  It has recently been proposed that Zamoldchikov's $T \bar{T}$ deformation of
two-dimensional CFTs describes the holographic theory dual to AdS$_3$ at finite
radius. In this note we use the Gauss-Codazzi form of the Einstein equations to
derive a relationship in general dimensions between the trace of the
quasi-local stress tensor and a specific quadratic combination of this stress
tensor, on constant radius slices of AdS. We use this relation to propose a
generalization of Zamoldchikov's $T \bar{T}$ deformation to conformal field
theories in general dimensions. This operator is quadratic in the stress tensor
and retains many but not all of the features of $T \bar{T}$. To describe
gravity with gauge or scalar fields, the deforming operator needs to be
modified to include appropriate terms involving the corresponding R currents
and scalar operators and we can again use the Gauss-Codazzi form of the
Einstein equations to deduce the forms of the deforming operators. We conclude
by discussing the relation of the quadratic stress tensor deformation to the
stress energy tensor trace constraint in holographic theories dual to vacuum
Einstein gravity.
