A holographic bound on the total number of computations in the visible universe

Information I in holographic imaging of massive particles by star-like screens is shown to represent the probability of detection based on their propagator. Results are derived for screens in the shape of a plane, cube and sphere from unitarity in the exponentially small transition probability for a detection outside. We derive I = 2πΔφ in log 2 bits for the imaging of a particle by a spherical screen at a relative de Broglie phase Δφ. Encoding mass, charge, angular momentum or radiation requires at minimum four bits. Minimal screens at maximal information density hereby recover Reissner–Nordström and extremal Kerr black holes. Applied to the visible Universe, the Hubble flow of galaxies through the cosmological event horizon leaves 10121 computations in the future.

Quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model

Using the Hamilton–Jacobi method a study of quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model is carried out. It is shown that there exist seas of positive and negative energy states in the vicinity of the cosmological event horizon and there also exists a forbidden energy gap between the two seas. The forbidden energy gap vanishes on the surface of the cosmological event horizon so that the positive and negative energy levels overlap. The width of the forbidden energy gap and the energy of the particle at the cosmological event horizon are found to depend on the cosmological constant, the rotation parameter, positions of the particle and the cosmological event horizon, angular momentum of the particle, evaporation rate and shape of the cosmological event horizon. The tunneling probability of the emitted particles constituting Hawking radiation is also deduced for stationary nonrotating de Sitter cosmological model and the standard Hawking temperature is recovered.