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The upcoming high energy experiments at the LHC are one of the most outstanding efforts for a better understanding of nature. It is associated with great hopes in the physics community. But there is also some fear in the public, that the conjectured production of mini black holes might lead to a dangerous chain reaction. In this Letter we summarize the most straightforward arguments that are necessary to rule out such doomsday scenarios.
Large extra dimensions could lower the Planck scale to experimentally accessible values. Not only is the Planck scale the energy scale at which effects of modified gravity become important. The Planck length also acts as a minimal length in nature, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime.
In this Letter we examine the influence of the minimal length on the Casimir energy between two plates.
It has been suggested that the existence of a non-Gaussian fixed point in general relativity might cure the ultraviolet problems of this theory. Such a fixed point is connected to an effective running of the gravitational coupling. We calculate the effect of the running gravitational coupling on the black hole production cross section in models with large extra dimensions.