BLACK-HOLE ENTROPY REVEALS A 12TH DIMENSION

The Bekenstein-Hawking black hole entropy in string theory and its gen eralizations, as expressed in terms of charges that correspond to cent ral extensions of the supersymmetry algebra, has more symmetries;than U duality. It is invariant under transformations of the charges, invol ving a twelfth (or thirteenth) ''dimension.'' This is an indication th at the secret theory behind string theory has a superalgebra involving Lorentz nonscalar extensions (that are not strictly central), as sugg ested in S theory, and which could be hidden in M or F theories. It is suggested that the idea of spacetime is broader than usual, and that a larger ''spacetime'' is partially present in black holes.