General Relativity and Holographic Interpretation via Zeta Functions: Unified Mathematical Framework for Spacetime Curvature and Information Conservation

We present a revolutionary theoretical framework that reinterprets Einstein's general relativity through Riemann zeta function analytical continuation mechanisms combined with holographic extensions of Hilbert space. We prove that spacetime curvature is essentially a compensation mechanism arising from quantum vacuum divergences through analytical continuation, and Einstein field equations can be expressed as natural results of zeta function spectral decomposition. Core innovations include: (1) establishing correspondence between metric tensor and zeta function zero point distribution; (2) proving Schwarzschild black hole event horizons correspond to Riemann critical line projections; (3) solving the black hole information paradox through multi-dimensional negative information networks; (4) reducing the cosmological constant problem to zeta function values at negative even points; (5) constructing gravitational waves as ripples in information geometry. This theory not only provides unified mathematical foundations for quantum gravity but also predicts new effects verifiable through LIGO/Virgo experiments, including fine structure in gravitational wave spectra, quantum corrections to black hole entropy, and dynamical evolution of dark energy. The information conservation law $\mathcal{I}_{total} = \mathcal{I}_+ + \mathcal{I}_- + \mathcal{I}_0 = 1$ permeates the entire theory, revealing gravity's informational nature. We demonstrate that negative information manifests physically as dark energy, with the multi-dimensional compensation network $\mathcal{I}_- = \sum_{k=0}^{\infty} \zeta(-2k-1)$ providing the stabilization mechanism that prevents divergent cosmological expansion while enabling creative gravitational dynamics.