Holography for stress-energy tensor flows

We study the holographic description for general stress-energy tensor deformations in arbitrary dimensions using the metric flow approach. Mixed boundary conditions corresponding to these deformations emerge from solutions to the metric flow equations. To test this proposal, we analyze planar anti-de Sitter black holes with such boundary conditions and find that the deformed energies satisfy flow equations consistent with the field theory interpretation. We further derive the commuting condition for stress-energy tensor deformations and extend the mixed boundary condition description to accommodate families of commuting deformations.