Related papers: Quantum Einstein's Equations and Constraints Algeb…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
The connection between gravity and thermodynamics is explored. Examining a perfect fluid in gravitational equilibrium we find that the entropy is extremal only if Einstein's equations are satisfied. Conversely, one can derive part of…
In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and…
It is well known that Einstein gravity is non-renormalizable; however this does not preclude the existence of a quantum form.
We study the algebra of constraints of quantum gravity in the loop representation based on Ashtekar's new variables. We show by direct computation that the quantum commutator algebra reproduces the classical Poisson bracket one, in the…
The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of…
Contrary to common belief, (electro)vacuum Brans-Dicke gravity does not reduce to general relativity for large Brans-Dicke coupling $\omega$, a problem which has never been fully solved. Two new approaches, independent from each other, shed…
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling…
The bare bones of a theory of quantum gravity are exposed. It may have the potential to solve the cosmological constant problem. Less certain is its behavior in the Newtonian limit.
One of the greatest challenges facing theoretical physics lies in reconciling Einstein's classical theory of gravity - general relativity - with quantum field theory. Although both theories have been experimentally supported in their…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
We give a summary of the theory of (weak) quantum vertex $\C((t))$-algebras and the association of quantum affine algebras with (weak) quantum vertex $\C((t))$-algebras.
We discuss the derivation of the so-called semi-classical equations for both mini-superspace and dilaton gravity. We find that there is no systematic derivation of a semi-classical theory in which quantum mechanics is formulated in a…
In this study, we investigate the influences of fermionic $q$-deformation on the Einstein equations by taking into account of Verlinde's entropic gravity approach and Strominger's proposal on quantum black holes. According to Verlinde's…
We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and prove existence of solutions in both the near-CMC and…
Up to now, Einstein's general theory of relativity has passed all experimental tests. But yet we know that it is not a fundamental theory and that it is incompatible with quantum theory. While several extended and improved gravitational…
We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the…