Implications of Some Static Spherically Symmetric Graviton-Dilaton Solutions in Brans-Dicke and Low Energy String Theory

Analysing the static, spherically symmetric graviton-dilaton solutions in low energy string and Brans-Dicke theory, we find the following. For a charge neutral point star, these theories cannot predict non trivial PPN parameters, $\beta$ and $\gamma$, without introducing naked singularities. We then couple a cosmological constant $\Lambda$ as in low energy string theory. We find that only in low energy string theory, a non zero $\Lambda$ leads to a curvature singularity, which is much worse than a naked singularity. Requiring its absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. If $r_* \simeq 1 {\rm Mpc}$ then $| \Lambda | < 10^{- 114}$ and, if $r_* \simeq 10^{28} {\rm cm}$ then $| \Lambda | < 10^{- 122}$ in natural units.