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Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

M. K. Zangeneh, F. S. N. Lobo, M. H. Dehgani

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an n -dimensional spacetime M4×Kn4 , where Kn4 is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum Kn4 space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and Λ , we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by ρ=(γpτ)/[ω(1+γ)] , we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant.

Physical Review D
Volume 92, Page 124049
2015 December

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Instituto de Astrof√≠sica e Ci√™ncias do Espa√ßo Universidade do Porto Faculdade de Ciências da Universidade de Lisboa Funda√ß√£o para a Ci√™ncia e a Tecnologia
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