Fernando Ruiz Ruiz | Searcharxiv

arXiv2026

Positive energy from timelike singularities

The energy of various asymptotically AdS and asymptotically flat solutions to the Einstein equations with time-translational invariance and a timelike singularity is computed, spaces with Kasner timelike singularities and black holes with negative masses among them. The definition used for gravitational energy is the on-shell Hamiltonian of the physical classical action proposed by Hawking and Horowitz thirty years ago and which agrees with the Abbott-Deser and ADM expressions. To deal with the singularity, a timelike regulating cut-off boundary surrounding the singularity compatible with a well-defined foliation in constant-time slices is introduced, so calculations are performed at a finite value of the regulating parameter, which is set to zero in the final expression for the energy. In all instances considered, the energy contribution from the singularity is finite and positive, its value depends on the geometry around the singularity and is such that the total gravitational energy is positive. Of the solutions reviewed, only the AdS soliton (which has no singularity) has negative gravitational energy relative to AdS space. The AdS and the Schwarzschild black holes with negative masses have respectively the same energies as AdS and Minkowski spaces.

gr-qc↗

arXiv2022

Yang-Mills model for centrally extended 2d gravity

A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the role of the dilaton is played by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are found. They are either black holes or have constant scalar curvature. Those with constant scalar curvature have constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a CFT interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of U(1) gauge transformations while preserving dS2 and AdS2 boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell gravity considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.

hep-th↗