Exploring Lovelock theory moduli space for Schr?dinger solutions

摘要

We look for Schr?dinger solutions in Lovelock gravity in D 4 . We span the entire parameter space and determine parametric relations under which the Schr?dinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schr?dinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern–Simons form. Schr?dinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z . This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.