The Gravity in Non-perturbative Regime. Holographic Principle and Quantum-Gravitational Corrections

Abstract

In the present work gravity is considered both in the discrete form (within the scope of the Regge Calculus) and at the limiting transition to a continuous pattern in the non-perturbative regime. Quantum-gravitational corrections have been found for all the fundamental quantities in following pictures: 1) when the physical space represents a black hole in stationary state (i.e. in the absorption and radiation processes absence) or after of minimal accretion, 2) and in a more general case, if it satisfies the Hooft– Susskind Holographic Principle. In the process a contribution of the given quantum-gravitational corrections in the Regge Calculus is calculated for every 2-simplex and also for the corresponding deficit angle at each hinge h (or same in a measure of curvature at h,i.e δ(h)). It is demonstrated that this contribution changes the geometry of each 2-simplex and that this variation is most significant as high (planck) energies are approached. The inferences from the obtained results are discussed including possible applications to cosmology.