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It is known that spherically symmetric static spacetimes admit a foliation by{\deg}at hypersurfaces. Such foliations have explicitly been constructed forsome spacetimes, using different approaches, but none of them have proved oreven discussed the uniqueness of these foliations. The issue of uniquenessbecomes more important due to suitability of {\deg}at foliations for studyingblack hole physics. Here {\deg}at spherically symmetric spacelike hy-persurfaces are obtained by a direct method. It is found that sphericallysymmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces,and that these hypersurfaces are unique up to translation under the time- likeKilling vector. This result guarantees the uniqueness of {\deg}at sphericallysymmetric foliations for such spacetimes.

Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes