Related papers: Hypersurface deformations
A phase-space approach to quantum-deformed gravity is developed. Following its reduction to an effective four-dimensional spacetime structure, we utilize it in reanalyzing the cosmic inflationary dynamics and quantum gravity. The…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…
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…
Stabilization, by deformation, of the Poincar\'{e}-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative…
Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly…
We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…
We show the existence of a deformation process of hypersurfaces from a product space $M_1\times R$ into another product space $M_2\times R$ such that the relation of the principal curvatures of the deformed hypersurfaces can be controlled…
Emergent modified gravity presents a new set of generally covariant gravitational theories in which the space-time metric is not directly given by one of the fundamental fields. A metric compatible with the modified dynamics of gravity is…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…
A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation…
We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories.…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…
The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…
What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…
We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike…