  In this paper we consider four dimensional (4D) linearized gravity (LG) with
a planar boundary, where the most general boundary conditions are derived
following Symanzik's approach. The boundary breaks diffeomorphism invariance
and this results in a breaking of the corresponding Ward identity. From this,
on the boundary we find two conserved currents which form an algebraic
structure of the Kac-Moody type, with a central charge proportional to the
action ``coupling''. Moreover, we identify the boundary degrees of freedom,
which are two symmetric rank-2 tensor fields, and derive the symmetry
transformations, which are diffeomorphisms. The corresponding most general 3D
action is obtained and a contact with the higher dimensional theory is
established by requiring that the 3D equations of motion coincide with the 4D
boundary conditions. Through this kind of holographic procedure, we find two
solutions~: LG for a single tensor field and LG for two tensor fields with a
mixing term. Curiously, we find that the Symanzik's 4D boundary term which
governs the whole procedure contains a mass term of the Fierz-Pauli type for
the bulk graviton.
