The Bañados-Teitelboim-Zanelli (BTZ) black hole metric solves the three-dimensional Einstein's theory with a negative cosmological constant as well as all the generic higher derivative gravity theories based on the metric; as such it is a universal solution. Here, we find, in all generic higher derivative gravity theories, new universal non-Einsteinian solutions obtained as Kerr-Schild type deformations of the BTZ black hole. Among these, the deformed non-extremal BTZ black hole loses its event horizon while the deformed extremal one remains intact as a black hole in any generic gravity theory.
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 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…
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…
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…
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 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 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…
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 set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the four-metric, reflecting a quadratic curvature nonlinearity but no higher than second order derivatives. In contrast with recent proposals to obtain 4dEGB theories through a singular rescaling of the Gauss-Bonnet coupling, this formalism requires no (classical) regularization of divergences and is inequivalent to Horndeski gravity, while being generally covaria…
For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity like e.g.\ the problem of time are discussed in this framework.
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 study the particle content of higher derivative theories of gravity built with contractions of the Riemann tensor and its covariant derivatives. In the absence of the latter, there is a family of theories exhibiting an Einsteinian spectrum known as generalized quasi-topological gravities. In turn, we present a no-go result for the construction of Einsteinian gravities involving covariant derivatives of the Riemann tensor. We find evidences suggesting that (truncated series) finite order Lagrangians with covariant derivatives of the Riemann tensor generically present ghosts in their spectrum…
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…
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…
Several rare coincidences of scales in standard particle physics are needed to explain (i) why neutrinos have mass, (ii) why the negative pressure of the cosmological dark energy (DE) coincides with the positive pressure of random motion of dark matter (DM) in bright galaxies, (iii) why Dark Matter in galaxies seems to have a finite phase-space density, and to follow the Tully-Fisher-Milgrom relation of galaxy rotation curves. The old idea of self-interacting DM is given a new spin: we propose that the neutrino spin-gravity coupling could lead to a cosmic neutrino dark fluid with a an internal…
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…
We study the condensation of a charged scalar field in a $(3+1)$-dimensional asymptotically AdS background in the context of Einsteinian cubic gravity, featuring a holographic superconductor with higher curvature corrections corresponding to a CFT with a non-vanishing value of the stress tensor three-point function $t_4$. As it was previously noticed for higher dimensional Gauss-Bonnet theory, we observe that the critical temperature of the superconducting phase transition is lowered as the higher curvature coupling grows.
The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac's quantization should be applicable.
The integrability of $R^2$-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed $iso(2,1)$-algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the centre of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmologic…
We develop a model-independent test of General Relativity that allows for the constraint of the gravitational wave (GW) polarization content with GW detections of binary compact object inspirals. We first consider three modified gravity theories (Brans-Dicke theory, Rosen's theory and Lightman-Lee theory) and calculate the response function of ground-based detectors to gravitational waves in the inspiral phase. This allows us to see how additional polarizations predicted in these theories modify the General Relativistic prediction of the response function. We then consider general power-law mo…
We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationsh…
We consider general theories of a massive spin-2 particle $h_{μν}$ on a Minkowski background. A decomposition of $h_{μν}$ in terms of helicity eigenstates allows us to directly test whether any given theory possesses a consistent description as a massive spin-2 representation of the Poincaré group. We demonstrate (i) that any nonlinear theory with an Einsteinian derivative structure either contains ghosts or does not describe a weakly coupled spin-2 and (ii) that there exists a two-parameter family of non-Einsteinian cubic self-interactions which constitute a ghost-free massive spin-2 theory.
We obtain a dynamical formulation of two-dimensional gravity from a non-Einsteinian phase in higher dimensions $(D=3+2n)$. The formalism is associated with (at least) one extra dimension of vanishing proper length, thus being inequivalent to either a Kaluza-Klein compactification or the Mann-Ross dimensional reduction defined upon a singular limit. The emergent solutions admit any arbitrary curvature in contrast with Jackiw-Teitelboim constant curvature gravity. We present the static and homogeneous solutions as explicit examples. The effective field equations are shown to remain unaffected by…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincaré gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian piece…
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…
An analysis of some modified gravity models, based on the study of pure Schwarzschild and of Schwarzschild-de Sitter black holes, and involving the use of the Noether charge method, is carried out. Corrections to the classical Einsteinian black hole entropy appear. It is shown explicitly how the condition of positive entropy can be used in order to constrain the viability of modified gravity theories.
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…
In this paper, we propose a new approach to study the dark sector of the universe by considering the dark energy as emerging a q-deformed bosonic scalar field which is not only interacting with the dark matter, but also non-minimally coupled to gravity, in the framework of standard Einsteinian gravity. In order to analyze the dynamic of the system, we first give the quantum field theoretical description of the q-deformed scalar field dark energy, then construct the action and the dynamical structure of these interacting and non-minimally coupled dark sector. As a second issue, we perform the p…
We study here the phase-transitional evolution between the Eguchi-Hanson soliton, the orbifolded Schwarzschild Anti de-Sitter black hole, and orbifolded thermal Anti de-Sitter space in Gauss-Bonnet gravity for a small Gauss-Bonnet coefficient $α$. Novel phase structure is uncovered for both negative and positive $α$ with spacetime configurations that are stable in Gauss-Bonnet gravity without being so in Einsteinian gravity. The evolutionary tracks taken towards such stable configurations are guided by quantum tunnelling and can be represented with a phase diagram constructed by comparing the …
We give a short outline, in Sec.\ 2, of the historical development of the gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external ($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the corresponding conserved currents. In Sec.\ 3, experimental results with neutron interferometers in the gravitational field of the earth, as inter- preted by means of the equivalence principle, can be predicted by means of the Dirac equation in an accelerated and rotating reference frame. Using the Dirac equation in such a non-inertial frame, we describe how in a gauge- the…
We define (non-Einsteinian) universal metrics as the metrics that solve the source-free covariant field equations of generic gravity theories. Here, extending the rather scarce family of universal metrics known in the literature, we show that the Kerr-Schild--Kundt class of metrics are universal. Besides being interesting on their own, these metrics can provide consistent backgrounds for quantum field theory at extremely high energies.
Generically, massive gravity gives a non-unique gravitational field around a star. For a special family of massive gravity theories, we show that the stellar gravitational field is unique and observationally acceptable, that is close to Einsteinian. The black hole solutions in this family of theories are also studied and shown to be peculiar. Black holes have a near-horizon throat and the curvature diverging at the horizon. We show that there exists a sub-family of these massive gravity theories with non-singular at horizon black holes.
We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and another that does not. In the latter, we find a deformation to the Schwarzschild metric that solves the modified field equations in the small coupling approximation. We calculate the event horizon shift, the innermost stable circular orbit shift, and corrections to gravitational waves, mapping them to the parametrized post-Einsteinian framework.
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…
Asymptotically flat black holes in $2+1$ dimensions are a rarity. We study the recently found black flower solutions (asymptotically flat black holes with deformed horizons), static black holes, rotating black holes and the dynamical black flowers (black holes with radiative gravitons ) of the purely quadratic version of new massive gravity. We show how they appear in this theory and we also show that they are also solutions to the infinite order extended version of the new massive gravity, that is the Born-Infeld extension of new massive gravity with an amputated Einsteinian piece. The same m…
The observation of the inspiral and merger of compact binaries by the LIGO/Virgo collaboration ushered in a new era in the study of strong-field gravity. We review current and future tests of strong gravity and of the Kerr paradigm with gravitational-wave interferometers, both within a theory-agnostic framework (the parametrized post-Einsteinian formalism) and in the context of specific modified theories of gravity (scalar-tensor, Einstein-dilaton-Gauss-Bonnet, dynamical Chern-Simons, Lorentz-violating, and extra dimensional theories). In this contribution we focus on (i) the information carri…
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
We consider theories that modify gravity at cosmological distances, and show that any such theory must exhibit a strong coupling phenomenon, or else it is either inconsistent or is already ruled out by the solar system observations. We show that all the ghost-free theories that modify dynamics of spin-2 graviton on asymptotically flat backgrounds, automatically have this property. Due to the strong coupling effect, modification of the gravitational force is source-dependent, and for lighter sources sets in at shorter distances. This universal feature makes modified gravity theories predictive …
We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.
We start by briefly reviewing the description of gravity theories as gauge theories in four dimensions. More specifically we recall the procedure leading to the results of General Relativity and Weyl Gravity in a gauge-theoretic manner. Then, after a brief reminder of the formulation of gauge theories on noncommutative spaces, we review our recent work, where gravity is constructed as a gauge theory on the fuzzy $dS_4$.
We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and locally scale covariant field equations are found by a first order variational formalism.
We perform a detailed analysis of holographic entanglement Rényi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Rényi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for thre…
Generalised Proca theories of gravity represent an interesting class of vector-tensor theories where only three propagating degrees of freedom are present. In this work, we propose a new teleparallel gravity analog to Proca theories where the generalised Proca framework is extended due to the lower order nature of torsion based gravity. We develop a new action contribution and explore the example of the Friedmann equations in this regime. We find that teleparallel Proca theories offer the possibility of a much larger class of models in which do have an impact on background cosmology.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn't happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version o…
We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity. We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions. No additional matter fields are required to obtain solutions with asymptotic Lifshitz behaviour, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a posit…
We argue, that in Einsteinian gravity the Planck length is the shortest length of nature, and any attempt of resolving trans-Planckian physics bounces back to macroscopic distances due to black hole formation. In Einstein gravity trans-Planckian propagating quantum degrees of freedom cannot exist, instead they are equivalent to the classical black holes that are fully described by lighter infra-red degrees of freedom and give exponentially-soft contribution into the virtual processes. Based on this property we argue that pure-Einstein (super)gravity and its high-dimensional generalizations are…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions are rather general and apply to large class of theories in which, already at the Newtonian level, gravity changes the regime at a certain very large crossover distance $r_c$. In such theories the cosmological evolution gets dramatically modified at the crossover scale, usually exhibiting a "self-accelerated" expansion, which can be differentiated from more c…
