Pablo A. Cano

Einsteinian cubic gravity

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.

Aspects of general higher-order gravities

We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in [P. Bueno and P. A. Cano, arXiv:1607.06463] to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify L(Riemann) theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity. In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghostlike spin-2 mode (but can propagate the scalar) is a linear combination of f(Lovelock) invariants, plus the Einsteinian cubic gravity term, plus a new ghost-free gravity term. Next, we construct the generalized Newton potential and the post-Newtonian parameter γ for general L(Riemann) gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald’s formalism for general L(Riemann) theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.

Four-dimensional black holes in Einsteinian cubic gravity

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordstrom-(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

f(Lovelock) theories of gravity

T

A gravitating Yang-Mills instanton

, the Wald entropy

On black holes in higher-derivative gravities

\mathsf{S}

Universal black hole stability in four dimensions

and the Abbott-Deser mass

Non-Abelian black string solutions of N = (2,0), d = 6 supergravity

M

Non-perturbative decay of non-Abelian hair

of the solutions analytically as functions of the horizon radius and the ECG coupling constant

Non-Abelian black string solutions of

\lambda