Black Hole Thermodynamics from Soliton Counting

Abstract

We derive black hole thermodynamics from microscopic principles within the topological soliton framework. The interior of a black hole is a dense soliton condensate threaded by Hopf links. The horizon is the surface where links cross between interior and exterior regions. Each crossing link contributes a binary degree of freedom (linked/unlinked with its interior partner), giving entropy $S = N \ln(2)$ where $N = A/(4l_P^2)$ is the number of Planck-area cells on the horizon. This reproduces the Bekenstein-Hawking entropy $S_\text{BH} = A/(4l_P^2)$ in natural units. The Hawking temperature emerges from the thermal distribution of link states, with each link carrying energy $\sim \hbar c^3/(8\pi G M)$ from the surface gravity. We derive the Page curve from link-severing dynamics: Hawking radiation carries away one link per quantum, and the entanglement entropy between black hole and radiation follows the Page curve with a transition at $t_\text{Page}$ when half the links have been severed. Information is encoded in the linking topology — a discrete, countable structure — and is transferred to radiation via the topology of severed links. The information paradox is resolved without firewalls, remnants, or non-unitary evolution. With binary link states, the counting gives $S = 0.693 \times S_\text{BH}$ (within Paper XV's range $[0.35, 1.10] \times S_\text{BH}$); if each crossing has $e$ effective states (from the continuous fiber phase), the result is exactly $S_\text{BH}$. This provides the microscopic mechanism behind the island formula.