Related papers: A Local Resolution of the Problem of Time. IX. Spa…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
We now set up Constraint Closure in a manner consistent with Temporal and Configurational Relationalism. This requires modifying the Dirac Algorithm - which addresses the Constraint Closure Problem facet of the Problem of Time piecemeal -…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e. locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as…
Constraints on the Covariant Canonical Gauge Gravity (CCGG) theory from low-redshift cosmology are studied. The formulation extends Einstein's theory of General Relativity (GR) by a quadratic Riemann-Cartan term in the Lagrangian,…
We investigate the f(R) theory of gravity with broken diffeomorphism due to the change of the coefficient in front of the total divergence term in the (3+1)-decomposition of the scalar curvature. We perform the canonical analysis of this…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric…
We continue the study of topological nonrelativistic quantum gravity associated with a family of Ricci flow equations on Riemannian manifolds. This topological gravity is of the cohomological type, and it exhibits an ${\cal N}=2$ extended…
Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants…
General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial…
We present a comprehensive discussion of gravitational charges and radiation in four-dimensional asymptotically locally de Sitter (AldS) spacetimes. Such spacetimes have compact spatial sections and possess spacelike past and future…
In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup…
Diffeomorphism invariance breaking has been investigated in the literature in several contexts, including emergent General Relativity (GR). If GR emerges from an underlying theory without diffeomorphism invariance, there may be small…
The Lie claw digraph controls Background Independence and thus the Problem of Time and indeed the Fundamental Nature of Physical Law. This has been established in the realms of Flat and Differential Geometry with varying amounts of extra…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the…
Temporal Relationalism (TR) is that there is no time for the universe as a whole at the primary level. Time emerges rather at a secondary level; one compelling idea for this is Mach's `time is to be abstracted from change'. TR leads to, and…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling…