We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D-dimensional cubic theory of gravity which satisfies the following properties: 1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; 2) the relative coefficients of the different curvature invariants involved are the same in all dimensions; 3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones: Einstein gravity, Gauss-Bonnet and cubic-Lovelock. Of course, the last two theories fail to satisfy requirement 3 as they are, respectively, topological and trivial in four dimensions. We show that, up to cubic order, there exists only one additional theory satisfying requirements 1 and 2. Interestingly, this theory is, along with Einstein gravity, the only theory which also satisfies 3.Keywords: Modified theories of gravity, Quantum gravity toy models, HolographyHigher-order gravities play a prominent role in different areas of high-energy physics. In cosmology, they have been countlessly considered in the search for a coherent picture of the history of the universe which can account for the observational evidence currently associated to early-time inflation, late-time acceleration or dark matter -see e.g., [1][2][3][4]. In holography [5][6][7], they are often used to study different aspects of strongly coupled conformal field theories (CFTs) and, in some occasions, they have been crucial in unveiling certain universal properties of general CFTs -see e.g., [8][9][10][11][12][13]. In fact, holography itself has motivated the construction of new higher-derivative theories like quasi-topological (QT) gravity [14][15][16].More broadly, higher-order corrections to the EinsteinHilbert term should be produced in the gravitational effective action by the corresponding underlying ultraviolet-complete theory -presumably String Theory [17][18][19]. A more practical approach in this direction consists in considering certain classes of higher-order gravities as quantum gravity toy models [20,21]. Popular examples of this are topologically massive gravity [22] and new massive gravity [23] in three dimensions, and critical gravity in four [24].A particularly relevant aspect of a given higher-order gravity is its linearized spectrum, i.e., the set of physical degrees of freedom propagated by metric perturbations on the vacuum. For example, in the context of holography, the linearized equations of a given higher-order gravity provide useful information about the corresponding holographic CFT stress-tensors, since these are dual to the metric perturbation -see e.g., [9,12,25,26].As we will see, there are cert...

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum.

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordstr\"om-(Anti-)de Sitter (RN-(A)dS) black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are determined by a single blackening factor which satisfies a non-linear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature $T$, the Wald entropy $\mathsf{S}$ and the Abbott-Deser mass $M$ of the solutions analytically as functions of the horizon radius and the ECG coupling constant $\lambda$. Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for non-trivial single-blackening factor generalizations of Schwarzschild- and RN-(A)dS which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.Comment: 13 pp, 5 figs; v3: minor modifications to match published versio