Covariant holographic entanglement entropy inversion to reconstruct bulk geometry

A

bstract

We derive exact inversion formulae for stationary homogeneous asymptotically AdS ₃ metrics from renormalized covariant holographic entanglement entropy and extend them to higher-dimensional strip data. Hamilton–Jacobi derivatives of S _ren (∆ t, ∆ x ) give E and J . At fixed κ = E/J , entropy and endpoint separations obey three Abel-type Volterra equations that determine the radial coordinate, two diagonal metric functions, and the shift v without background expansion or field equations. Equal-time entropy is exactly invariant under v ↦ − v , and at linear order about AdS ₃ its inverse problem is the radial sector of the spatial tensor Radon transform, where the shift perturbation is absent; unequal-time dependence fixes the shift orientation. The higher-dimensional extension adds translationally invariant directions with independent radial warp factors. Extending the boundary interval along them produces a strip. Integrating them out these directions leaves the radial Abel form intact, with the added warp factors entering only through an area density. Unequal-time strip entropy then determines the shift along the finite-width direction and the projected null directions independently of that density. We give consistency and overlap conditions, verify the map in rotating BTZ and an Einstein–scalar black brane, and apply the strip construction to a boosted black brane.