Waves propagating in a curved spacetime develop tails. In particular, it is well established that the late-time dynamics of gravitational collapse is dominated by a power-law decaying tail of the form $Mt^{-(2l+3)}$, where $M$ is the black-hole mass. It should be emphasized, however, that in a typical evolution scenario there is a considerable time window in which the signal is no longer dominated by the black-hole quasinormal modes, but the leading order power-law tail has not yet taken over. Higher-order terms may have a considerable contribution to the signal at these intermediate times. It is therefore of interest to analyze these higher-order corrections to the leading-order power-law behavior. We show that the higher-order contamination terms die off at late times as $M^2t^{-4}\ln(t/M)$ for spherical perturbations, and as $M^2t^{-(2l+4)}\ln^2(t/M)$ for non-spherical $(l\neq0)$ perturbations. These results imply that the leading-order power-law tail becomes "pure" (namely, with less than 1% contamination) only at extremely late times of the order of $10^4M$.
Comment on "High-order contamination in the tail of gravitational collapse''
我们面对S的预言。Hod，Phys. Rev. D 60，104053（1999），用数值数据计算黑洞扰动的晚期衰变率。具体来说，我们问两个问题：第一，价格尾部的修正是否如Hod所预测的那样，由对数项主导？第二，如果有对数校正项，它们是否采取Hod论文中预测的特定形式？这两个问题的答案都是“不”。''
We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.
We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an osc…
The collapse scenario of a scalar field along with a perfect fluid distribution is investigated for a conformally flat spacetime. The theorem for the integrability of an anharmonic oscillator has been utilized. For a pure power law potential of the form $ϕ^{n+1}$, it is found that a central singularity is formed which is covered by an apparent horizon for $n>0$ and $n<-3$. Some numerical results have also been presented for a combination of two different powers of $ϕ$ in the potential.
We consider gravitational collapse in the recently proposed 4D limit of Einstein-Gauss-Bonnet gravity. We show that for collapse of a sphere made of homogeneous dust the process is qualitatively similar to the case of pure Einstein's gravity. The singularity forms as the endstate of collapse and it is trapped behind the horizon at all times. However, and differently from Einstein's theory, as a consequence of the Gauss-Bonnet term, the collapsing cloud reaches the singularity with zero velocity, and the time of formation of the singularity is delayed with respect to the pure Einstein case.
We study how the gravitational wave signal from stellar collapse in scalar-tensor gravity varies under the influence of scalar self-interaction. To this end, we extract the gravitational radiation from numerical simulations of stellar collapse for a range of potentials with higher-order terms in addition to the quadratic mass term. Our study includes collapse to neutron stars and black holes and we find the strong inverse-chirp signals obtained for the purely quadratic potential to be exceptionally robust under changes in the potential at higher orders; quartic and sextic terms in the potentia…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck den…
Some dynamical aspects of gravitational collapse are explored in this paper. A time-dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with a perfect fluid consisting of two purely radial fluxes -the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of unintercting collapsing shells. Our results show an…
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院量子联合研究中心和物理系）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）；Department of Physics, University of Tehran（德黑兰大学物理系）
We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner-Nordström solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in th…
We show that the quasinormal spectrum of gravitational perturbations of Schwarzschild - de Sitter black holes contains a new branch of purely imaginary modes. These modes are not algebraically special and we showed that the sum of them form the well-known in the literature exponential asymptotic tail. When the ratio of the event horizon radius to the cosmological horizon vanishes, these quasinormal modes approach modes of empty de Sitter spacetime. Thus, the spectrum consists of the two branches: Schwarzschild branch deformed by the cosmological constant and de Sitter branch deformed by the bl…
We present results from the first generation of multi-dimensional general relativistic neutrino hydrodynamics simulations of core-collapse supernovae. A comparison with models computed using either the purely Newtonian approximation or the "effective gravitational potential" approach reveals appreciable quantitative differences in the heating conditions and the gravitational wave spectra. Our results underscore the important role of general relativity in the supernova problem (which appears to be on par with other important factors such as the dimensionality and the equation of state) both for…
This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass s…
In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in $(n+2)$-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we h…
