A major new chapter has been added to the No-Time Universe (NTU) framework with the introduction of a complete reinterpretation of Schwarzschild geometry, event horizons, and black holes.

This development extends the recently introduced NTU tensor, which describes how the causal front is transformed as it propagates through the fractal surfaces generated by the NTU substrate.

Within the NTU framework, gravitation emerges from the rigidification of closed pre-link surfaces. The NTU tensor acts as a transformation matrix that converts this underlying discrete structure into the continuous spacetime geometry observed by a 4D observer.

The closed gravitational surface is defined by:$$\Sigma_G = (1-\chi) \,\ell_P^2 \,N^{D_{\mathrm{eff}}}$$

where:$$\chi$$

is the non-closure ratio of pre-links,$$N = \frac{\lambda_{dB}}{\ell_P}$$

and:$$D_{\mathrm{eff}} \simeq 2.1$$

is the effective fractal dimension independently obtained through Fractal Thermodynamics and NTU calculations. The corresponding NTU tensor is:$$T_{\mu\nu}^{\mathrm{NTU}} = – \frac{2}{\sqrt{-g}} \frac{\delta S_{\mathrm{NTU}}} {\delta g^{\mu\nu}}$$

whose gravitational projection generates the Einstein tensor through:$$G_{\mu\nu} = \frac{8\pi G}{c^4} \,T_{\mu\nu}^{\mathrm{NTU}}$$

For a static spherical mass distribution, the NTU framework naturally recovers the Schwarzschild solution:$$ds^2 = – \left( 1-\frac{r_s}{r} \right)c^2dt^2 + \left( 1-\frac{r_s}{r} \right)^{-1}dr^2 + r^2d\Omega^2$$

with:$$r_s = \frac{2GM}{c^2}$$

the Schwarzschild radius.