Shock waves and Birkhoff’s theorem in Lovelock gravity

Abstract

Spherically symmetric shock waves are shown to exist in Lovelock gravity. They amount to a change of branch of the spherically symmetric solutions across a null hypersurface. The implications of their existence for the status of Birkhoff's theorem in the theory is discussed. * Electronic address: eliasgravanis@netscape.net 1 Useful additional background on Birhoff's theorem in Einstein gravity is provided in the Refs.[5][6].

Lovelock black holes with maximally symmetric horizons

“…Note that if the assumption of twice differentiability of the metric is relaxed, the Jebsen-Birkhoff theorem is violated. Explicit examples were found in [47] and [48]. In the latter, impulsive spherically symmetric gravitational shock waves were found.…”

Gauss-Bonnet LagrangianGlnGand cosmological exact solutions

“…To circumvent the vanishing of its variational derivative, essentially three ways have been gone: Models in dimension larger than 4, see e.g. [23], [24], [25], [26], [27], and [28], models where G is multiplied by a scalar φ, see [29], [30], and models where F (G) instead of G is used in the lagrangian with a suitably chosen non-linear function F , see e.g. [31].…”

Hamiltonian dynamics of Lovelock black holes with spherical symmetry

“…If the theory admits simply degenerate vacua, the following is also a vacuum solution: [19]. If one removes the assumption of C 2 -differentiability of the spacetime, then more vacuum solutions exist [35,36].…”