Aron D. Kovacs, Harvey S. Reall
We study the initial value problem for Lovelock and Horndeski theories of gravity. We show that the equations of motion of these theories can be written in a form that, at weak coupling, is strongly hyperbolic and therefore admits a well-posed initial value problem. This is achieved by introducing a new class of "modified harmonic" gauges for general relativity.
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We review and discuss some recent progress in Lovelock and Horndeski theories modifying Einstein's General Relativity. Using as our guide the uniqueness properties of these modified gravity theories we then discuss how Kaluza-Klein reduction of Lovelock theory can lead to effective scalar-tensor actions including several important terms of Horndeski theory. We show how this can be put to practical use by mapping analytic black hole solutions of one theory to the other. We then elaborate on the subset of Horndeski theory that has self-tuning properties and review a generic method giving scalar-…
The Horndeski theories are extended into the Lovelock gravity theory. When the canonical scalar field is uniquely kinetically coupled to the Lovelock tensors, it is named after Lovelock scalar field. The Lovelock scalar field model is a subclass of the new Horndeski theories. A most attractive feature of the Lovelock scalar field is its equation of motion is second order. So it is free of ghosts. We study the cosmology of Lovelock scalar field in the background of $7$ dimensional spacetime and present a class of cosmic solutions. These solutions reveal the physics of the scalar field is rather…
We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we pro…
Holographic Renormalization of String-Derived Lovelock--Horndeski Theory
针对五维弦导出的洛夫洛克-霍恩德斯基理论，构建了其渐近局域 AdS 分支的重整化生成泛函，证明全息响应可重构高维参数，为弦约化提供边界指纹。
We construct a large class of explicit, asymptotically flat and regular wormhole solutions in higher order scalar tensor theories. The solutions are vacuum solutions of scalar tensor theory and no matter (exotic or regular) is introduced in order to support them. They are constructed via a general disformal transformation of a seed black hole solution. The seed solutions belong to a particular Horndeski theory which requires the presence of all extended Galileons and has a higher dimensional Lovelock origin. As a result, the resulting wormholes are always solutions of general beyond Horndeski …
In this paper we construct new exact solutions in Einstein-Gauss-Bonnet and Lovelock gravity, describing asymptotically flat black strings. The solutions exist also under the inclusion of a cosmological term in the action, and are supported by scalar fields with finite energy density, which are linear along the extended direction and have kinetic terms constructed out from Lovelock tensors. The divergenceless nature of the Lovelock tensors in the kinetic terms ensures that the whole theory is second order. For spherically, hyperbolic and planar symmetric spacetimes on the string, we obtain an …
We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and sphe…
3d Lovelock gravity and the holographic c-theorem: Proof at all orders and resummation
本文证明了三维Lovelock引力在所有阶和任意耦合下满足全息c-定理，并给出了重求和形式的拉格朗日量、c-函数和中心电荷，其核心贡献是建立了尺度不变但非共形的对偶理论。
We reformulate the recently proposed regularized version of Lovelock gravity in four dimensions as a scalar-tensor theory. By promoting the warp factor of the internal space to a scalar degree of freedom by means of Kaluza-Klein reduction, we show that regularized Lovelock gravity can be described effectively by a certain subclass of the Horndeski theory. Cosmological aspects of this particular scalar-tensor theory are studied. It is found that the background with a scalar charge is generically allowed. The consequences of this scalar charge are briefly discussed.
Stealth Ellis Wormholes In Horndeski theories
本文在广义Horndeski理论中证明Ellis虫洞是由与Gauss-Bonnet项非平凡耦合的引力理论解析支持的隐形解，并提出共形变换和自发标量化两种机制为其赋予有效ADM质量。
Holographic Conformal Anomaly and a-Theorem in 5D Scalar-Tensor Theories from Heterotic Strings
本文通过统一机制推导了五维标量-张量理论中的 holographic 一致性异常，并建立了 a 定理，验证了 AdS/CFT 在非最小标量耦合和高曲率项下的一致性。
Selecting Horndeski theories without apparent symmetries and their black hole solutions
本文由广义 Kaluza-Klein 作用量导出球对称场方程的可积条件，识别无明显对称性的 Horndeski 理论，并构造由两个耦合常数刻画的带次生毛黑洞及一般解族。
Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
该研究通过欧几里得方法研究了低维Lovelock引力中静态黑洞的热力学，证明了平面黑洞热力学普适性及扩展第一定律在低维成立，并基于约化作用的标度性质推导了Smarr关系及其修正形式。
There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imp…
We consider extensions of the Einstein-Hilbert Lagrangian to a general functional of metric and Riemann curvature tensor. A given such Lagrangian describes two different theories depending on considering connection and metric (Palatini formulation), or only the metric (metric formulation) as independent dynamical degrees of freedom. Equivalence of the Palatini and metric formulations at the level of equations of motion, which as we will argue is a manifestation of the Equivalence Principle, is the physical criterion that restricts form of the Lagrangians of modified gravity theories. We prove …
According to Lovelock's theorem, the Hilbert-Einstein and the Lovelock actions are indistinguishable from their field equations. However, they have different scalar-tensor counterparts, which correspond to the Brans-Dicke and the \emph{Lovelock-Brans-Dicke} (LBD) gravities, respectively. In this paper the LBD model of alternative gravity with the Lagrangian density $\mathscr{L}_{\text{LBD}}=\frac{1}{16π}\left[ϕ\left( R +\frac{a}{\sqrt{-g}}{}^*RR + b\mathcal{G}\right)-\frac{ω_{\text{L}}}ϕ\nabla_αϕ\nabla^αϕ\right]$ is developed, where ${}^*RR$ and $\mathcal{G}$ respectively denote the topologica…
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.
We perform a space-time analysis of the D>4 quadratic curvature Lanczos-Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D constraints, of zeroth and first time derivative order. In the "linearized" - here necessarily cubic - limit, we give an explicit formulation in terms of the usual ADM metric decomposition, incidentally showing that time derivatives act only on its transverse-traceless spatial components. Unsurprisingly, pure LL has no Hamiltonian formulation, nor are even it…
We analyzed static spherically symmetric solutions of the five dimensional (5D) Lovelock gravity in the first order formulation. In the Riemannian sector, when torsion vanishes, Boulware-Deser black hole represents a unique static spherically symmetric black hole solution for the generic choice of the Lagrangian parameters. We showed that the special choice of the Lagrangian parameters, different from the Lovelock Chern-Simons gravity, leads to the existence of the static black hole solution with torsion, which metric is asymptotically AdS. We calculate conserved charges and thermodynamical qu…
We study spherically symmetric gravitational collapse in cubic Horndeski theories of gravity. By varying the coupling constants and the initial amplitude of the scalar field, we determine the region in the space of couplings and amplitudes for which it is possible to construct global solutions to the Horndeski theories. Furthermore, we identify the regime of validity of effective field theory as the sub-region for which a certain weak field condition remains small at all times. We evolve the initial data using the CCZ4 formulation of the Einstein equations and horizon penetrating coordinates w…
We study the local well-posedness of the initial value problem for cubic Horndeski theories. Three different strongly hyperbolic modifications of the ADM formulation of the Einstein equations are extended to cubic Horndeski theories in the weak field regime. In the first one, the equations of motion are rewritten as a coupled elliptic-hyperbolic system of partial differential equations. The second one is based on the BSSN formulation with a generalised Bona-Massó slicing (covering the 1+log slicing) and non-dynamical shift vector. The third one is an extension of the CCZ4 formulation with a ge…
We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under…
We present a general framework for studying the relativistic star perturbations on a static and spherically symmetric background in full Horndeski theories. We take a perfect fluid into account as a form of the Schutz-Sorkin action. Our formulation is sufficiently versatile in that the second-order actions of perturbations in odd- and even-parity sectors are derived without choosing particular gauge conditions, so they can be used for any convenient gauges at hand. The odd-parity sector contains one dynamical gravitational degree of freedom coupled to a time-independent four velocity of the fl…
We define the concept of Levi Civita truncation for a Lagrangian in the Palatini formulation with an arbitrary connection, and show that its consistency uniquely identifies the Lovelock Lagrangians.
We obtain the classical holographic relation for the general Lovelock gravity and decompose the full Lagrangian into the bulk term and the surface term, expressed as a total derivative $\partial_μJ^μ$. By classical holographic relation, we mean that $J^μ$ is determined completely by the bulk term. We find that the bulk term is not degenerate, or first-order in this foliation-independent approach. We then consider the Arnowitt-Deser-Misner (ADM) formalism where the foliation coordinate $w$ is treated as special. We obtain the classical holographic-degenerate relation with the first-order bulk t…
Intersecting hypersurfaces in classical Lovelock gravity are studied exploiting the description of the Lovelock Lagrangian as a sum of dimensionally continued Euler densities. We wish to present an interesting geometrical approach to the problem. The analysis allows us to deal most efficiently with the division of space-time into a honeycomb network of cells produced by an arbitrary arrangement of membranes of matter. We write the gravitational action as bulk terms plus integrals over each lower dimensional intersection. The spin connection is discontinuous at the shared boundaries of the cell…
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in th…
Logarithmic correction to the entropy of near-extremal higher-curvature black holes
该研究利用二维Horndeski理论对应关系，证明近极端黑洞熵的对数修正具有普适性，并给出其主导尺度的一般形式，适用于多种高曲率引力理论。
We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that have been used to establish well-posed initial value problems for these theories, and discuss well-posed formulations of the constraint equations. We also discuss global aspects of exact, strongly coupled solutions to some of Horndeski gravity theories: the formation of shocks, the loss of hyperbolicity, and the formation of naked curvature singularities. Fin…
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…
This paper is a pedagogical introduction to models of gravity and how to constrain them through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of General Relativity have been proposed ever since its early years. Because of Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostr…
Gravitational waves (GWs) have opened a new window on fundamental physics in a number of important ways. The next generation of GW detectors may reveal more information about the polarization structure of GWs. Additionally, there is growing interest in theories of gravity beyond GR. One such theory which remains viable within the context of recent measurements of the speed of propagation of GWs is the teleparallel analogue of Horndeski gravity. In this work, we explore the polarization structure of this newly proposed formulation of Horndeski theory. In curvature-based gravity, Horndeski theor…
Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether-Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved c…
Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity
研究体对偶为洛夫洛克引力的全息共形场论中的类时纠缠第一定律，通过双维克旋转公式和雅各布森 - 迈尔斯熵泛函计算线性变化，发现其与洛夫洛克引力线性化场方程在特定区域内等价。
We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases evolution of the system, treated as a hyperbolic initial boundary value problem, leads to the equations of motion becoming ill-posed when the elliptic region forms. No singularities or discontinuities are encountered on the corresponding effective "Cauchy horizon". Therefore it…
We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of motion, without approximation, for general spacetimes. While we concentrate on the specific example of shift-symmetric ESGB, our methods, which make use of a recently proposed modification to the generalized harmonic formulation, should be generally applicable to all Horndeski theories of gravity (including general relativity). We demonstrate that these methods c…
In this note we perform the $n+1$ decomposition, or Arnowitt Deser Misner (ADM) formulation of $f($Lovelock$)$ gravity theory. The hamiltonian form of Lovelock gravity was known since the work of C. Teitelboim and J. Zanelli in 1987, but this result had not yet been extended to $f($Lovelock$)$ gravity. Besides, field equations of $f($Lovelock$)$ have been recently be computed by P. Bueno et al., though without ADM decomposition. We focus on the non-degenerate case, ie. when the Hessian of $f$ is invertible. Using the same Legendre transform as for $f(\mathrm{R})$ theories, we can identify the …
We derive the conformal constraints satisfied by classical vertices of a (Einstein) Gauss-Bonnet theory around flat space, in general dimensions and at $d=4$ (4d EGB). In $4d$ EGB they are obtained by a singular limit of the integral of the Euler-Poincarè density. Our analysis exploits the relation between this theory and the conformal anomaly action, which allows to uncover some interesting features of the GB vertex at cubic and quartic level. If we introduce a conformal decomposition of the metric, the resulting theory can be formulated in two different versions, which are regularization dep…
We revise two regularization mechanisms for Lovelock gravity with AdS asymptotics. The first one corresponds to the Dirichlet counterterm method, where local functionals of the boundary metric are added to the bulk action on top of a Gibbons-Hawking-Myers term that defines the Dirichlet problem in gravity. The generalized Gibbons-Hawking term can be found in any Lovelock theory following the Myers' procedure to achieve a well-posed action principle for a Dirichlet boundary condition on the metric, which is proved to be equivalent to the Hamiltonian formulation for a radial foliation of spaceti…
Black hole thermodynamics in Horndeski theories
本文在Horndeski理论中通过Iyer-Wald方法推导静态球对称黑洞的热力学第一定律，并证明静态标量场黑洞满足面积定律，而时间依赖标量场黑洞的熵依赖标量场分布，且在某些参数范围内具有非平凡标量场的Schwarzschild-(A)dS黑洞比广义相对论情形更热力学稳定。
Static anisotropic stars in Lovelock gravity: Universal closed-form equations
该研究将Lovelock引力中静态理想流体的特征多项式公式扩展至各向异性物质领域，推导了相关闭式方程，证实内部Schwarzschild几何的唯一性，消除d=2N+1维纯Lovelock球的障碍，并积分得到d=10、11维的恒星方程，发现高阶项可增大最大质量。
Phenomenology of Horndeski Gravity under Positivity Bounds
本文重新审视Horndeski引力的正定性约束，将其转化为暗能量有效场论的可行性条件并实现于EFTCAMB中，发现这些约束显著收紧了背景演化和线性扰动的理论预测，特别是增强了μ与Σ的相关性及对引力波光速的约束。
Multisymplectic Formalism for Cubic Horndeski Theories
该研究构建了三次Horndeski理论的协变多辛形式体系，分析了其协变哈密顿形式中庞加莱-嘉当形式投影到$J^1π$的条件，探究了仅用多动量表述的可行性，并讨论了不满足投影条件的一般情况的意义。
We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to the molecule deformation. Finally, we investigate the…
Among single-field scalar-tensor theories, there is a special class called "cuscuton," which is represented as some limiting case of k-essence in general relativity. This theory has a remarkable feature that the number of propagating degrees of freedom is only two in the unitary gauge in contrast to ordinary scalar-tensor theories with three degrees of freedom. We specify a general class of theories with the same property as the cuscuton in the context of the beyond Horndeski theory, which we dub as the extended cuscuton. We also study cosmological perturbations in the presence of matter in th…
Perturbations and stability of black holes with static scalar hair in general GLPV theories
该研究推导了一般GLPV理论中带静态标量毛黑洞的微扰与稳定性相关方程，确定了保证稳定的相容性条件，构造了标量-高斯-博内黑洞的超越Horndeski形变并分析了其稳定性。
The recent observation of the the gravitational wave event GW170817 and of its electromagnetic counterpart GRB170817A, from a binary neutron star merger, has established that the speed of gravitational waves deviates from the speed of light by less than one part in $10^{15}$. As a consequence, many extensions of General Relativity are inevitably ruled out. Among these we find the most relevant sectors of Horndeski gravity. In its original formulation, mimetic gravity is able to mimic cosmological dark matter, has tensorial perturbations that travel exactly at the speed of light but has vanishi…
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 perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degene…
The gravitational-wave event GW170817 from a binary neutron star merger together with the electromagnetic counterpart showed that the speed of gravitational waves $c_t$ is very close to that of light for the redshift $z<0.009$. This places tight constraints on dark energy models constructed in the framework of modified gravitational theories. We review models of the late-time cosmic acceleration in scalar-tensor theories with second-order equations of motion (dubbed Horndeski theories) by paying particular attention to the evolution of dark energy equation of state and observables relevant to …
In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framewor…
Effective Field Theory of Black Hole Perturbations with Timelike Scalar Profile: Formulation
本文构建了标量张量理论中非均匀背景上的微扰有效场论，保持标量场类时以自发破缺时间微分同胚，推导出空间微分同胚不变性的一致性关系，并计算了球对称静态黑洞背景方程。
Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge-Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein's theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized methods. As a…
We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the backgr…
In this work we study static black holes in the regularized 4D Einstein-Gauss-Bonnet theory of gravity; a shift-symmetric scalar-tensor theory that belongs to the Horndeski class. This theory features a simple black hole solution that can be written in closed form, and which we show is the unique static, spherically-symmetric and asymptotically-flat black hole vacuum solution of the theory. We further show that no asymptotically-flat, time-dependent, spherically-symmetric perturbations to this geometry are allowed, which suggests that it may be the only spherically-symmetric vacuum solution th…
A quasi-static approximation (QSA) for modified gravity can be applied in a number of ways. We consider three different analytical formulations based on applying this approximation to: (1) the field equations; (2) the equations for the two metric potentials; (3) the use of the attractor solution derived within the Equation of State (EoS) approach. We assess the veracity of these implementations on the effective gravitational constant ($μ$) and the slip parameter ($η$), within the framework of Horndeski models. In particular, for a set of models we compare cosmological observables, i.e., the ma…
Alternative formulations of the thermodynamics of scalar-tensor theories
本文研究了 Horndeski 引力与 Eckart 一阶热力学类比的替代表述，通过标量场流体有效应力-能量张量的恒等式映射本构关系，并探讨了与 Einstein 引力不同耦合对热力学形式的影响，最终在传统标量-张量理论中找到简化形式。
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under Local Lorentz Transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations…
We propose the almost-geodesic motion of self-gravitating test bodies as a possible selection rule among metric theories of gravity. Starting from a heuristic statement, the "gravitational weak equivalence principle", we build a formal, operative test able to probe the validity of the principle for any metric theory of gravity, in an arbitrary number of spacetime dimensions. We show that, if the theory admits a well-posed variational formulation, this test singles out only the purely metric theories of gravity. This conclusion reproduces known results in the cases of general relativity (also w…
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely differen…
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