Robinson–Trautman solutions with scalar hair and Ricci flow

Abstract

The vacuum Robinson-Trautman solution admits a shear-free and twist-free null geodesic congruence. We perform a comprehensive classification of solutions exhibiting this property in Einstein's gravity with a massless scalar field. We find that these solutions can be grouped into three distinct classes: (I-a) a natural extension of the Robinson-Trautman family incorporating a scalar hair satisfying the time derivative of the Ricci flow equation, (I-b) a novel non-asymptotically flat solution characterized by two functions satisfying Perelman's pair of the Ricci flow equations, and (II) a dynamical solution possessing SO(3), ISO(2) or SO(1, 2) symmetry. We provide a complete list of all explicit solutions falling into Petrov type D for classes (I-a) and (I-b). Moreover, leveraging the massless solution in class (I-a), we derive the neutral Robinson-Trautman solution to the N = 2 gauged supergravity with the prepotential F (X) = -iX0X1. By flipping the sign of the kinetic term of the scalar field, the Petrov-D class (I-a) solution leads to a time-dependent wormhole with an instantaneous spacetime singularity. Although the general solution is unavailable for class (II), we find a new dynamical solution with spherical symmetry from the AdS-Roberts solution via AdS/Ricci-flat correspondence.

Nonlinear gravitational waves in Horndeski gravity: scalar pulse and memories

“…For simple enough theories such as Brans-Dicke gravity, exact radiative solutions have been worked out [59,60]. However, when considering higher-order scalar-tensor theories, constructing exact radiative solutions turns out to be a difficult task due to the high complexity JCAP05(2024)026 of the field equations (see [61][62][63][64] for some examples).…”