Fate of the first traversible wormhole: Black-hole collapse or inflationary expansion

Hisa-aki Shinkai; Sean A. Hayward

doi:10.1103/PhysRevD.66.044005

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Fate of the first traversible wormhole: Black-hole collapse or inflationary expansion

Hisa-aki Shinkai^*

Sean A. Hayward^†

Computational Science Division, Institute of Physical & Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama, 351-0198, Japan

Department of Science Education, Ewha Womans University, Seoul 120-750, Korea

^*Email address: shinkai@atlas.riken.go.jp
^†Email address: hayward@mm.ewha.ac.kr

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Phys. Rev. D 66, 044005 – Published 16 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.044005

Abstract

We study numerically the stability of the first Morris-Thorne traversible wormhole, shown previously by Ellis to be a solution for a massless ghost Klein-Gordon field. Our code uses a dual-null formulation for spherically symmetric space-time integration, and the numerical range covers both universes connected by the wormhole. We observe that the wormhole is unstable against Gaussian pulses in either exotic or normal massless Klein-Gordon fields. The wormhole throat suffers a bifurcation of horizons and either explodes to form an inflationary universe or collapses to a black hole if the total input energy, is, respectively, negative or positive. As the perturbations become small in total energy, there is evidence for critical solutions with a certain black-hole mass or Hubble constant. The collapse time is related to the initial energy with an apparently universal critical exponent. For normal matter, such as a traveller traversing the wormhole, collapse to a black hole always results. However, carefully balanced additional ghost radiation can maintain the wormhole for a limited time. The black-hole formation from a traversible wormhole confirms the recently proposed duality between them. The inflationary case provides a mechanism for inflating, to macroscopic size, a Planck-sized wormhole formed in space-time foam.

References (17)

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Once the wormhole is perturbed, this hypersurface loses its specific geometrical meaning as the wormhole throat $l = 0$ . However, one can say that it is composed of minimal surfaces in some family of spatial hypersurfaces, which are locally close to the constant- $t$ family for small perturbations.
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[c1] M.S. Morris and K.S. Thorne, Am. J. Phys. 56, 395 (1988).

[c2] M. Visser, Lorentzian Wormholes (AIP Press, New York, 1995).

[c3] S.A. Hayward, Int. J. Mod. Phys. D 8, 373 (1999).

[c4] S.A. Hayward, S.-W. Kim, and H. Lee, Phys. Rev. D 65, 064003 (2002).

[c5] G. Clément, Am. J. Phys. 57, 967 (1989).

[c6] H.G. Ellis, J. Math. Phys. 14, 395 (1973).

[c7] S.A. Hayward, Class. Quantum Grav. 10, 779 (1993).

[c8] S.A. Hayward, Phys. Rev. D 53, 1938 (1996).

[c9] S.A. Hayward, Class. Quantum Grav. 15, 3147 (1998).

[c10] S.A. Hayward, Phys. Rev. D 49, 6467 (1994).

[c11] Once the wormhole is perturbed, this hypersurface loses its specific geometrical meaning as the wormhole throat $l = 0$ . However, one can say that it is composed of minimal surfaces in some family of spatial hypersurfaces, which are locally close to the constant- $t$ family for small perturbations.

[c12] K.A. Bronnikov, G. Clément, C.P. Constantinidis, and J.C. Fabris, Phys. Lett. A 243, 121 (1998).

[c13] C. Armendariz-Picon, Phys. Rev. D 65, 104010 (2002).

[c14] M.W. Choptuik, Phys. Rev. Lett. 70, 9 (1993).

[c15] J.A. Wheeler, Ann. Phys. (N.Y.) 2, 604 (1957).

[c16] T.A. Roman, Phys. Rev. D 47, 1370 (1993).

[c17] I.H. Redmount and W.-M. Suen, Phys. Rev. D 47, 2163 (1993).

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Fate of the first traversible wormhole: Black-hole collapse or inflationary expansion

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