When gravity couples to scalar fields in Anti-de Sitter space, the geometry
becomes non-AdS and develops singularities generally. We propose a criterion
that the singularity is physically admissible if the integral of the on-shell
Lagrangian density over the finite range is finite everywhere. For all classes
of the singularities studied here, the criterion suggested in this paper
coincides with an independent proposal made by Gubser that the potential should
be bounded from above in the solution. This gives a reason why Gubser's
conjecture works.Comment: 14 pages, revtex, 1 table, references added, two other criteria
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