In the Gravity from Entropy framework, spherically symmetric black holes acquire r^{-4} corrections to Schwarzschild geometry, with large-mass evaporation at constant rate -β/24 and intermediate-mass loss following the classical Hawking M^{-2} scaling.
The Thermodynamics of the Gravity from Entropy Theory
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abstract
The Gravity from Entropy (GfE) action posits that gravity that is fundamentally given by the information encoded in the interplay between matter and geometry. The GfE Lagrangian is given by the Geometric Quantum Relative Entropy (GQRE) between the physical metric and the metric induced by matter and curvature, leading to modified gravitational field equations with an emergent dynamical effective dark energy term, which reduce to Einstein's equations in the low energy, small curvature limit. Adopting a thermodynamic viewpoint, we identify the GfE energy density with this emergent effective dark energy term. For homogeneous and isotropic FRW spacetimes, we show that GfE universes admit a thermal description: locally, they are characterized by $k$-temperatures and $k$-pressures satisfying a first law of GfE thermodynamics. In the low energy, small curvature regime with perfect-fluid matter and radiation, GfE solutions are well approximated by Friedmann cosmologies. While the total GQRE per unit volume does not increase, the total entropy of GfE universes is non-decreasing in time. We show that, while the total GQRE per unit volume does not increase, consistent with its nature as a relative entropy, the total entropy of GfE universes is non-decreasing in time. These results provide a thermodynamic interpretation of GfE cosmologies and of general relativity (GR) itself, recovered in the low energy, small curvature limit of the theory, offering a framework to reconcile local order and complexity with the global increase of entropy in the universe.
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Spatial entropy can fall as webs form while phase-space entropy rises; anisotropy is cast as a free-energy order parameter that activates earlier for nonlocal tidal operators than for local curvature.
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Spherically symmetric black holes in Gravity from Entropy and spontaneous emission
In the Gravity from Entropy framework, spherically symmetric black holes acquire r^{-4} corrections to Schwarzschild geometry, with large-mass evaporation at constant rate -β/24 and intermediate-mass loss following the classical Hawking M^{-2} scaling.
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Emergence of Complex Web Structures
Spatial entropy can fall as webs form while phase-space entropy rises; anisotropy is cast as a free-energy order parameter that activates earlier for nonlocal tidal operators than for local curvature.