Hamiltonian formalism for nonlocal gravity models

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

Dark effects in $$\tilde{f}(R,P)$$ gravity

In the present paper a new cosmological model is proposed by extending the Einstein–Hilbert Lagrangian with a generic functional $$\tilde{f}(R,P)$$ f ~ ( R , P ) , which depends on the scalar curvature R and a term P which encodes a possible influence from specific cubic contractions of the Riemann tensor. After proposing the corresponding action, the associated modified Friedmann relations are deduced, in the case where the generic functional has the following decomposition, $$\tilde{f}(R,P)=f(R)+g(P)$$ f ~ ( R , P ) = f ( R ) + g ( P ) . The present study takes into account the power-law and the exponential decomposition for the specific form of the corresponding generic functional. For the analytical approach the specific method of dynamical system analysis is employed, revealing the fundamental properties of the phase space structure, discussing the dynamical consequences for the cosmological solutions obtained. It is revealed that the cosmological solutions associated to the critical points can explain various dynamical eras, with a high sensitivity to the values of the corresponding parameters, encoding different effects due to the geometrical nature of the specific couplings.

Hidden relations of central charges and OPEs in holographic CFT

It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓeff∂a/∂ℓeff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Elements of the Metric–Affine gravity I: Aspects of F(R) theories reductions and the topologically massive gravity

Some classical aspects of Metric–Affine Gravity are reviewed in the context of the [Formula: see text] type models (polynomials of degree [Formula: see text] in the Riemann tensor) and the topologically massive gravity. At the nonperturbative level, we explore the consistency of the field equations when the [Formula: see text] models are reduced to a Riemann–Christoffel (RCh) space–time, either via a Riemann–Cartan (RC) space or via an Einstein–Weyl (EW) space. It is well known for the case [Formula: see text] that any path or reduction “classes” via RC or EW leads to the same field equations with the exception of the [Formula: see text] theories for [Formula: see text]. We verify that this discrepancy can be solved by imposing nonmetricity and torsion constraints. In particular, we explore the case [Formula: see text] for the interest in expected physical solutions as those of conformally flat class. On the other hand, the symmetries of the topologically massive gravity are reviewed, as the physical content in RC and EW scenarios. The appearance of a nonlinearly modified selfdual model in RC and existence of many nonunitary degrees of freedom in EW with the suggestion of a modified model for a massive gravity which cure the unphysical propagations shall be discussed.

On conformally reducible pseudo-Riemannian spaces

The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.

Energy and angular momentum in D-dimensional Kerr-Ads black holes — New formulation

Recently, it was shown that the conserved charges of asymptotically anti-de Sitter spacetimes can be written in an explicitly gauge-invariant way in terms of the linearized Riemann tensor and the Killing vectors. Here, we employ this construction to compute the mass and angular momenta of the [Formula: see text]-dimensional Kerr-AdS black holes, which is one of the most remarkable Einstein metrics generalizing the four-dimensional rotating black hole.

Inductive Rectilinear Frame Dragging and Local Coupling to the Gravitational Field of the Universe

There is a drag force on objects moving in the background cosmological metric, known from galaxy cluster dynamics. The force is quite small over laboratory timescales, yet it applies in principle to all moving bodies in the universe. The drag force can be understood as inductive rectilinear frame dragging because it also exists in the rest frame of a moving object, and it arises in that frame from the off-diagonal components induced in the boosted-frame metric. Unlike the Kerr metric or other typical frame-dragging geometries, cosmological inductive dragging occurs at uniform velocity, along the direction of motion, and dissipates energy. Proposed gravito-magnetic invariants formed from contractions of the Riemann tensor do not capture inductive dragging effects, and this might be the first identification of inductive rectilinear dragging. The existence of this drag force proves it is possible for matter in motion through a finite region to exchange momentum and energy with the gravitational field of the universe. The cosmological metric can in principle be determined through this force from local measurements on moving bodies, at resolutions similar to that of the Pound–Rebka experiment.

PSEUDO-RIEMANNIAN SPACES WITH A SPECIAL RIEMANN TENSOR

The paper considers pseudo-Riemannian spaces, the Riemann tensor of which has a special structure. The structure of the Riemann tensor is given as a combination of special symmetric and obliquely symmetric tensors. Tensors are selected so that the results can be applied in the theory of geodetic mappings, the theory of holomorphic-projective mappings of Kähler spaces, as well as other problems arising in differential geometry and its application in general relativity, mechanics and other fields. Through the internal objects of pseudo-Riemannian space, others are determined, which are studied depending on what problems are solved in the study of pseudo-Riemannian spaces. By imposing algebraic or differential constraints on internal objects, we obtain special spaces. In particular, if constraints are imposed on the metric we will have equidistant spaces. If on the Ricci tensor, we obtain spaces that allow φ (Ric)-vector fields, and if on the Einstein tensor, we have almost Einstein spaces. The paper studies pseudo-Riemannian spaces with a special structure of the curvature tensor, which were introduced into consideration in I. Mulin paper. Note that in his work these spaces were studied only with the requirement of positive definiteness of the metric. The proposed approach to the specialization of pseudo-Riemannian spaces is interesting by combining algebraic requirements for the Riemann tensor with differential requirements for its components. In this paper, the research is conducted in tensor form, without restrictions on the sign of the metric. Depending on the structure of the Riemann tensor, there are three special types of pseudo-Riemannian spaces. The properties which, if necessary, satisfy the Richie tensors of pseudoriman space and the tensors which determine the structure of the curvature tensor are studied. In all cases, it is proved that special tensors satisfy the commutation conditions together with the Ricci tensor. The importance and usefulness of such conditions for the study of pseudo-Riemannian spaces is widely known. Obviously, the results can be extended to Einstein tensors. Proven theorems allow us to effectively investigate spaces with constraints on the Ricci tensor.

Spacetimes with continuous linear isotropies II: boosts

Conditions are found which ensure that local boost invariance (LBI), invariance under a linear boost isotropy, implies local boost symmetry (LBS), i.e. the existence of a local group of motions such that for every point P in a neighbourhood there is a boost leaving P fixed. It is shown that for Petrov type D spacetimes this requires LBI of the Riemann tensor and its first derivative. That is also true for most conformally flat spacetimes, but those with Ricci tensors of Segre type [1(11,1)] may require LBI of the first three derivatives of curvature to ensure LBS.