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As numerical calculations of inspiralling neutron-star binaries reach values of accuracy that are comparable with those of binary black holes, a fine budgeting of the various sources of error becomes increasingly important. Among such…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
{This paper is a comparison of the Minkowski, Einstein and Einstein dual theories of relativity. The dual is based on an identity relating the observer time and the proper time as a contact transformation on configuration space, which…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a…
We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A…
We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in…
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
The characteristic Cauchy problem of the Einstein field equations has been recently addressed from a completely abstract viewpoint by means of hypersurface data and, in particular, via the notion of double null data. However, this…
A straightforward method to compute Hamilton's density for theories that are linear in the spacetime curvature is provided. It is shown that the lapse function and shift vector still give rise to primary constraints, while the induced…
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum…
We highlight a non-canonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in non-isotropic systems, including internal gravity waves on a vertical plane, inertial and Rossby waves.…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or…