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We calculate the potential contributions of the Hamiltonian in harmonic coordinates up 6PN for binary mass systems to O ( G N 4 ) and perform comparisons to recent results in the literature [1] and [2] .

We calculate small correction terms to gravitational potential near an asymmetric BPS brane embedded in a 5D AdS-Minkowski space in the context of supergravity. The normalizable wave functions of gravity fluctuations around the brane describe only massive modes. We compute such wave functions analytically in the thin wall limit. We estimate the correction to gravitational potential for small and long distances, and show that there is an intermediate range of distances in which we can identify 4D gravity on the brane below a crossover scale. The 4D gravity is metastable and for distances much larger than the crossover scale the 5D gravity is recovered., 6 pages, 2 figures, version to appear in PLB

Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. The final form of the potential involves a self-adjoint extension parameter $\alpha$, which plays a role of an additional mass (or distance) scale. The striking feature of Newton potential in this setup is that the potential behaves as seven-dimensional in long range when $\alpha$ is nonzero. For small $\alpha$ there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of $\alpha$ from zero. In the short range the four-dimensional behavior is recovered. The physical implication of this result is discussed in the context of the accelerating behavior of universe., Comment: 13 pages, no figure

We solve the Einstein equations in the Dvali-Gabadadze-Porrati model with a static, spherically symmetric matter distribution on the physical brane and obtain an exact expression for the gravitational field outside the source to the first order in the gravitational coupling. Although when confined on the physical brane this expression reproduces the correct 4D Newtonian potential for distances r_s << r << {\lambda}, where {\lambda} is a characteristic length scale of the model, it does not coincide with the standard linearized form of the 4D Schwarzschild metric. The solution reproduces the 5D Schwarzschild metric in the linearized approximation for r >> {\lambda}., Comment: 9 pages, plain Tex, no figures

Considering a nine-parameter lagrangian quadratic in torsion and curvature, we derive the general condition which must be satisfied by the parameters in order to obtain, in the weak field limit, a Yukawa-type correction to the static Newton potential. This condition is shown to be in general not incompatible with a different set of restrictions needed to avoid the presence of ghosts and tachyons.

Using a fixed-energy amplitude in Randall-Sundrum single brane scenario, we compute the Newton potential on the brane. It is shown that the correction terms to the Newton potential involve a logarithmic factor. Especially, when the distance between two point masses are very small compared to $AdS$ radius, the contribution of KK spectrum becomes dominant compared to the usual inversely square law. This fact may be used to prove the existence of an extra dimension experimentally., Comment: 7 pages, 1 figure

Ghost condensation has been recently proposed as a mechanism inducing the spontaneous breaking of Lorentz symmetry. Corrections to the Newton potential generated by a static source have been computed: they yield a limit M < 10 MeV on the symmetry breaking scale, and - if the limit is saturated - they are maximal at a distance L ~ 1000 km from the source. However, these corrections propagate at a tiny velocity, v_s ~ 10^{-12} m/s, many orders of magnitude smaller than the velocity of any plausible source. We compute the gravitational potential taking the motion of the source into account: the standard Newton law is recovered in this case, with negligible corrections for any distance from the source up to astrophysical scales. Still, the vacuum of the theory is unstable, and requiring stability over the lifetime of the Universe gives a limit for M which is not too far from the one given above. In the absence of a direct coupling of the ghost to matter, signatures of this model will have to be searched in the form of exotic astrophysical events., 13 pages