https://neckpinch.com/authors/roberto-tateo/New arXiv papers by Roberto Tateo, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2411.10265/arxiv:2411.10265Fri, 15 Nov 2024 00:00:00 GMTTommaso Morone, Roberto Tateo — We investigate the relation between stress-tensor deformations of matter theories coupled to gravity and the Ricci flow. We identify the quadratic stress-tensor deformation whose associated metric evolution, on solutions of the Einstein equations, coincides with the Ricci-flow vector field. We show that this pointwise identification does not in general extend to finite deformation parameter: the coupled evolution of the metric and stress tensor must additionally preserve the Einstein equations. We formulate this requirement as the invariance of the Einstein constraint surface and derive the corresponding geometric compatibility condition. We illustrate the resulting obstruction with simple examples and exhibit the Bertotti-Robinson/Born-Infeld flow as a nontrivial sector in which the correspondence is exact. Finally, we introduce an Einstein-compatible completion of the deformation which leaves its associated evolution of the metric unchanged while modifying the stress-tensor evolution so that the Einstein constraint surface is invariant by construction. The completed evolution therefore generates genuine Ricci-flow trajectories from arbitrary Einstein-matter initial data, whenever the corresponding local evolution exists and is unique.Ricci flowPhysics https://neckpinch.com/papers/2408.06031/arxiv:2408.06031Mon, 12 Aug 2024 00:00:00 GMTNicolò Brizio, Tommaso Morone, Roberto Tateo — This paper reviews and extends the recently discovered connections between marginal and irrelevant stress-energy tensor deformations and gravity theories in arbitrary space-time dimensions. We start by discussing how TT and Root-TT deformations of two-dimensional field theories can be equivalently interpreted as the coupling of the undeformed matter sector to a gravity theory. We then extend this duality to higher-dimensional scenarios by using an approach that relies on the non-trivial eigenvalue degeneracy characterising the energy-momentum tensor of specific physical theories. We also explore incorporating dynamical degrees of freedom in the gravity sector, and show that the deformed space-time geometry induced by the TT-like deformations defines a Ricci-Bourguignon flow of the metric tensor, which reduces to a Ricci flow in four dimensions. Finally, exploiting a dressing-type mechanism for the action functional characterizing a broad class of TT-like deformations we study explicit examples, such as Einstein-Ricci solitons, (d-1)-form field theories, and spherically symmetric electrovacuum solutions.Ricci flowRicci solitonsSurfacesRotational symmetry & warped productsEigenvalues & spectrumPhysics