ar X iv : g r - qc / 0 30 50 13 v 1 2 M ay 2 00 3 Ambiguities in formulation of GR - based braneworld models

We study braneworld scenarios within the framework of five-dimensional general relativity. The braneworld Einstein field equations (BEFE) of Shiromizu, Maeda and Sasaki (SMS) possess two salient features which distinguish them from the analogous Einstein field equations, namely a Weyl term and a term Q quadratic in the braneworld energy-momentum. The former is commonly neglected, while the precise form of Q is kept. We demonstrate that there is a great deal of freedom to reformulate the BEFE. An important consequence of this is that the resulting truncated braneworld equations, which arise from the generalization of the neglect of the Weyl term in the SMS equations, are usually inequivalent. We give examples of formulations of BEFE in which either (or indeed both) of the above salient features are absent. This could have important consequences for very early universe studies in braneworld scenarios. This highlights the potential dangers in using the Q obtained by truncation of the usual SMS BEFE. PACS number: 04.50+h