We show that, in all metric theories of gravity with a general covariant action, gravity couples to the gravitational energy-momentum tensor in the same way it couples to the matter energy-momentum tensor order by order in the weak field approximation around flat spacetime. We discuss the relation of this property to the Strong Equivalence Principle. We also study the gauge transformation properties of the gravitational energy-momentum tensor.
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 …
The equivalence between the path integrals for first order gravity and the standard torsion-free, metric gravity in 3+1 dimensions is analyzed. Starting with the path integral for first order gravity, the correct measure for the path integral of the metric theory is obtained.
We give a pedagogical introduction into the field of (modified) teleparallel theories of gravity. Our presentation is fairly self-contained. In particular, we carefully explain the basic principles of metric-affine approaches to gravity. This contribution is based on our talk "Teleparallel gravity, its modifications, and the local Lorentz invariance" at the 9th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics in Belgrade, September 2017.
Intrigued by the holographic principle, Padmanabhan recently proposed a novel idea, saying that our cosmic space is emergent as cosmic time progresses. In particular, the expansion rate of the Universe is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. In this note, we generalize this interesting paradigm to brane world, scalar-tensor gravity, and f(R) theory, respectively, and find that in the cosmological setting the Friedmann equations can be successfully derived.
We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe the so called {\it Geometric Trinity of Gravity}. Specifically, we consider General Relativity, constructed upon the metric tensor and based on the curvature $R$; Teleparallel Equivalent of General Relativity, formulated in terms of torsion $T$ and relying on tetrads and spin connection; Symmetric Teleparallel Equivalent of General Relativity, built up on non-metr…
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…
A physical and geometrical interpretation of previously introduced tensor operator algebras of U(2,2) in terms of algebras of higher-conformal-spin quantum fields on the anti-de Sitter space AdS_5 is provided. These are higher-dimensional W-like algebras and constitute a potential gauge guide principle towards the formulation of induced conformal gravities (Wess-Zumino-Witten-like models) in realistic dimensions. Some remarks on quantum (Moyal) deformations are given and potentially tractable versions of noncommutative AdS spaces are also sketched. The role of conformal symmetry in the microsc…
A recent proposal by Shuler regarding a postulate-based derivation of a family of metrics describing the gravitational field outside a static spherically symmetric mass distribution is reviewed. All of Shuler's gravities agree with the Schwarzschild solution in the weak-field limit, but they differ in the strong-field domain, i.e., close enough to a sufficiently compact source of the field. It is found that the evoked postulates of i) momentum conservation and ii) consistency of field strength measurement are satisfied in all metric theories of gravity compatible with the Einstein equivalence …
General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in this report is applied on two examples.
We consider the Principle of Equivalence along with Weyl theorem to discuss the interpretation of gravity as a geometric effect; we study what are the restrictions on the connections that must be required for this geometrization to occur in the most general case.
The Hessling improvement of the Haag, Narnhofer and Stein principle is analysed in the case of a massless scalar field propagating outside of an extremal R-N black hole. It is found that this sort of ``Quantum (Einstein's) Equivalence Principle'' selects only the R-N vacuum as a physically sensible state, i.e., it selects the temperature $T=0$ only.
We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at non-vanishing T. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quanti…
Humboldt-Universität zu Berlin（柏林洪堡大学）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Universidad Complutense de Madrid（马德里康普顿斯大学）；Dublin Institute for Advanced Studies（都柏林高等研究院）；Charles University（查理大学）
Limits for the applicability of the equivalence principle are considered in the context of low-energy effective field theories. In particular, we find a class of higher-derivative interactions for the gravitational and electromagnetic fields which produce dispersive photon propagation. The latter is illustrated by calculating the energy-dependent contribution to the deflection of light rays.
We compare the response function of an Unruh-DeWitt detector for different space-times and different vacua and show that there is a {\it detailed} violation of the equivalence principle. In particular comparing the response of an accelerating detector to a detector at rest in a Schwarzschild space-time we find that both detectors register thermal radiation, but for a given, equivalent acceleration the fixed detector in the Schwarzschild space-time measures a higher temperature. This allows one to locally distinguish the two cases. As one approaches the horizon the two temperatures have the sam…
The presence of gravity implies corrections to the Einstein-Planck formula $E=h ν$. This gives hope that the divergent blueshift in frequency, associated to the presence of a black hole horizon, could be smoothed out for the energy. Using simple arguments based on Einstein's equivalence principle we show that this is only possible if a black hole emits, in first approximation, not just a single particle, but thermal radiation.
As an extension of our previous work [J.Qiao, T.Zhu, W.Zhao & A.Wang, arXiv:1909.03815], in this article, we calculate the effects of parity violation on gravitational-wave (GW) waveforms during their propagation in the most general parity-violating gravities, including Chern-Simons modified gravity, ghost-free scalar-tensor gravity, symmetric teleparallel equivalence of GR theory, Hořava-Lifshitz gravity and so on. For this purpose, we consider the GWs generated by the coalescence of compact binaries and concentrate on the imprints of the parity violation in the propagation of GWs. With a uni…
We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We also discuss its generalisation to a theory of quantum gravity. Our analysis suggests that only the strong equivalence principle can be considered fundamental enough to be generalised to a quantum gravity context, since all other flavors of equivalence principle hold only approximately already at the classical level.
We consider possible violations of the equivalence principle through the exchange of a light `dilaton-like' scalar field. Using recent work on the quark-mass dependence of nuclear binding, we find that the dilaton-quark-mass coupling induces significant equivalence-principle-violating effects varying like the inverse cubic root of the atomic number - A^{-1/3}. We provide a general parameterization of the scalar couplings, but argue that two parameters are likely to dominate the equivalence-principle phenomenology. We indicate the implications of this framework for comparing the sensitivities o…
We discuss the current bounds on the Equivalence Principle, in particular from structure formation and, reexamine in this context, the recent claim on the evidence of the interaction between dark matter and dark energy in the Abell Cluster A586 and the ensued violation of the Equivalence Principle.
Klein-Gordon gravity, 1920s-30s particle physics, and 1890s Neumann-Seeliger modified gravity suggest a "graviton mass term" *algebraic* in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is invariant under the Poincaré group but not the 15-parameter conformal group. It thus exhibits the whole Minkowski space-time structure, indirectly for volumes. Massive scalar gravity is plausible as a field theory, but violates Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide: matter sees a conformally flat metric d…
The work argues the principle of equivalence to be a theorem and not a principle (in a sense of an axiom). It contains a detailed analysis of the concepts of normal and inertial frame of reference. The equivalence principle is proved to be valid (at every point and along every path) in any gravitational theory based on linear connections. Possible generalizations of the equivalence principle are pointed out.
By using the equivalence between metric and Palatini f(R) (or "modified") gravities with omega=0, -3/2 Brans-Dicke theories, it is shown that the Ehlers-Geren-Sachs theorem of general relativity is extended to modified gravity. In the case of metric f(R) gravity previously studied, this agrees with previous literature.
We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativist…
We find that the Abell Cluster A586 exhibits evidence of the interaction between dark matter and dark energy and argue that this interaction suggests evidence of violation of the Equivalence Principle. This violation is found in the context of two different models of dark energy-dark matter interaction.
The equivalence principle is the conceptual basis for general relativity. In contrast Mach's principle, although said to have been influential on Einstein in his formulation of general relativity, has not been shown to be central to the structure of general relativity. In this essay we suggest that the quantum effects of Hawking and Unruh radiation are a manifestation of a {\it thermal} Mach's principle, where the local thermodynamic properties of the system are determined by the non-local structure of the quantum fields which determine the vacuum of a given spacetime. By comparing Hawking and…
An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the fiel…
We analyze possible violations of the Equivalence Principle in scalar-tensor gravity at finite temperature $T.$ Before we present an approach where the Equivalence Principle violation is achieved within the framework of Quantum Field Theory. After, we rely on an alternative approach first proposed by Gasperini, which leads to the same outcome obtained in the framework of Quantum Field Theory (one-loop corrections) at finite $T$. Finally, we exhibit the application of the above formalism both to a generic diagonal metric, cast in spherical coordinates, and to the Brans-Dicke theory. In the last…
The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization of course. The scalar equivalence principle is violated only for objects for which ei…
We present a direct confirmation of the validity of the equivalence principle for unstructured test bodies in scalar tensor gravity. Our analysis is complementary to previous approaches and valid for a large class of scalar-tensor theories of gravitation. A covariant approach is used to derive the equations of motion in a systematic way and allows for the experimental test of scalar-tensor theories by means of extended test bodies.
The Einstein equivalence principle is based on the equality of gravitational mass and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities. Here, we will provide a simple protocol based on creating large spatial superposition states in a laboratory to test the fully qua…
We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.
We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.
The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and i…
Equivalence principles played a central role in the development of general relativity. Furthermore, they have provided operative procedures for testing the validity of general relativity, or constraining competing theories of gravitation. This has led to a flourishing of different, and inequivalent, formulations of these principles, with the undesired consequence that often the same name, "equivalence principle", is associated with statements having a quite different physical meaning. In this paper we provide a precise formulation of the several incarnations of the equivalence principle, clari…
Point particles fall freely along geodesics; strings do not. In string theory all probes of spacetime structure, including photons, are extended objects and therefore always subject to tidal forces. We illustrate how string theory modifies the behavior of light in weak gravitational fields and limits the applicability of the principle of equivalence. This gives in principle a window on the short-distance structure of geometry in quantum gravity where one can see in a model-independent way how some of its predictions differ from those of classical gravity. We compare this with the lessons of hi…
The Einstein-Hilbert action of general theory of relativity (GR) is the integral of the scalar curvature $R$. It is a theory that is drawn from the Equivalence principle, and has predictions that come out as a consequence of the principle, in observables. Testing such observables to find confirmation/infirmation of the principle have formed a significant chunk of tests of GR itself. It is expected that quantum corrections to GR may add additional higher powers of $R$ to the Einstein-Hilbert action, or more generally, modifying the action into a generic class of functions of the Ricci scalar. T…
The Einstein's equivalence principle is formulated in terms of the accuracy of measurements and its dependence of the size of the area of measurement. It is shown that different refinements of the statement 'the spacetime is locally flat' lead to different conculsions about the spacetime geometry.
We consider possible tests of the Einstein Equivalence Principle for quantum-mechanical vacuum energies by evaluating the Lamb shift transition in a class of non-metric theories of gravity described by the \tmu formalism. We compute to lowest order the associated red shift and time dilation parameters, and discuss how (high-precision) measurements of these quantities could provide new information on the validity of the equivalence principle.
Long before the general theory of relativity was finally formulated in 1916, arguments based entirely on Einstein's equivalence principle predicted the well known phenomenon of the gravitational red shift. Precisely the same arguments are widely being used today to derive the same phenomenon. Accordingly, it is often claimed that the observed gravitational red shift is a verification of the equivalence principle rather than a verification of the full theory of general relativity. Here we show that, contrary to these claims, the arguments based on the equivalence principle are false and that \i…
Bekenstein has shown that violation of Weak Equivalence Principle is strongly supressed in his model of charge variation. In this paper, it is shown that nuclear magnetic energy is large enough to produce observable effects in Eotvos experiments.
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.
String theory suggests the existence of gravitational-strength scalar fields ("dilaton" and "moduli") whose couplings to matter violate the equivalence principle. This provides a new motivation for high-precision clock experiments, as well as a generic theoretical framework for analyzing their significance.
On incorporating special relativity theory into an extended equivalence principle, post-Newtonian gravitational phenomena beyond that originally predicted by Einstein are predicted (required), such as geodetic and gravitomagnetic precessions of local inertial frames, and precession of Mercury's orbital perihelion. Why were not these phenomena predicted in the years 1907-1911? The unique 1/c^2 order dynamical equations for clock rates and motion of both bodies and light in local gravity are derived which guarantee fulfillment of the special relativistic equivalence principle.
The gedanken-experiment of Einstein's lift is analyzed in order of determining whether the free-falling observer inside the lift can detect the eventual topological non-triviality of space-time
A study of kinematics of a 2-body system is used to show that the Mach principle, previously rejected by general relativity, can still serve as an alternative to the concept of absolute space, if one takes into account that the background of distant stars (galaxies) determines {\it both} the inertial and the gravitational masses of a body.
String theory suggests the existence of gravitational-strength scalar fields (``dilaton'' and ``moduli'') whose couplings to matter violate the equivalence principle. This provides a new motivation for high-precision clock experiments, as well as a generic theoretical framework for analyzing their significance.
Nordstrom's theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a 'Nordstrom-Katz' superpotential.
A seemingly obvious extension of the weak equivalence principle, in which all matter must respond to Post-Newtonian gravitational fields, such as Lense-Thirring and radiation fields, in a composition-independent way, is considered in light of the Kramers-Kronig dispersion relations for the linear response of any material medium to these fields. It is argued that known observational facts lead to violations of this extended form of the equivalence principle. (PACS numbers: 04.80.Cc, 04.80.Nn, 03.65.Ud, 67.40.Bz)
