We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a non-vanishing $g_{tϕ}$ component. Similarly to the static case, the order of the equation determining such component can be reduced twice, giving rise to a second-order differential equation which can be easily solved numerically as a function of the ECG coupling. We study how various physical properties of the solutions are modified with respect to the Einstein gravity case, including its angular velocity, photon sphere, photon rings, shadow, and innermost stable circular orbits (in the case of timelike geodesics).
We investigate the predictions of Einsteinian Cubic Gravity (ECG) for the lensing effects due to supermassive black holes at the center of Milky Way and other galaxies. Working in the context of spherical symmetry, we obtain the metric function from a continued fraction method and find that both time delays and the angular positions of images considerably deviate from general relativity, as large as milliarcseconds. This suggests that observational tests of ECG are indeed feasible.
We study slowly rotating black hole solutions in the six independent theories of Einstein Quartic Gravity (EQG) in four dimensions. Unlike in the static case for which all six theories yield the same solution, for rotating black holes we obtain distinct results for five out of the six theories. Working to leading order in the rotation parameter, we find that the equations characterizing these black holes can be reduced to second order for each theory, similar to what has already been done for Einstein Cubic Gravity. We construct approximate and numerical solutions to these equations, and study…
In this note we discuss the strong coupling issues inherent to the defining requirement for the so-called Einsteinian Cubic Gravity and its quasi-topological generalisations.
We show that there exists a critical point for the coupling constants in Einsteinian cubic gravity where the linearized equations on the maximally-symmetric vacuum vanish identically. We construct an exact isotropic bounce universe in the critical theory in four dimensions. The comoving time runs from minus infinity to plus infinity, yielding a smooth universe bouncing between two de Sitter vacua. In five dimensions we adopt numerical approach to construct a bounce solution, where a singularity occurred before the bounce takes place. We then construct exact anisotropic bounces that connect two…
Using numerical and perturbative methods, we construct the first examples of black hole solutions in Einsteinian cubic gravity and study their thermodynamics. Focusing first on four dimensional solutions, we show that these black holes have a novel equation of state in which the pressure is a quadratic function of the temperature. Despite this, they undergo a first order phase transition with associated van der Waals behaviour. We then construct perturbative solutions for general $D \ge 5$ and study the properties of these solutions for $D=5$ and $D=6$ in particular. We note that for $D >4$ th…
We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(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 $λ$. Using these we show that t…
In this paper, we study four-dimensional topological black hole solutions of Einsteinian cubic gravity in the presence of nonlinear Born-Infeld electrodynamics and a bare cosmological constant. First, we obtain the field equations which govern our solutions. Employing Abbott-Deser-Tekin and Gauss formulas, we present the expressions of conserved quantities, namely total mass and total charge of our topological black solutions. We disclose the conditions under which the model is unitary and perturbatively free of ghosts with asymptotically (A)dS and flat solutions. We find that, for vanishing b…
Black holes are the simplest objects in the universe. They correspond to extreme deformations of spacetime geometry, and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theo…
We obtain new solutions of Einsteinian cubic gravity coupled to a Maxwell field that describe the near-horizon geometry of charged and rotating black holes. We show that the AdS$_2\times\mathbb{S}^2$ near-horizon geometry of Reissner-Nordström black holes receives no corrections, but deviations with respect to the extremal Kerr-Newman solution appear as we turn on the angular momentum. We construct the profile of these corrected geometries using both numerical methods and slowly-spinning expansions, but we also find additional solutions that do not reduce to AdS$_2\times\mathbb{S}^2$ geometrie…
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 invar…
Einsteinian cubic gravity provides a holographic toy model of a nonsupersymmetric CFT in three dimensions, analogous to the one defined by Quasi-topological gravity in four. The theory admits explicit non-hairy AdS$_4$ black holes and allows for numerous exact calculations, fully nonperturbative in the new coupling. We identify several entries of the AdS/CFT dictionary for this theory, and study its thermodynamic phase space, finding interesting new phenomena. We also analyze the dependence of Rényi entropies for disk regions on universal quantities characterizing the CFT. In addition, we show…
We conduct a preliminary investigation into the phenomenological implications of Einsteinian cubic gravity (ECG), a 4-dimensional theory of gravity cubic in curvature of interest for its unique formulation and properties. We find an analytic approximation for a spherically symmetric black hole solution to this theory using a continued fraction ansatz. This approximate solution is valid everywhere outside of the horizon and we use it to study the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. We compute constraints on the ECG coupling…
We construct, for the first time, charged rotating black string solutions in four-dimensional Einsteinian cubic gravity, which are asymptotically anti de Sitter. By assuming that the solutions are completely regular at the horizon and studying their near-horizon behavior, we find some thermodynamic properties, which can be accessed analytically. We compute independently the Hawking temperature, the Wald entropy, the mass, the angular momentum, the charge, and the electrostatic potential of the solutions, analytically. Using these, we show that the first law of thermodynamics for rotating black…
In the present work we investigate wormhole configurations described by a constant redshift function in Einstein-Cubic gravity ({\sf ECG}). We derive analytical wormhole geometries by assuming a particular equation of state ({\sf EoS}) and investigate the possibility that these solutions satisfy the standard energy conditions. We introduce exact asymptotically flat and anti-de Sitter (AdS) spacetimes that admit traversable wormholes. These solutions are obtained by imposing suitable values for the parameters of the theory so that the resulted geometries satisfy the weak energy condition ({\sf …
In this paper we investigate the cosmological dynamics of an up to cubic curvature correction to General Relativity (GR) known as Cosmological Einsteinian Cubic Gravity (CECG), whose vacuum spectrum consists of the graviton exclusively and its cosmology is well-posed as an initial value problem. We are able to uncover the global asymptotic structure of the phase space of this theory. It is revealed that an inflationary matter-dominated bigbang is the global past attractor which means that inflation is the starting point of any physically meaningful cosmic history. Given that higher order curva…
We show that the combination of cubic invariants defining five-dimensional quasitopological gravity, when written in four dimensions, reduce to the version of four-dimensional Einsteinian gravity recently proposed by Arciniega, Edelstein & Jaime, that produces second order equations of motion in a FLRW ansatz, with a purely geometrical inflationary period. We introduce a quartic version of the four-dimensional Einsteinian theory with similar properties, and study its consequences. In particular we found that there exists a region on the space of parameters which allows for thermodynamically st…
We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects of the potential, including some non-dispersive terms that lead to black hole solutions (include quantum corrections) that agree with those derived in Einsteinian cubic gravity (ECG). We show that these non-dispersive terms could be obtained from theories that include the Gauss-Bonnet cubic invariant $G_3$. In addition, we derive the one-loop scattering amplitud…
Using on-shell amplitude methods, we derive a rotating black hole solution in a generic theory of Einstein gravity with additional terms cubic in the Riemann tensor. We give an explicit expression for the metric in Einsteinian Cubic Gravity (ECG) and low energy effective string theory, which correctly reproduces the previously discovered solutions in the zero angular-momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential, and we comment on the relation to the Janis…
We present an up to cubic curvature correction to General Relativity with the following features: (i) its vacuum spectrum solely consists of a graviton and is ghost-free, (ii) it possesses well-behaved black hole solutions which coincide with those of Einsteinian cubic gravity, (iii) its cosmology is well-posed as an initial value problem and, most importantly, (iv) it entails a geometric mechanism triggering an inflationary period in the early universe (driven by radiation) with a graceful exit to a late-time cosmology arbitrarily close to $Λ$CDM.
We consider quasinormal modes and Hawking radiation of four-dimensional asymptotically flat black holes in the most general up to-cubic-order-in-curvature dimension-independent Einsteinian theory of gravity that shares its graviton spectrum with the Einstein theory on constant curvature backgrounds. We show that damping rate and real oscillation frequencies of quasinormal modes for scalar, electromagnetic and Dirac fields are suppressed once the coupling with the cubic term is on. The intensity of Hawking radiation is suppressed as well, leading to, roughly, one order longer lifetime at a suff…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable properties: i) it has a well-defined Einstein gravity limit ii) it admits `Schwarzschild-like' solutions characterized by a single metric function iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity iv) Lovelock and quasi-topological gravities, as well as the recently developed Einsteinian cubic gravity [ArXiv…
Using a continued fraction ansatz we obtain an analytic approximation for a spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG), the next simplest Generalized Quasi-Topological Gravity (GQTG) after Einsteinian Cubic Gravity (ECG). This approximate solution is valid everywhere outside of the horizon and we use it to investigate the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. Using Shapiro time delay we calculate the constraints on the EQG coupling parameter. Finally we compute the shadow of an EQG black h…
While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theori…
We consider the generic massless cubic gravities coupled to a negative bare cosmological constant mainly in $D=5$ and $D=4$ dimensions, which are Einstein gravity extended with cubic curvature invariants where the linearized excited spectrum around the AdS background contains no massive modes. The generic massless cubic gravities are more general than Myers quasi-topological gravity in $D=5$ and Einsteinian cubic gravity in $D=4$. It turns out that the massless cubic gravities admit the black holes at least in a perturbative sense with the coupling constants of the cubic terms becoming infinit…
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 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 $\mathcal{L}($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 (ECG). In addition, …
In this work, we perform observational data analysis on Einsteinian cubic gravity and $f(P)$ gravity to constrain the parameter space of the theories. We use the 30-point $z-H(z)$ cosmic chronometer data as the observational tool for our analysis along with the BAO and the CMB peak parameters. The $χ^2$ statistic is used for the fitting analysis and it is minimized to obtain the best fit values for the free model parameters. We have used the Markov chain Monte Carlo algorithm to obtain bounds for the free parameters. To achieve this we used the publicly available CosmoMC code to put parameter …
Recently, the identification of new higher-curvature interactions known as Einsteinian cubic gravity (ECG) and Generalized quasi-topological gravities (GQGs) has allowed for important advances in the study of black hole solutions and holographic applications of higher-order gravity. These theories are characterized by having second-order linearized equations on maximally symmetric background and by possessing static, spherically symmetric (SSS) black hole solutions satisfying $g_{tt}g_{rr}=-1$, and whose thermodynamic properties can be studied analytically in a fully non-perturbative fashion. …
The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit…
