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Relativistic MOND Theory from Modified Entropic Gravity

A. Rostami, K. Rezazadeh, M. Rostampour

TL;DR

The paper addresses the lack of a relativistic basis for MOND by deriving a relativistic MOND (RMOND) framework from entropic gravity with temperature-dependent corrections to the equipartition law, encoded in a Debye-like factor f(T). By linking temperature to acceleration via the Unruh relation and formulating a generalized Einstein equation, the authors obtain a weak-field, static, spherically symmetric solution with A(r)=1+C_A r^ε and a MOND-like transition, yielding a rotation profile v ∝ r^{ε/2} and an acceleration scale a_t related to a0. Applied to NGC 3198, the RMOND model fits the outer rotation curve as well as, or better than, a dark-matter halo in certain regions, with χ^2 values close to the DM model and significantly better than a baryons-only Newtonian fit; the transition occurs at a_t ≈ 2.8×10^−11 m s^−2. Overall, the work provides a thermodynamically grounded, relativistic underpinning for MOND and motivates further tests in lensing, cosmology, and larger galaxy samples.

Abstract

We derive a relativistic extension of Modified Newtonian Dynamics (MOND) within the framework of entropic gravity by introducing temperature-dependent corrections to the equipartition law on a holographic screen. Starting from a Debye-like modification of the surface degrees of freedom and employing the Unruh relation between acceleration and temperature, we obtain modified Einstein equations in which the geometric sector acquires explicit thermal corrections. Solving these equations for a static, spherically symmetric spacetime in the weak-field, low-temperature regime yields a corrected metric that smoothly approaches Minkowski space at large radii and naturally contains a characteristic acceleration scale. In the very-low-acceleration regime, the model reproduces MOND-like deviations from Newtonian dynamics while providing a relativistic underpinning for that phenomenology. We confront the theory with rotation-curve data for NGC~3198 and perform a Bayesian parameter inference, comparing our relativistic MOND (RMOND) model with both a baryons-only Newtonian model and a dark-matter halo model. We find that RMOND and the dark-matter model both fit the data significantly better than the baryons-only Newtonian prediction, and that RMOND provides particularly improved agreement at $r\gtrsim 20\,\mathrm{kpc}$. These results suggest that temperature-corrected entropic gravity provides a viable relativistic framework for MOND phenomenology, motivating further observational tests, including gravitational lensing and extended galaxy samples.

Relativistic MOND Theory from Modified Entropic Gravity

TL;DR

The paper addresses the lack of a relativistic basis for MOND by deriving a relativistic MOND (RMOND) framework from entropic gravity with temperature-dependent corrections to the equipartition law, encoded in a Debye-like factor f(T). By linking temperature to acceleration via the Unruh relation and formulating a generalized Einstein equation, the authors obtain a weak-field, static, spherically symmetric solution with A(r)=1+C_A r^ε and a MOND-like transition, yielding a rotation profile v ∝ r^{ε/2} and an acceleration scale a_t related to a0. Applied to NGC 3198, the RMOND model fits the outer rotation curve as well as, or better than, a dark-matter halo in certain regions, with χ^2 values close to the DM model and significantly better than a baryons-only Newtonian fit; the transition occurs at a_t ≈ 2.8×10^−11 m s^−2. Overall, the work provides a thermodynamically grounded, relativistic underpinning for MOND and motivates further tests in lensing, cosmology, and larger galaxy samples.

Abstract

We derive a relativistic extension of Modified Newtonian Dynamics (MOND) within the framework of entropic gravity by introducing temperature-dependent corrections to the equipartition law on a holographic screen. Starting from a Debye-like modification of the surface degrees of freedom and employing the Unruh relation between acceleration and temperature, we obtain modified Einstein equations in which the geometric sector acquires explicit thermal corrections. Solving these equations for a static, spherically symmetric spacetime in the weak-field, low-temperature regime yields a corrected metric that smoothly approaches Minkowski space at large radii and naturally contains a characteristic acceleration scale. In the very-low-acceleration regime, the model reproduces MOND-like deviations from Newtonian dynamics while providing a relativistic underpinning for that phenomenology. We confront the theory with rotation-curve data for NGC~3198 and perform a Bayesian parameter inference, comparing our relativistic MOND (RMOND) model with both a baryons-only Newtonian model and a dark-matter halo model. We find that RMOND and the dark-matter model both fit the data significantly better than the baryons-only Newtonian prediction, and that RMOND provides particularly improved agreement at . These results suggest that temperature-corrected entropic gravity provides a viable relativistic framework for MOND phenomenology, motivating further observational tests, including gravitational lensing and extended galaxy samples.

Paper Structure

This paper contains 8 sections, 58 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Generalized Einstein Equations
  3. Solution of Modified Einstein Equations
  4. Comparison with Observational Data
  5. Conclusions
  6. Discussion of Results
  7. Future Directions
  8. Final Remarks

Figures (4)

  • Figure 1: 1D likelihoods and 2D contours for the parameters in 68% and 95% CL marginalized joint regions for the ND model.
  • Figure 2: 1D likelihoods and 2D contours for the parameters in 68% and 95% CL marginalized joint regions for the DM model.
  • Figure 3: 1D likelihoods and 2D contours for the parameters in 68% and 95% CL marginalized joint regions for the RMOND model.
  • Figure 4: Rotational velocity versus distance from the galaxy center for the ND, DM, and RMOND models. The data points from the measurements of the galaxy NGC 3198 are also presented in the figure.