Related papers: Weighing the curvature invariants
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on…
Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…
We give a family of monotone quantities along smooth solutions to the inverse curvature flows in Euclidean spaces. We also derive a related geometric inequality for closed hypersurfaces with positive k-th mean curvature.
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding…
Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
Within the framework of projective geometry, we investigate kinematics and symmetry in $(\alpha,\beta)$ spacetime-one special types of Finsler spacetime. The projectively flat $(\alpha,\beta)$ spacetime with constant flag curvature is…
Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics…
We derive a Weyl invariant equation for Gravity by gauging the global Weyl invariance of vacuum Einstein equations. The equation is linear in the curvature and a natural generalization of Einstein equations to Weyl geometry. The system has…
It is shown that modified gravity theories with a Lagrangian composed of the three quadratic invariants of the Riemann curvature tensor are not appropriate. The field equations are either incompatible and/or irregular [like f(R)-gravities],…
We look for sufficient conditions such that the scalar curvature, Ricci and Kretchmann scalars be bounded in Hyperextended Scalar Tensor theory for Bianchi models. We find classes of gravitation functions and Brans-Dicke coupling functions…
We unearth spacetime structure of massive vector bosons, gravitinos, and gravitons. While the curvatures associated with these particles carry a definite spin, the underlying potentials cannot be, and should not be, interpreted as single…
We address the group classification problem for gravitational field equations within the context of brane-world cosmology, considering the presence of a bulk scalar field. Our investigation revolves around a five-dimensional spacetime, with…
We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…
Curvature and torsion are the two tensors characterizing a general Riemannian spacetime. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
We revise the extended uncertainty relations for the Rindler and Friedmann spacetimes recently discussed by Dabrowski and Wagner in [9]. We reveal these results to be coordinate dependent expressions of the invariant uncertainty relations…
The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincar\'e noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two…