By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the two vacua with the same scale factor $a$, but opposite $\dot a$. The tunneling from one vacuum to the other provides a robust mechanism for bounce universes; it always occurs for systems with positive energy density. For suitable matter energy-momentum tensor we also construct cyclic universes. Cosmological solutions that resemble the classical time crystals can be constructed in massive gravity.
In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an $a$-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and $a$-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gra…
We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curv…
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 obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.
The aim of this note is to unveil a striking equivalence between the one-loop divergences in 7D Einstein and 6D Conformal Gravities. The particular combination of 6D pointwise Weyl invariants of the 6D Conformal Gravity corresponds to that of Branson's Q-curvature and can be written solely in terms of the Ricci tensor and its covariant derivatives. The quadratic metric fluctuations of this action, 6D Weyl graviton, are endowed with a sixth-order kinetic operator that happens to factorize on a 6D Einstein background into product of three shifted Lichnerowicz Laplacians. We exploit this feature …
Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.
We consider massless higher-order gravities in general $D=d+1$ dimensions, which are Einstein gravity extended with higher-order curvature invariants in such a way that the linearized spectrum around the AdS vacua involves only the massless graviton. We derive the covariant holographic two-point functions and find that they have a universal structure. In particular, the theory-dependent overall coefficient factor $\mathcal{C}_T$ can be universally expressed by $(d-1) \mathcal{C}_T=\ell (\partial a/\partial\ell)$, where $a$ is the holographic $a$-charge and $\ell$ is the AdS radius. We verify t…
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 work, we provide consistent compactifications of Einstein-Maxwell and Einstein-Maxwell-Lovelock theories on direct product spacetimes of the form $\mathcal{M}_D=\mathcal{M}_d\times\mathcal{K}^{p}$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. For these compactifications to take place, it is required the distribution of a precise flux of $p$-forms over the internal manifold. The dynamic of the $p$-forms are demanded to be controlled by two types of interaction. First, by specific couplings with the curvature tensor and, second, by a suitable interaction …
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries…
It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes incompatible with the metric, the metric factors and the square of the connection in Einstein - Hilbert Lagrangian have nonperturbative additions. In the simplest approximation both additions can be considered as functions of one scalar field. The scalar field can be excluded from the Lagrangian obtaining $F(R)-$gravity. The essence of quantum correction to the affin…
We first present a review, intended for classical relativists, of the ultraviolet difficulties faced by local quantum gravity theories in both the usual Einstein versions and in their supergravity extensions, at least perturbatively. These problems, present in arbitrary dimensions, are traceable to the dimensionality of the Einstein constant. We then summarize very recent results about supergravity at the highest allowed dimension, D=11, showing that also this unique model suffers from infinities already at 2 loops, despite its high degree of supersymmetry. The conclusion is that there is no v…
In this article we propose a new efficient strategy to construct exact solutions of Einstein gravities with a minimally coupled self-interacting scalar field. The strategy is to use the symmetry of the equations of motion (EOMs) to give a proper ansatz for scalar field first, then derive the metric and the corresponding scalar potential later. Using this strategy we give a simple example of constructing exact circular solutions in three dimensional gravities, these solutions contain the HMTZ black holes as a special case and some other new solutions. We also talk about thermodynamics of these …
We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, w…
We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize the Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use of the Inonu-Wigner contraction method. In the same way, by gauging the AdSL5 spacetime algebra, the Einstein-Hilbert gravity is extended including the vector fields kab and ha which are associated with non-Abelian tensors and non Abelian vectors charges in the AdSL5 algebra. The B5 extension of Einstein gravity…
We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual AdS vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Liftshitz black holes in conformal grav…
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 paper, we investigate the growth rates of action for the anti-de Sitter black holes in massive-Einstein gravity models and obtain the universal behaviors of the growth rates of action (the rates of holographic complexity) within the "Wheeler-DeWitt"(WDW) patch at the late limit. Furthermore, we find that, for the static neutral cases, when the same mass of black holes is given, the computational speed of the neutral massive black hole is the same as its Einstein gravity counterpart, which is independent with the effect of the graviton mass terms, nevertheless, for the static charged ca…
A (3+1)-dimensional Einstein-Gauss-Bonnet effective description of gravity has been recently formulated as the $D \to 4$ limit of the higher dimensional field equations after the rescaling of the coupling constant. This approach has been recently extended to the four-dimensional Einstein-Lovelock gravity. Although validity of the regularization procedure has not been shown for the general case, but only for a wide class of metrics, the black-hole solution obtained as a result of such a regularization is also an exact solution in the well defined 4D Einstein-Gauss-Bonnet theory suggested by Aok…
We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. We consider two explicit examples in four and five dimensions and compute the central charges of the asymptotic symmetry algebras of the near horizon geometries, using the improved version of the BBC formalism that encompasses the information of the Lagrangian. We find that the resulting Cardy entropy differs from the Wald entropy, caused by the Riemann-squared $R^{μνρσ}R_{μνρσ}$ term.
We define the notion of energy, and compute its values, for gravitational systems involving terms quadratic in curvature. While our construction parallels that of ordinary Einstein gravity, there are significant differences both conceptually and concretely. In particular, for D=4, all purely quadratic models admit vacua of arbitrary constant curvature. Their energies, including that of conformal (Weyl) gravity, necessarily vanish in asymptotically flat spaces. Instead, they are proportional to that of the Abbott-Deser (AD) energy expression in constant curvature backgrounds and therefore also …
Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical/toric/hyperbolic isometries in these theories. This allows us to derive/rederive the first laws for a wide range of black holes in literature. Furthermore, we construct many new exact solutions and obtain their first laws.
The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities hav…
The recently proposed restricted phase space thermodynamics is shown to be applicable to a large class of higher dimensional higher curvature gravity models coupled to Maxwell field, which are known as black hole scan models and are labeled by the spacetime dimension $d$ and the highest order $k$ of the Lanczos-Lovelock densities appearing in the action. Three typical example cases with $(d,k)=(5,1), (5,2)$ and $(6,2)$ are chosen as example cases and studied in some detail. These cases are representatives of Einstein-Hilbert, Chern-Simons and Born-Infield like gravity models. Our study indicat…
We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on higher-order modified gravity, and in particular on: (i) $f(G)$ Gauss-Bonnet gravity, and $f(P)$ cubic gravities, arising respectively through the use of the quadratic-curvature Gauss-Bonnet $G$ term, and the cubic-curvature combination, (ii) string-inspired quadratic Gauss-Bonnet gravity coupled to the dilaton field, (iii) models with string-inspired quartic curvature corrections, and (iv) running vacuum models. We perform a detailed investigation of the BBN epoch and we calculate the deviations of the freeze-out tem…
We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of some parameters the obtained cosmological models can be generically divided into three classes, leading to both singular and nonsingular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that…
We consider spherically symmetric and static charged black holes in Einstein-Gauss-Bonnet-Maxwell gravities in general $D\ge 5$ dimensions and study their photon spheres and black hole shadows. We show that they all satisfy the sequence of inequalities recently proposed relating a black hole's horizon, photon sphere, shadow and its mass.
The holographic bound has been extended to the different theory of gravities such as scalar-tensor gravity and $f(R)$ gravity according to the Noether charge definition of the entropy for a black hole surface. We have introduced some popular examples of the flat FRW cosmology in order to investigate holographic bound in scalar-tensor and $f(R)$ gravity. Using the holographic bound, we put an additional constraint on the scalar-tensor gravity and $f(R)$ gravity parameters. We also discuss about the transformation from Jordan frame to Einstein frame.
Recently proposed "critical" higher-derivative gravities in $AdS_D$ $D>3$ are expected to carry logarithmic representation of the Anti de Sitter isometry group. In this note, we quantize linear fluctuations of these critical gravities, which are known to be either identical with linear fluctuations of Einstein's gravity or else satisfy logarithmic boundary conditions at spacial infinity. We identify the scalar product uniquely defined by the symplectic structure implied by the classical action, and show that it does not posses null vectors. Instead, we show that the scalar product between any …
The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the $D\rightarrow 2\&4$ limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two-dimensional or four-dimensional scalar-…
We study the gravitational shock wave generated by a massless high energy particle in the context of higher order gravities of the form $F(R,R_{μν}R^{μν},R_{μναβ}R^{μναβ})$. In the case of $F(R)$ gravity, we investigate the gravitational shock wave solutions corresponding to various cosmologically viable gravities, and as we demonstrate the solutions are rescaled versions of the Einstein-Hilbert gravity solution. Interestingly enough, other higher order gravities result to the general relativistic solution, except for some specific gravities of the form $F(R_{μν}R^{μν})$ and $F(R,R_{μν}R^{μν})…
In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out to be more restrictive than their counterparts in General Relativity as in other extended theories of gravity. In fact, the general junction conditions on the matching hypersurfaces depend on the underlying theory and a new condition on the induced tetrads in order to avoid delta-like distributions in the field equations. This result imposes strict consequenc…
We generalize the local surface counterterm prescription suggested in Einstein gravity for higher derivative (HD) and Weyl gravities. Explicitly, the surface counterterm is found for three- and five-dimensional HD gravities. As a result, the gravitational action for asymptotically AdS spaces is finite and gravitational energy-momentum tensor is well-defined. The holographic trace anomaly for d2 and d4 boundary (gauge) QFT dual to above HD gravity is calculated from gravitational energy-momentum tensor. The calculation of AdS black hole mass in HD gravity is presented within above prescrition. …
We construct the pure gravity Becchi-Rouet-Stora-Tyutin (BRST) Einstein-Hilbert Lagrangian, to cubic order, using the BRST convolution product of two Yang-Mills theories, in conjunction with the Bern-Carrasco-Johansson (BCJ) double-copy.
Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity characterized by the existence of non-hairy generalizations of the Schwarzschild black hole which satisfy $g_{tt}g_{rr}=-1$, as well as for having second-order linearized equations around maximally symmetric backgrounds. In this paper we provide strong evidence that any gravitational effective action involving higher-curvature corrections is equivalent, via metric redefinitions, to some GQTG. In the case of theories involving invariants constructed from contractions of the Riemann tensor and the…
We perform the stability analysis of Schwarzschild-AdS (SAdS) black hole in the Einstein-Ricci cubic gravity. It shows that the Ricci tensor perturbations exhibit unstable modes for small black holes. We call this the mass-induced instability of SAdS black hole because the instability of small black holes arises from the massiveness in the linearized Einstein-Ricci cubic gravity, but not a feature of higher-order derivative theory giving ghost states. Also, we point out that the correlated stability conjecture holds for the SAdS black hole by computing the Wald entropy of SAdS black hole in Ei…
We employ the Noether procedure to derive a general formula for the radially conserved heat current in AdS planar black holes with certain transverse and traceless perturbations, for a general class of gravity theories. For Einstein gravity, the general higher-order Lovelock gravities and also a class of Horndeski gravities, we derive the boundary stress tensor and show that the resulting boundary heat current matches precisely the bulk Noether current.
A general approach to viable modified $f(R)$ gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models are explicitly considered, but the analysis is extensible to $N$-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, un…
In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, we construct the near horizon and asymptotic solutions as the first step. Then, the approximate analytic solutions are obtained through continued fraction expansion. We also compute the thermodynamic quantities and use the first law and Smarr formula to obtain the analytic solutions for the near horizon quantities. Finally, we follow the same approach to obtain the new static black hole solutions with different metric functions.
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 establish various general results concerning static and spherically symmetric black hole solutions of general higher-derivative extensions of Einstein gravity. We prove that the only theories susceptible of admitting solutions with $g_{tt}g_{rr}=-1$ and representing the exterior field of a spherically symmetric distribution of mass are those that only propagate a massless and traceless graviton on the vacuum. Then, we provide a simple (and computationally powerful) sufficient condition for a theory to admit solutions of that kind, as well as a systematic way for constructing them for a give…
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…
We implement a universal method for renormalizing AdS gravity actions applicable to arbitrary higher curvature theories in up to five dimensions. The renormalization procedure considers the extrinsic counterterm for Einstein-AdS gravity given by the Kounterterms scheme, but with a theory-dependent coupling constant that is fixed by the requirement of renormalization for the vacuum solution. This method is shown to work for a generic higher curvature gravity with arbitrary couplings except for a zero measure subset, which includes well-known examples where the asymptotic behavior is modified an…
We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happ…
Accelerating vacua with maximally symmetric, but not necessarily spherical, sections for Einstein and Gauss-Bonnet gravities in generic dimensions are obtained. The acceleration parameter has the effect of shifting the cosmological constants in Einstein gravity, whereas in Gauss-Bonnet gravity the effective cosmological constants remain the same in the presence of acceleration as in the case without acceleration.
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 resp…
