Abstract
We construct a regular five-dimensional brane-world with localised gravity on a flat 3-brane. The matter content in the bulk is parametrised by an analog of a non-linear fluid with equation of state p=gamma rho ^lambda between the ‘pressure’ p and the ‘density’ rho dependent on the 5th dimension. For gamma negative and lambda >1, the null energy condition is satisfied and the geometry is free of singularities within finite distance from the brane, while the induced four-dimensional Planck mass is finite.
Highlights
It is important to emphasise that these solutions are regular independently of the presence of the brane. When the latter is taken into account a cutting and matching procedure is needed for half of the space, as explained above, which can be done in a way that the integral for the induced 4d effective Planck mass is finite, leading to localised gravity on the brane for any value of the exponent λ > 1
We write down the system of dynamical equations holding in the bulk (Y -coordinate), together with the nonlinear equation of state assumed for the bulk fluid
We setup the field equations of a brane embedded in a 5-bulk space which is filled with an imperfect fluid with a nonlinear equation of state, and write down the restrictions imposed by the energy conditions on the bulk fluid quantities by the 5-dimensional geometry
Summary
We setup the field equations of a brane embedded in a 5-bulk space which is filled with an imperfect fluid with a nonlinear equation of state, and write down the restrictions imposed by the energy conditions on the bulk fluid quantities by the 5-dimensional geometry
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