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arxiv: 2511.14869 · v3 · pith:MQ2A6YM3new · submitted 2025-11-18 · 🌀 gr-qc · hep-th

From minimal-length quantum theory to modified gravity

Rocco D'Agostino , Pasquale Bosso , Giuseppe Gaetano Luciano This is my paper

Pith reviewed 2026-05-21 18:43 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords minimal lengthgeneralized uncertainty principlemodified gravityf(R) gravityblack hole entropyWald formalismlight deflectionquantum gravity phenomenology
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The pith

Entropy corrections from a minimal length in quantum theory reconstruct specific modifications to Einstein gravity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper connects generalized uncertainty principles that incorporate a minimal length to effective extensions of general relativity. It starts from the resulting corrections to black hole entropy and applies Wald's formalism to reconstruct the corresponding gravitational actions in f(R) and f(R, RμνRμν) theories. The mapping ties the parameters of the minimal length directly to the coefficients of higher-order curvature terms in the Lagrangian. A sympathetic reader would care because the approach turns an abstract quantum feature into concrete corrections for observable gravitational effects such as the bending of light.

Core claim

By examining quantum gravity-motivated corrections to black hole entropy induced by the GUP and employing Wald's formalism, the authors reconstruct modifications to Einstein's gravity within the contexts of f(R) and f(R, Rμν Rμν) theories, establishing a direct mapping between the GUP parameters and the higher-order curvature coefficients in the gravitational Lagrangian.

What carries the argument

Wald's formalism applied to GUP-corrected black hole entropy, used to reconstruct the effective action and map deformation parameters to curvature coefficients.

If this is right

  • The reconstructed modified gravity yields explicit corrections to the general-relativistic prediction for light deflection.
  • These corrections permit an upper bound on the minimal measurable length from astrophysical data.
  • GUP-induced effects embed consistently into extended gravity theories.
  • The construction supplies a framework for testing quantum gravity phenomenology through observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same entropy-to-action reconstruction could be applied to other observables such as black-hole shadows or gravitational-wave propagation.
  • Combining the resulting bounds with cosmological data sets might tighten constraints on the minimal length scale.
  • The mapping suggests that minimal-length effects could alter early-universe dynamics within the reconstructed modified-gravity models.

Load-bearing premise

GUP-induced corrections to black-hole entropy can be inverted through Wald's formalism to obtain a unique effective gravitational action.

What would settle it

A high-precision measurement of light deflection by a compact object that deviates from both general relativity and the specific GUP-derived correction for every allowed value of the minimal-length parameter.

read the original abstract

In this work, we consider generalized uncertainty principles (GUPs) that incorporate a minimal length through generic momentum-dependent deformation functions. We thus develop a systematic approach connecting such a framework to effective gravitational actions extending general relativity. By examining quantum gravity-motivated corrections to black hole entropy induced by the GUP and employing Wald's formalism, we reconstruct modifications to Einstein's gravity within the contexts of $f(R)$ and $f(R, R_{\mu\nu} R^{\mu\nu})$ theories. In this way, we establish a direct mapping between the GUP parameters and the higher-order curvature coefficients in the gravitational Lagrangian. As an illustrative application, we compute corrections to the general relativistic prediction for light deflection, which in turn allows us to infer a stringent upper bound on the minimal measurable length. Our results show that GUP-induced effects can be consistently embedded into extended gravity theories, offering a promising framework for testing quantum gravity phenomenology through astrophysical and cosmological observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a systematic approach connecting generalized uncertainty principles (GUPs) that incorporate a minimal length through generic momentum-dependent deformation functions to effective gravitational actions extending general relativity. By examining GUP-induced corrections to black hole entropy and employing Wald's formalism, it reconstructs modifications to Einstein gravity in the contexts of f(R) and f(R, R_μν R^μν) theories, establishing a direct mapping between GUP parameters and higher-order curvature coefficients in the gravitational Lagrangian. As an application, corrections to the general relativistic prediction for light deflection are computed to infer an upper bound on the minimal measurable length.

Significance. If the reconstruction is shown to be unique and the derivations are made explicit with checks against known limits, the result would provide a concrete bridge between minimal-length quantum effects and modified gravity theories. This could enable embedding GUP phenomenology into extended gravity models and testing via astrophysical observations such as light deflection, offering a promising framework for quantum gravity phenomenology.

major comments (2)
  1. [Reconstruction procedure] Reconstruction step (detailed after introduction of Wald's formalism and GUP entropy corrections): the claim of a 'direct mapping' between GUP parameters and the higher-order curvature coefficients is not supported by a demonstration of uniqueness. Wald's Noether-charge formula yields S = 2π ∫_H (δL/δR_μνρσ) ε^μν ε^ρσ; recovering a specific L from a prescribed S on a fixed horizon generally admits multiple solutions, and the manuscript does not rule out that other invariants (e.g., Gauss-Bonnet) could produce identical entropy corrections.
  2. [Illustrative application] Application to light deflection (illustrative example section): it is unclear whether the computed correction constitutes a genuine prediction of the reconstructed theory or reduces to a parameter already adjusted to match data, since no explicit derivation, error estimate, or consistency check against the GR limit is supplied for the deflection angle.
minor comments (2)
  1. The abstract would benefit from a brief explicit example of the momentum-dependent deformation function used for the GUP.
  2. Notation for the higher-order curvature terms in the f(R, R_μν R^μν) Lagrangian should be introduced with an equation number at first appearance for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of our reconstruction procedure and the illustrative application. We address each major comment below and will revise the manuscript to incorporate clarifications and additional details as needed.

read point-by-point responses

  1. Referee: Reconstruction step (detailed after introduction of Wald's formalism and GUP entropy corrections): the claim of a 'direct mapping' between GUP parameters and the higher-order curvature coefficients is not supported by a demonstration of uniqueness. Wald's Noether-charge formula yields S = 2π ∫_H (δL/δR_μνρσ) ε^μν ε^ρσ; recovering a specific L from a prescribed S on a fixed horizon generally admits multiple solutions, and the manuscript does not rule out that other invariants (e.g., Gauss-Bonnet) could produce identical entropy corrections.

    Authors: We agree that, in general, the inverse problem of recovering the gravitational Lagrangian from the entropy on a fixed horizon is not unique, as different higher-order curvature terms can yield equivalent entropy corrections. Our manuscript constructs a specific mapping by assuming modified gravity actions of the form f(R) and f(R, R_μν R^μν) and determining the coefficients to reproduce the GUP-corrected entropy via Wald's formula. This provides a direct correspondence within these classes of theories rather than a claim of uniqueness over all possible extensions. We will revise the relevant section to explicitly state the assumptions and scope of the mapping, and note that other invariants are not considered in this work. revision: yes

  2. Referee: Application to light deflection (illustrative example section): it is unclear whether the computed correction constitutes a genuine prediction of the reconstructed theory or reduces to a parameter already adjusted to match data, since no explicit derivation, error estimate, or consistency check against the GR limit is supplied for the deflection angle.

    Authors: The deflection angle correction is computed within the reconstructed modified gravity theory, where the higher-order coefficients are fixed by the GUP entropy matching, making it a derived prediction rather than an independent fit. Nevertheless, we acknowledge that the presentation lacks sufficient detail on the explicit steps, including the perturbative expansion, error analysis, and the reduction to the GR limit when the minimal length parameter approaches zero. We will expand the illustrative example section with these derivations, estimates, and consistency checks to clarify the predictive nature of the result. revision: yes

Circularity Check

0 steps flagged

No significant circularity: reconstruction via Wald formalism yields explicit mapping without reducing to input by construction

full rationale

The central chain starts from a GUP-deformed entropy (area-law correction) and applies Wald's Noether-charge formula to extract higher-curvature coefficients in assumed f(R) and f(R,RμνRμν) forms. This produces a direct parametric mapping rather than an identity or tautology; the functional inversion is performed under explicit ansatz choices for the Lagrangian, which are stated as part of the reconstruction rather than smuggled. The light-deflection application then uses the resulting modified metric to compute an observable correction and bound the minimal-length parameter against external data, without evidence that the deflection shift is pre-tuned to the same dataset used for the entropy input. No load-bearing self-citations, uniqueness theorems from prior author work, or fitted parameters renamed as predictions appear in the derivation. The paper remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of Wald's formalism to GUP-corrected entropy and on the existence of a unique inversion from entropy to the gravitational Lagrangian; no new entities are postulated.

free parameters (1)
  • GUP deformation function parameters
    These control the strength of the minimal-length correction and are mapped to curvature coefficients.
axioms (1)
  • domain assumption Wald's entropy formalism remains valid for the GUP-modified black-hole thermodynamics
    Invoked to reconstruct the effective gravitational action from the corrected entropy.

pith-pipeline@v0.9.0 · 5693 in / 1259 out tokens · 40502 ms · 2026-05-21T18:43:32.461379+00:00 · methodology

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