Black hole interiors and temporal completion: SMM/DTT and unimodular gravity

01The question behind this comparison

Black-hole interiors test whether a theory can connect local physics, causal horizons and global information consistently. Classical general relativity describes a horizon and, in simple solutions, an interior singularity. Quantum field theory on that background predicts Hawking radiation in an appropriate state. A complete microscopic account would explain the quantum degrees of freedom and their evolution beyond the regime of the semiclassical approximation.

DTT’s retained-source picture offers a way to distinguish inaccessible information from destroyed information. An exterior completed archive may omit relations still present in the full source. That distinction is useful, but it does not itself solve the information problem: the theory must show how the final accessible state is related to the initial state and how its entropy evolves. A hidden archive that never influences observable radiation is not automatically a unitary evaporation mechanism. ^{[3] [4] [5]}

02The SMM/DTT starting point

The Single Monad Model begins with one nonspatial generative source. The Duality of Time Theory distinguishes the source’s inner production from the outer order in which completed records become accessible. Its six inner levels are nested functional roles of one process: a higher role organizes lower-level work. The seventh is the completion or observation interface. They are neither six independent clocks nor six additional time coordinates.

This distinction supplies a useful research question: which features of an observed world can follow from the way a source produces, retains and releases information? A concrete answer needs a state space, an autonomous update, retained memory and a rule connecting completion to an accessible measurement. In the constructions discussed here, those mathematical ingredients are stated explicitly. A successful finite example establishes what its specified mechanism can do; further arguments connect it to physical particles, spacetime or universal laws. ^[1]

03How the comparator works

Unimodular formulations reorganize the gravitational equations so that the cosmological constant can arise as an integration constant rather than as a conventional fixed coupling in the action. In a common classical presentation, the metric equation is trace-free. With covariant conservation of matter, integration restores an Einstein equation with a constant term. Different covariant and constrained formulations can differ in their quantization and treatment of global variables.

This is relevant to SMM/DTT because a completion or normalized-response rule may remove sensitivity to an additive offset in a particular observable. But mathematical insensitivity to a constant and prediction of the constant’s measured value are different results. Unimodular gravity does not automatically select that value or explain every radiative contribution. A DTT link would need a dynamical reason that its generated geometry obeys the trace-free equation or its covariant equivalent, together with a rule fixing the global integration data. Calling the source vacuum offset unobservable in a local response is insufficient to establish its gravitational absence. ^[2]

04The decisive comparison

Unimodular formulations can admit the usual black-hole geometries with an integration constant, so they do not automatically solve the interior singularity or information problem. DTT’s retention-and-completion mechanism would be an additional microscopic proposal. Its relation to unimodular gravity is meaningful only if the source dynamics derives the relevant volume constraint or global variable and explains how it enters the black-hole state.

The entropy and temperature benchmarks test the resulting theory independently of how Λ is named. A change in the cosmological term may alter an asymptotic or cosmological horizon structure, but it does not by itself supply a unitary radiation channel. A source archive must specify what information is encoded, when it becomes accessible and how energy is conserved in the release. The positive opportunity is to connect global source constraints with local horizon thermodynamics through one action or state-counting construction. Without that link, offset control, singularity regularization and information recovery remain three separate problems. The comparison helps keep a valid result in one area from being overextended into an unproved solution of all three. ^{[2] [3] [4] [5]}

05Worked benchmark

For a nonrotating, uncharged black hole, the Schwarzschild radius is rs=2GM/c² and the Hawking temperature is TH=ℏc³/(8πGMkB). Doubling the mass doubles the radius and halves the temperature. Its Bekenstein–Hawking entropy scales as M², so doubling the mass multiplies the entropy by four. These different scalings constrain any proposed source capacity and release law simultaneously.

For an illustrative solar-mass black hole, rs is about 2.95 kilometres and TH about 6.2×10⁻⁸ kelvin. These are semiclassical predictions for the stated idealized system, not direct laboratory measurements of its radiation. A DTT model that uses completion events as radiation emissions must recover the thermal low-order spectrum in this regime while also specifying the correlations needed for unitary information recovery. A curve that reproduces only the temperature does not decide whether the radiation’s fine-grained entropy ultimately decreases. ^{[3] [4] [5]}

06What follows for the source programme

The strongest source-based contribution would be a finite model with a controlled exterior limit, an explicit internal memory and a demonstrably unitary transfer of information into radiation. Island calculations provide a separate benchmark for entropy in certain controlled gravitational models. Reproducing their qualitative Page-curve shape is insufficient by itself; the microphysical map and its domain of validity remain central to the explanatory claim. ^{[3] [4] [5]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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