Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/0511163

Cauchy-perturbative matching revisited: tests in spherical symmetry

Burkhard Zink·Enrique Pazos·Peter Diener·Manuel Tiglio
View original source ↗Read source document ↗Export metadata ↓

Abstract

During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan to analyze CPM in the light of these new results. Here we start by testing high-order summation-by-parts operators, penalty boundaries and contraint-preserving boundary conditions applied to CPM in a setting that is simple enough to study all the ingredients in great detail: Einstein's equations in spherical symmetry, describing a black hole coupled to a massless scalar field. We show that with the techniques described above, the errors introduced by Cauchy-perturbative matching are very small, and that very long term and accurate CPM evolutions can be achieved. Our tests include the accretion and ring-down phase of a Schwarzschild black hole with CPM, where we find that the discrete evolution introduces, with a low spatial resolution of Δr = M/10, an error of 0.3% after an evolution time of 1,000,000 M. For a black hole of solar mass, this corresponds to approximately 5 s, and is therefore at the lower end of timescales discussed e.g. in the collapsar model of gamma-ray burst engines. (abridged)

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Burkhard Zink, Enrique Pazos, Peter Diener, Manuel Tiglio. 2005-11-30. Cauchy-perturbative matching revisited: tests in spherical symmetry. https://doi.org/10.1103/physrevd.73.084011

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Massive quantum divergence on the Cauchy horizon of a black hole

We investigate a quantum {\it massive} scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization (in both states) generically {\it diverges} on the Cauchy horizon, in stark contrast to what happens for massless fields; also, the angular components of the quantum stress-energy tensor generically {\it diverge} on the Cauchy horizon and, in at least one of the two states, they do so more strongly than for massless fields. Furthermore, we calculate the energy fluxes in Eddington-Finkelstein coordinates $\{u,v\}$. We show that these fluxes in both states on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates $\{U,V\}$ the ingoing flux diverges like $V^{-2}$ on the Cauchy horizon (where $V=0$). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.

gr-qc↗
arXiv2026

Scattering of massless scalar waves by higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics

We study the scattering of planar massless scalar waves by the family of higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics, which unifies the Bardeen and Hayward models in any dimension. The scalar field is a neutral test field that propagates in the bulk, and in the geometric-optics limit, its rays are the null geodesics of the spacetime, so that the unstable circular null geodesics of the background geometry control the scattering. We combine the classical scattering of null geodesics, the glory approximation, which we generalize to $D$ dimensions, and the partial-wave analysis in $D=5,6,7$. We show that at a fixed frequency, the wave cross section diverges in the forward direction as $θ^{-4}$ in any dimension, with a coefficient fixed by the mass, while the steeper classical law $θ^{-(D-2)^{2}/(D-3)}$ appears only at larger angles and higher frequencies. The charge parameter decreases the critical and the glory impact parameters and widens the glory fringes, and in higher dimensions, the glory pattern has fewer and wider fringes and a weaker backward intensity. For the matched configurations studied here, backward intensity and low-frequency absorption provide the clearest differences, while the intermediate-to-high-frequency spectra are close.

gr-qc↗
arXiv2026

Self-interacting $p$-forms and the shear-free anisotropic cosmological model

The cosmological principle may require more than observations demand: what is needed is isotropic expansion without vorticity. Extended Friedmann-Lemaitre-Robertson-Walker (eFLRW) cosmologies realise this with a non-vanishing anisotropic spatial curvature that is balanced by an anisotropic stress while the shear vanishes. Thorsrud and others investigated such scenarios for free differential $p$-forms. Here we extend the analysis to non-Abelian $p$-forms ($p=0,\dots,4$) with self interactions. The balance requires the anisotropic stress to decay as $a^{-2}$, $a$ being the cosmological scale factor, which we combine with the gauge-field continuity equation. The general results indicate that, in the presence of a potential, fine-tuning of the same is needed in order to balance the curvature. Notably, this is not the case for a $3$-form field $\underline{H}^a$ with a potential term $V(\underline{H}^2)=A+B\,\underline{H}^2$, where $A$ and $B$ are constants: in Bianchi class A, an uncharged 3-form balances the curvature with this potential without any tuning, and a charged one does so for a suitably chosen connection. This is the only candidate we have found where the potential does not require tuning. It is also an interesting candidate as it can be interpreted as a cosmological constant in combination with a dark-matter sector mimicking curvature.

gr-qc↗