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In this case therefore a negative Weyl energy contributes to binding the star to the brane. Since this effect is independent of the brane tension, it makes the star more stable than in the general relativistic case. We see it in a very special limiting case when the exterior is Schwarzschild. In this case (U + = 0 = Π+ ), eqs. 25) imply that the interior must have dark radiation density: U − (r) = − 2 4πGN ρ [ρ + p(r)]4 . 57) It follows that the mass function in eq. 58) 0 which is reduced by the negative Weyl energy density, relative to the solution in the previous section and to the general relativity solution.

The natural scenario, where deviations from general relativity occur, is cosmology. g. the review [90] for further references). But this is not all. Significant deviations from Einstein’s theory in fact occur also in astrophysics. Indeed very compact objects and gravitational collapse to black holes, can leave traces of the extra dimensions. For example, when an horizon forms, even if the high-energy effects eventually become disconnected from the outside region on the brane, they could leave a signature on the brane [19].

E. to the Schwarzschild interior solution [80]. We can now calculate the pressure. 30) where 2GN M ∆(r) = 1 − r r R 3 ρ 1+ 2λ 1/2 . 31) 40 CHAPTER 4. 1: Qualitative comparison of the pressure p(r), in general relativity (upper curve), and in a braneworld model with λ = 5 × 108 MeV4 (lower curve). In the general relativity limit, λ−1 → 0, we regain the known exact solution [80]. The high-energy corrections considerably complicate the exact solution. Since ∆(R) must be real, we find an astrophysical lower limit on λ, independent of the Newton-law and cosmological limits: λ≥ GN M R − 2GN M ρ for all uniform stars .

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