Emergence III: Black Holes and Cosmology from Wave Intersections on a Pre-Geometric Canvas

This paper completes the derivation of black hole physics and cosmology from the canvas model — a unified framework where spacetime emerges from wave intersections on a pre-geometric canvas.

Starting from the six core equations of Emergence I, we provide step-by-step derivations of the fundamental phenomena of black holes and the universe.

Black Hole Physics

Hawking radiation is derived via a full Bogoliubov transformation between Schwarzschild and Kruskal modes, starting from the canvas wave equation rather than assuming quantum field theory in curved space. Black hole entropy follows from horizon voxel counting, giving the Bekenstein-Hawking area law as a theorem, not a postulate. The information paradox is resolved through unitary back-reaction dynamics: the entanglement entropy of Hawking radiation follows the Page curve, and no information is lost.

The canvas model also predicts that black hole evaporation halts at the Planck mass, leaving stable Planck-mass remnants. These remnants have negligible interaction cross sections and are a natural dark matter candidate, with an abundance calculation showing that a formation fraction of about one quarter at the Planck epoch yields the observed dark matter density.

Cosmology

Inflation emerges from residual lattice tension after the initial formation of spacetime voxels. The canvas lattice, still settling into its lowest energy configuration, drives exponential expansion of the universe. When inflation ends, the stored tension energy is released through parametric resonance, creating the particles that thermalize into the hot big bang.

Primordial gravitational waves arise from quantized tensor perturbations during inflation, producing a nearly scale-invariant spectrum that matches the predictions of single-field inflation but is derived from canvas dynamics rather than assumed. Baryon acoustic oscillations are imprinted in the pre-recombination photon-baryon fluid as sound waves propagate on the expanding lattice.

The cosmological constant is addressed through a baseline subtraction mechanism. The vacuum energy of quantum fields does not gravitate at all — only deviations from the baseline canvas oscillation compress the lattice. A tiny asymmetry between space and time wave amplitudes, with a magnitude of about one part in ten to the one hundred twenty-second power, produces the observed small positive cosmological constant. This recasts the famous one hundred twenty order of magnitude problem from a cancellation nightmare into a multiplicative smallness parameter.

Finally, the arrow of time emerges from the intrinsic pulsation of the time oscillator on the canvas. Our universe exists during the rising phase of this pulsation, during which the spacetime lattice expands and entropy increases.

What This Paper Achieves

Unlike other approaches to quantum gravity, the canvas model does not merely claim compatibility with black hole physics and cosmology. It derives Hawking radiation, black hole entropy, and the Page curve from first principles. It explains why vacuum energy does not gravitate. It provides a physical mechanism for inflation and reheating. It predicts Planck-mass remnants as dark matter. It gives a physical origin for the arrow of time.

Open Problems Acknowledged Honestly

The asymmetry parameter that gives the observed cosmological constant is not derived from deeper principles; its tiny value is a parameter of the initial canvas state. This is an open problem for future work.

This paper is for physicists and cosmologists interested in quantum gravity, black hole thermodynamics, dark matter, and the origin of the universe. All derivations are shown step by step; no results are assumed.

Keywords: canvas model, black holes, Hawking radiation, information paradox, black hole remnants, dark matter, inflation, primordial gravitational waves, reheating, baryon acoustic oscillations, cosmological constant, arrow of time, quantum gravity