Related papers: Scaling Laws in Gravitational Collapse
This article reviews classical and quantum aspects of critical phenomena in gravitational collapse. We pay special attention to the origin of the scaling law for black hole mass, and to phase transitions in which black hole formation turns…
Scaling laws for critical phenomena take pivotal status in almost all branches of physics. However, as scaling laws are commonly guaranteed by the renormalization group theory, systems that violate them have rarely been found. In this…
We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a…
Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical scaling near the jamming transition point,…
Critical gravitational collapse and self similarity are used to probe the mass distribution of subsolar objects. We demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that…
The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
General relativity as well as Newtonian gravity admits self-similar solutions due to its scale-invariance. This is a review on these self-similar solutions and their relevance to gravitational collapse. In particular, our attention is…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
We present a discussion on some physical aspects of gravitational collapse which is based on a list of questions related to relevant issues in the study of that phenomenon. Providing answers to those questions we bring out the role played…
Gravitational collapse of a class of spherically symmetric stars are investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with…
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…
We investigate the threshold of gravitational collapse with angular momentum, under the assumption that the critical solution is spherical and self-similar and has two growing modes, namely one spherical mode and one axial dipole mode…
We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these…
In this paper, we examine the scaling laws in gravitational system from the perspective of free energy landscape and the scaling hypothesis. It has been found that for some special black holes, their critical exponents $(0,1,2,3)$ are…
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these…
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…