A theoretical preprint reports that reconstructing modified gravitational dynamics from a chosen horizon entropy does not yield one inevitable theory. The result depends on the area–curvature branch—the rule linking horizon area to curvature—and switching branches can reverse the stability conditions applied to the reconstruction.
The work is an analytic modeling study, not an analysis of participants, observations or an empirical dataset. It examines prescribed entropy–area relations and metric f(R) geometries in vacuum Schwarzschild-de Sitter settings, comparing a maximally symmetric branch with a fixed-mass massive branch.
The choice that controls the reconstruction
At the center is the Wald construction. It determines f_R from S(A): in ordinary language, the proposed relation between entropy and horizon area fixes the derivative of the gravitational function with respect to curvature. But completing the reconstruction requires an area–curvature map, and that map is not unique within the Schwarzschild-de Sitter family.
On the maximally symmetric branch—the case with the exact area–curvature relation—the map is A = 48π/R. This reduces the reconstruction to a single non-perturbative integral and yields closed-form Lagrangians. Entropy powers are reflected in the curvature terms through q → 2 − q.
The resulting corrections occupy distinct curvature regimes. The reported Kaniadakis reconstruction contains an inverse-curvature 1/R correction, while the logarithmic entropy prescription produces an R² ln R term.
Stability depends on the branch
To assess viability, the paper applies the Dolgov-Kawasaki criterion, an analytic stability check for these reconstructed models. Its sign requirement flips with branch: d(S/s)/ds must be below zero on the maximally symmetric branch and above zero on the massive branch.
On the maximally symmetric branch, Rényi is Dolgov-Kawasaki stable for every λ > 0. Barrow is unstable for every Δ > 0, Kaniadakis is unstable throughout, and logarithmic stability requires α(1 − ln s) < 0.
A separate scalaron condition gives m_sc² = S′(s)/(3f_RR) on that branch. Positive, monotonically increasing entropy combined with f_RR > 0 implies a non-tachyonic scalaron. For power-law entanglement, Dolgov-Kawasaki stability requires μβ > 0, while the scalaron condition additionally requires S′(s) > 0.
The fixed-mass massive branch produces a different pattern. Barrow is stable throughout its physical parameter range, Kaniadakis is perturbatively stable for sufficiently small deformation, and no positive-λ interval makes the Rényi reconstruction satisfy both the Dolgov-Kawasaki and non-tachyonic scalaron conditions. The study treats the two branches as different reconstructions, not approximations to one another.
The fixed-mass result comes with a warning
That qualification is important. The fixed-mass expressions shown in the main text are perturbative resummations: they reproduce O(Δ), O(κ²) and O(λ) terms, but they are not exact finite-deformation quadratures. The area–curvature map itself is an expansion around the Schwarzschild point.
A quasi-local consistency check uses the weak-isolated-horizon residual boost charge. It recovers the selected perturbative generalized entropies with a common normalization of N = 1/4 in units where G = 1.
Taken together, the calculations give analytic, branch-specific reconstructions and theoretical viability conditions, not an empirical verdict about real horizons or observed systems. Their conclusions remain conditional on the stated vacuum assumptions and the chosen area–curvature branch. The document is an arXiv preprint identified as arXiv:2608.25722v1 [gr-qc] and dated 26 Aug 2026.
Paper data and sources
Original title: Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians
Authors: Ankit Anand, Sahil Devdutt, Kimet Jusufi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text