Quantum Trans-Planckian Physics inside Black Holes and its Spectrum

Abstract

We provide a quantum unifying picture for black holes of all masses and their main properties covering classical, semiclassical, Planckian and trans-Planckian gravity domains: Space-time, size, mass, vacuum ("zero point") energy, temperature, partition function, density of states and entropy. Novel results of this paper are: Black hole {\bf interiors} are always {\bf quantum}, trans-Planckian and of constant curvature: This is so for {\it all} black holes, including the most macroscopic and astrophysical ones. The black hole interior trans-Planckian vacuum is similar to the earliest cosmological vacuum which classical gravity dual is the low energy gravity vaccum: today dark energy. There is {\it no} singularity boundary at $r = 0$, not at any other place: The quantum space-time is {\bf totally regular}. The {\it quantum} Penrose diagram of the Schwarschild-Kruskal black hole is displayed. The complete black hole {\it instanton} (imaginary time) covers the known classical Gibbons-Hawking instanton plus a {\it new} central highly dense {\it quantum core} of Planck length radius and {\it constant curvature}. The complete partition function, entropy, temperature, decay rate, discrete levels and density of states {\it all} include the trans-Planckian domaine. The semiclassical black hole entropy (the Bekenstein-Hawking entropy)$ (\sqrt{n})^2$ "interpolates" between the quantum point particle (QFT) entropy $(n)$ and the quantum string entropy $\sqrt{n}$, while the quantum trans-Planckian entropy is $1/(\sqrt{n})^2$. Black hole evaporation ends as {\it a pure (non mixed)} quantum state of particles, gravitons and radiation.