Scalar waves in a wormhole geometry

Sayan Kar; Deshdeep Sahdev; Biplab Bhawal

doi:10.1103/PhysRevD.49.853

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Scalar waves in a wormhole geometry

Sayan Kar^* and Deshdeep Sahdev^†

Biplab Bhawal^‡

Department of Physics, Indian Institute of Technology, Kanpur 208 016, India

Mehta Research Institute of Mathematics and Mathematical Physics 10, Kasturba Gandhi Marg, Allahabad 211 002, India

^*Electronic address: kars@iitk.ernet.in
^†Electronic address: ds@iitk.ernet.in
^‡Present address: IUCAA, Post Bag 4, Ganeshkind, Pune 411 007, India. Electronic address: biplab@iucaa.ernet.in

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Phys. Rev. D 49, 853 – Published 15 January, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.853

Abstract

The reflection and transmission of massless scalar waves in the curved background geometry of a typical Lorentzian wormhole (in 2+1 and 3+1 dimensions) are discussed. Using the exact solutions which involve modified Mathieu (in 2+1 dimensions) and radial oblate spheroidal (in 3+1 dimensions) functions, explicit analytic expressions are obtained for the reflection and transmission coefficients at specific values of the quantity $ω b_{0}$ ( $ω$ being the energy of the scalar wave and $b_{0}$ the throat radius of the wormhole). It is found that both near-perfect reflection as well as transmission are possible for specific choices of certain parameters.

References (25)

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[c1] M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988)

[c2] M. S. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Lett. 61, 1446 (1988)

[c3] H. Epstein, V. Glaser, and A. Jaffe, Nuovo Cimento 36, 2296 (1965)

[c4] H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

[c5] D. Hochberg and T. W. Kephart, Phys. Lett. B 268, 377 (1991)

[c6] D. Hochberg, Phys. Lett. B 251, 349 (1990)

[c7] J. W. Moffat and T. Svobada, Phys. Rev. D 44, 429 (1991)

[c8] B. Bhawal and S. Kar, Phys. Rev. D 46, 2464 (1992)

[c9] M. Visser, Phys. Rev. D 39, 3182 (1989) Nucl. Phys. B328, 203 (1989)

[c10] J. Friedman, M. S. Morris, I. D. Novikov, F. Echeverria, G. Klinkhammer, K. S. Thorne, and U. Yurtsever, Phys. Rev. D 42, 1915 (1990) J. Friedman and M. S. Morris, Phys. Rev. Lett. 66, 401 (1991)

[c11] S. Y. Kim, Phys. Rev. D 46, 2428 (1992)

[c12] T. A. Roman, Phys. Rev. D 47, 1370 (1993)

[c13] D. Hochberg and T. W. Kephart, Phys. Rev. Lett. 70, 2665 (1993)

[c14] Sayan Kar, Phys. Rev. D 49, 862 (1994)

[c15] G. Clement, Int. J. Theor. Phys. 23, 335 (1984)

[c16] H. Ellis, J. Math. Phys. 14, 104 (1973)

[c17] Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965)

[c18] National Bureau of Standards, Tables Relating to Mathieu Functions (Columbia University Press, New York, 1951)

[c19] A. Leitner and R. D. Spence, J. Franklin Inst. 249, 229 (1950)

[c20] F. M. Arscott, Periodic Differential Equations (Macmillan, New York, 1964)

[c21] N. W. MacLachlan, Theory and Applications of Mathieu Functions (Dover, New York, 1964)

[c22] C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, CA, 1957)

[c23] J. A. Stratton, P. M. Morse, L. J. Chu, and R. A. Hutner, Elliptic Cylinder and Spheroidal Wave Functions (Wiley, New York, 1941)

[c24] P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953)

[c25] Higher Transcendental Functions (Bateman Manuscript Project), edited by A. Erdelyi (McGraw-Hill, New York, 1953), Vol. 3

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Scalar waves in a wormhole geometry

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