Phys. A35, 1297 (2002).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Saharian, A.A. Quantum Vacuum Effects in the Gravitational Field of a Global Monopole. Astrophysics 47, 260–272 (2004). https://doi.org/10.1023/B:ASYS.0000031841.59310.c2
Issue Date:
DOI: https://doi.org/10.1023/B:ASYS.0000031841.59310.c2