Universality of curvature invariants in critical vacuum gravitational collapse
Tomáš Ledvinka, Anton Khirnov
备注：
5 pages, 3 figures. This updated version matches the published letter. The changes include the values of echo scaling ratios, simplified initial data description and a more readable Fig. 2
We report on a numerical study of gravitational waves undergoing gravitational collapse due to their self-interaction. We consider several families of asymptotically flat initial data which, similar to the well known Choptuik's discovery, can be fine-tuned between dispersal into empty space and collapse into a black hole. We find that near-critical spacetimes exhibit behavior similar to the collapse of scalar field: For different families of initial data, we observe universal "echoes" in the form of irregularly repeating approximate scaled copies of the same piece of spacetime.
We study the spherical collapse of an over-density of a barotropic fluid with linear equation of state in a cosmological background. Fully relativistic simulations are performed by using the Baumgarte-Shibata-Shapiro-Nakamura formalism jointly with the Valencia formulation of the hydrodynamics. This permits us to test the universality of the critical collapse with respect to the matter type by considering the constant equation of state parameter $ω$ as a control parameter. We exhibit, for a fixed radial profile of the energy-density contrast, the existence of a critical value $ω^*$ for the equ…
When does a sphere fall like a point particle? Quadrupole universality and Weyl-driven hexadecapole deviations in vacuum general relativity
Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas（坎皮纳斯州立大学格莱布·瓦塔金物理研究所）；Centro de Ciências Naturais e Humanas, Universidade Federal do ABC（ABC联邦大学自然与人文科学中心）
We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling $ρ_{\rm max}\sim (η_*-η)^{-2γ}$ of the maximum density in the time evolution of near-subcritical data with $γ\simeq 0.145$, where $η$ is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $Δ\simeq 0.55$. The critical solution is approximately the same for two families of initial data, providing some evidence of univ…
The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of $\hbar$, it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in- and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel …
The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. It is a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previ…
The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a wide variety of initial conditions. In particular, the density contrast of the collapsing domain at the turnaround is shown to be significantly smaller than the value provided by Eulerian perturbative (homogeneous and spherical) model. Combined curvature and kinematical backreaction are shown to be of the order of the energy density. Possible improvements of …
We develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri, Garfinkle & Yau 2019/20), the numerical grid remains fixed during the evolution and no points need to be removed or added. Increasing coordinate refinement of the central region as the field collapses is achieved solely through the choice of spatial gauge and particularly its boundary condition. We apply this method to study critical collapse of a massless scalar field in spherical symmetry using maximal sl…
Near universality of nonlinear transverse and radial velocity responses in spherical collapse with arbitrary radial profiles
Universidade Federal de Ouro Preto（欧罗普雷托联邦大学）；INAF – Osservatorio Astronomico di Trieste（意大利国家天体物理研究所的里雅斯特天文台）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
