N-dimensional static and evolving Lorentzian wormholes with a cosmological constant

Mauricio Cataldo, Paola Meza, and Paul Minning
Phys. Rev. D 83, 044050 – Published 25 February 2011

Abstract

We present a family of static and evolving spherically symmetric Lorentzian wormhole solutions in N+1-dimensional Einstein gravity. In general, for static wormholes, we require that, at least, the radial pressure has a barotropic equation of state of the form pr=ωrρ, where the state parameter ωr is constant. On the other hand, it is shown that, in any dimension N3, with ϕ(r)=Λ=0 and anisotropic barotropic pressure with constant state parameters, static wormhole configurations are always asymptotically flat spacetimes, while, in 2+1 gravity, there are not only asymptotically flat static wormholes but also more general ones. In this case, the matter sustaining the three-dimensional wormhole may be only a pressureless fluid. In the case of evolving wormholes with N3, the presence of a cosmological constant leads to an expansion or contraction of the wormhole configurations: for positive cosmological constants, we have wormholes which expand forever, and, for negative cosmological constants, we have wormholes which expand to a maximum value and then recollapse. In the absence of a cosmological constant, the wormhole expands with constant velocity, i.e., without acceleration or deceleration. In 2+1 dimensions, the expanding wormholes always have an isotropic and homogeneous pressure, depending only on the time coordinate.

  • Received 17 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.044050

© 2011 American Physical Society

Authors & Affiliations

Mauricio Cataldo*

  • Departamento de Física, Facultad de Ciencias, Universidad del Bío—Bío, Avenida Collao 1202, Casilla 5-C, Concepción, Chile

Paola Meza and Paul Minning

  • Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile

  • *mcataldo@ubiobio.cl
  • paolameza@udec.cl
  • pminning@udec.cl

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Issue

Vol. 83, Iss. 4 — 15 February 2011

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