Gravitational field equations in a braneworld with Euler-Poincare term

We present the effective gravitational field equations in a 3-brane world with Euler-Poincare term and a cosmological constant in the bulk spacetime. The similar equations on a 3-brane with $\mathbb{Z}_2$ symmetry embedded in a five dimensional bulk spacetime were obtained earlier by Maeda and Torii using the Gauss-Coddazzi projective approach in the framework of the Gaussian normal coordinates. We recover these equations on the brane in terms of differential forms and using a more general coordinate setting in the spirit of Arnowitt, Deser and Misner (ADM). The latter allows for acceleration of the normals to the brane surface through the lapse function and the shift vector. We show that the gravitational effects of the bulk space are transmitted to the brane through the projected ``electric'' 1-form field constructed from the conformal Weyl curvature 2-form of the bulk space. We also derive the evolution equations into the bulk space for the electric 1-form field, as well as for the ``magnetic'' 2-form field part of the bulk Weyl curvature 2-form. As expected, unlike on-brane equations, the evolution equations involve terms determined by the nonvanishing acceleration of the normals in the ADM-type slicing of spacetime

Exact metric around a wiggly cosmic string

The exact metric around a wiggly cosmic string is found by modifying the energy momentum-tensor of a straight infinitely thin cosmic string to include an electric current along the symmetry axis.Comment: 5 page

Vacuum Fluctuations of a massless spin-1/2 field around multiple cosmic strings

We study the interaction of a massless quantized spinor field with the gravitational filed of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force attraction between two parallel cosmic strings.Comment: Class. Quantum Grav. 14(1997) 321