Late-time behavior of stellar collapse and explosions. I. Linearized perturbations

Abstract

We study the power-law tails in the evolution of massless fields around a fixed background geometry corresponding to a black hole. We give analytical arguments for their existence at scri+, at the future horizon, and at future timelike infinity. We confirm their existence with numerical integrations of the curved spacetime wave equation on the background of a Schwarzschild and a Reissner-Nordstrom black hole. These results are relevant to studies of mass inflation and the instability of Cauchy horizons. The analytic arguments also suggest the behavior of the full nonlinear dynamics, which we study numerically in a companion paper. PACS number(s): 04.30.Db, 04.25.Dm, 04.40.Dg

Stability and thermodynamics of brane black holes

“…In order to analyze quasinormal mode phase and latetime behavior of the perturbations, we apply a numerical characteristic integration scheme based in the light-cone variables u = t − r ⋆ and v = t + r ⋆ used, for example, in [26,27,28]. In addition, to check some results obtained in "time-dependent" approach we employ the semi-analytical WKB-type method developed in [29] and improved in [30].…”

“…For simplicity we model the matter field by a scalar field Φ confined on the brane obeying the massless (m = 0) version of the Klein-Gordon equation (26). We expect that massive fields (m = 0) should show rather different tail behavior, but such cases will not be treated in the present paper.…”

Slowly decaying tails of massive scalar fields in spherically symmetric spacetimes

“…where M , Q and Q are some parameters characterizing the background field in more details in addition to the gravitational mass M. Expanding (13) in the same manner and neglecting 3 ] and higher, we obtain the approximated form…”

“…Gundlach et.al. [3] showed that power-law tails also characterize the late-time evolution of radiative fields at future null infinity, while the decay rate is different from that of timelike infinity. Furthermore, they showed that power-law tails are a genuine feature of gravitational collapse [4]: Late-time tails develop even when no horizon is present in the background, which means that power-law tails should be present in perturbations of stars, or after the implosion and subsequent explosion of a massless field which does not result in black hole formation.…”

Decay of massive scalar hair in the background of a black hole with a global monopole

“…For instance, It has been shown in Ref. [6] that an oscillatory power-law tail of the form ∼ t −l− 3 2 sin(µt) for massive scalar fields develops at the intermediate late-time characterized by µM 1 in Reissner-Nordström background. Here µ is the mass of the scalar field and M is that of the black hole.…”