相关论文: Choptuik scaling and the scale invariance of Einst…

A numerical simulation is performed of the gravitational collapse of a spherically symmetric scalar field. The algorithm uses the null initial value formulation of the Einstein-scalar equations, but does {\it not} use adaptive mesh…

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik…

We discuss recently introduced scale-free Einstein equations, where the information from their trace part is lost. These equations are classically equivalent to General Relativity, yet the Newton constant becomes a constant of integration…

The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…

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…

The scaling of the spatio-temporal response of coarsening systems is studied through simulations of the 2D and 3D Ising model with Glauber dynamics. The scaling functions agree with the prediction of local scale invariance, extending…

In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in…

We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in…

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…

At the level of the Planck scale, the spacetime metric has to be considered a quantum variable. Conformal quantum fluctuations of the metric tensor are studied here. They lead to an extra term in the Einstein equations which can be…

As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…

The dynamical scaling of ageing ferromagnetic systems can be generalized to a local scale invariance. This yields a prediction for the causal two-time response function, which has been numerically confirmed in the Glauber-Ising model…

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…

Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…

The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic…

This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar…

We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…

Recently, the variation of the Planck mass in the General Relativistic Einstein-Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing Standard Model vacuum energy from freely gravitating and…

We show that promoting the trace part of the Einstein equations to a trivial identity results in the Newton constant being an integration constant. Thus, in this formulation the Newton constant is a global dynamical degree of freedom which…

We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…