Related papers: First order hyperbolic formalism for Numerical Rel…

A canonical analysis of the Einstein-Hilbert action S_d (d>2) is considered, using the first order form with the metric and affine connection as independent fields. We adopt a conservative approach to using the Dirac constraint formalism;…

We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate. We prove the local exact one-sided boundary null controllability of…

We will analyze the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We will be able to find a set of involutive, as well as a set of non-involutive constraints. Using…

We consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the "flux" is defined as a flux field of n-forms depending on a parameter (the unknown…

We show that, given an arbitrary shift, the lapse $N$ can be chosen so that the extrinsic curvature $K$ of the space slices with metric $\overline g$ in arbitrary coordinates of a solution of Einstein's equations satisfies a quasi-linear…

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised…

This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…

We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…

We consider the non-relativistic limit of gravity in four dimensions in the first order formalism. First, we revisit the case of the Einstein-Hilbert action and formally discuss some geometrical configurations in vacuum and in the presence…

A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions…

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the…

Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static…

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…

The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity, using its first order form in any dimension higher than two, is analyzed. This Hamiltonian formulation allows to explicitly show where peculiarities of three dimensional case…

In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium…

This paper aims to determine the initial conditions for quasi-linear hyperbolic equations that include nonlocal elements. We suggest a method where we approximate the solution of the hyperbolic equation by truncating its Fourier series in…

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…