Compact objects of spherical symmetry in beyond Horndeski theories

Abstract

We analyse in all generality beyond Horndeski theories of shift symmetry in a static and spherically symmetric spacetime. By introducing four auxiliary functions, we write the field equations in a particularly compact form. We show that assuming additionally parity symmetry renders the system directly integrable giving multiple families of black-hole solutions. These have typically an asymptotically-flat Reissner-Nordstrom behaviour, and emerge in the presence of a canonical kinetic term for the scalar field. In the absence of parity symmetry, we present a general method which allows us to integrate the field equations by choosing the form of only one coupling function and an auxiliary quantity. This method leads to asymptotically flat and AdS black hole solutions with differing properties. We finally discuss disformal transformations within this context as a means of obtaining wormhole and black hole solutions in different theories.

Nonlinear gravitational waves in Horndeski gravity: scalar pulse and memories

“…When combined to the Petrov classification, it provides a powerful tool to organize the construction of new solutions [76]. See [71][72][73][74] for the construction of new black hole solutions beyond the stealth sector in DHOST gravity, among which exact rotating black holes solutions [73][74][75].…”

“…Provided a given seed solution is known for a given DHOST theory, one can generate a new exact solution for another DHOST theory belonging to the same degeneracy class (which are stable under disformal field redefinition). This trick was first explored in [70] and further used in [71][72][73][74][75] to construct both non-stealth spherically symmetric and rotating black hole solutions (see also [77][78][79][80][81][82] for related works on stars and cosmological perturbations). While being a pure field redefinition, this map generates new physics when one assumes that matter minimally couples to the disformed metric.…”

Stealth Ellis wormholes in Horndeski theories

“…As expected, the majority of analytical solutions for compact objects in Horndeski theories have been obtained within the subclass of theories that enjoy parity symmetry ϕ → −ϕ and/or shift symmetry ϕ → ϕ + cst [54,[67][68][69][70][71][72][73][74]. However, under physical grounds there are no compelling reasons to restrict ourselves to theories with such symmetries, and in consequence, this freedom opens the possibility to explore spacetime geometries with quite different properties than GR [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92].…”

“…In this context, exotic matter is reduced or even not needed when wormholes solutions are realized on alternative theoretical frameworks. Traversable wormholes have been found in many modified gravitational theories, such as in f (R) gravity [12][13][14][15][16][17][18], f (R, T ) gravity [19][20][21][22], modified teleparallel gravity [23], non-minimal couplings [24,25], extra fundamental fields [26][27][28][29][30][31], Einstein-Gauss-Bonnet gravity [32][33][34], Einstein-Scalar-Gauss-Bonnet gravity [35,36], Brans-Dicke theory [37][38][39], Randal-Sundrum model [40], braneworld configurations [41], metric-Palatini gravity [42,43], with thin shells [44][45][46][47][48], Einsteinian Cubic gravity [49], Einstein-Dirac-Maxwell [50], massive JCAP11(2023)055 gravity [51] and by disformal transformations [52][53][54][55][56],...…”