We show that the braneworld rotating Kerr-Newman black hole and naked singularity spacetimes with both positive and negative braneworld tidal charge parameter can be separated into fourteen classes according to properties of circular geodesics governing the Keplerian accretion. We determine efficiency of the Keplerian accretion disks for all braneworld Kerr-Newman spacetimes. We demonstrate occurrence of an infinitely deep gravitational potential in Kerr-Newman naked singularity spacetimes having the braneworld dimensionless tidal charge b ∈ (1/4, 1) and the dimensionless spin 1)), implying unbound efficiency of the Keplerian accretion and possibility to extract the whole naked singularity mass. Therefore, we call them braneworld "mining-unstable" Kerr-Newman naked singularity spacetimes. Fundamental restriction on the relevance of the extraordinary but fully classical phenomenon of the mining instability is given by validity of the assumption of geodesic motion of the accreting matter.

We study ultra-high-energy particle collisions and optical effects in the extraordinary class of mining braneworld Kerr-Newman (KN) naked singularity spacetimes, predicting extremely high efficiency of Keplerian accretion, and compare the results to those related to the other classes of the KN naked singularity and black hole spacetimes. We demonstrate that in the mining KN spacetimes the ultra-high centre-of-mass energy occurs for collisions of particles following the extremely-lowenergy stable circular geodesics of the "mining regime", colliding with large family of incoming particles, e.g., those infalling from the marginally stable counter-rotating circular geodesics. This is qualitatively different situation in comparison to the standard KN naked singularity or black hole spacetimes where the collisional ultra-high centre-of-mass energy can be obtained only in the nearextreme spacetimes. We also show that observers following the stable circular geodesics of the mining regime can register extremely blue-shifted radiation incoming from the Universe, and see strongly deformed sky due to highly relativistic motion along such stable orbits. The strongly blue-shifted radiation could be thus a significant source of energy for such orbiting observers.

We provide a simple derivation of the corrections for Schwarzschild and Schwarzschild-Tangherlini black hole entropy without knowing the details of quantum gravity. We will follow Bekenstein, Wheeler and Jaynes ideas, using summations techniques without calculus approximations, to directly find logarithmic corrections to well-known entropy formula for black holes. Our approach is free from pathological behaviour giving negative entropy for small values of black hole mass M . With the aid of "Universality" principle we will argue that this purely classical approach could open a window for exploring properties of quantum gravity.