Abstract
We present a family of static and evolving spherically symmetric Lorentzian wormhole solutions in -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 , where the state parameter is constant. On the other hand, it is shown that, in any dimension , with and anisotropic barotropic pressure with constant state parameters, static wormhole configurations are always asymptotically flat spacetimes, while, in 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 , 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 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