Black hole production in particle collisions and higher curvature gravity

The problem of black hole production in trans-Planckian particle collisions is revisited, in the context of large extra dimensions scenarios of TeV-scale gravity. The validity of the standard description of this process (two colliding Aichelburg–Sexl shock waves in classical Einstein gravity) is questioned. It is observed that the classical spacetime has large curvature along the transverse collision plane, as signaled by the curvature invariant ${(R}_{\mu \nu \lambda \sigma }{)}^2.$ Thus quantum gravity effects, and in particular higher curvature corrections to the Einstein gravity, cannot be ignored. To give a specific example of what may happen, the collision is reanalyzed in the Einstein–Lanczos–Lovelock gravity theory, which modifies the Einstein–Hilbert Lagrangian by adding a particular “Gauss–Bonnet” combination of curvature squared terms. The analysis uses a series of approximations, which reduce the field equations to a tractable second order nonlinear PDE of the Monge–Ampère type. It is found that the resulting spacetime is significantly different from the pure Einstein case in the future of the transverse collision plane. These considerations cast serious doubts on the geometric cross section estimate, which is based on the classical Einstein gravity description of the black hole production process.