Stability of the GRS model

We discuss the compatibility between the weaker energy condition and the st ability of Gregory, Rubakov and Sibiryakov (GRS) model. Because the GRS spa cetime violates the weak energy condition, it may cause the instability Tn the GRS model, the four-dimensional gravity can be described by the massive KK modes with the resonance. Hence, instead of considering the weaker ener gy condition, we require for the stability of this model: no tachyon and no ghost condition for graviton modes (h(mu nu)). No tachyonic condition (m(h )(2) greater than or equal to 0) is satisfied because the lowest state m(h) = 0 is supersymmetric vacuum state. Further, no ghost state condition is a chieved if one requires some relations for the matter sourer: 2T(55) = T-mu (mu) = 3(T-22 + T-33) It turns out that, although the GRS spacetime does no t satisfy the weaker energy condition, it is stable against small perturbat ion. (C) 2001 Published by Elsevier Science B.V.