Vishveshwara Catalog

Vishveshwara Catalog

Binary black-hole coalescence waveforms from tiered small-mass-ratio black-hole perturbation theory

Release · · binaries · waveforms

Tousif Islam · tousifislam24@gmail.com

The catalog gives a tiered description of the dynamics beyond the leading adiabatic approximation. Each binary is evolved several times at identical parameters, and the runs differ only in which finite-mass-ratio effects are included in the dynamics: horizon absorption, the first-order conservative self-force, the second-order dissipative flux, and the spin of the secondary. Comparing tiers at fixed parameters allows the effect of individual perturbative ingredients to be isolated in a way that is not directly available from a numerical-relativity waveform.

Simulations are performed with gwTeukolsky and gwKerrDynamics (Islam 2026). Nearly every binary is set up at the parameters of a numerical-relativity simulation, so each tier can be compared with it directly.

Named after C. V. Vishveshwara, whose work established the stability of the Schwarzschild black hole and helped lay the foundations of black-hole quasinormal ringing.

Contents
Mass ratio
Primary spin χ1z
Secondary spin χ2z
Orbitsquasicircular, aligned or precessing; eccentric and generic in the demonstration set
Modesℓ ≤ 9 aligned; ℓ ≤ 3, all m, precessing
NR counterparts
FamilyBinaries Waveforms
The radiation from TEUK:BBH:00004 (q = 15, χ1 = 0.5, tier 0PA-H-C-F1): r h+ on the orbital plane out to 150 M at retarded time, summed over all modes with ℓ ≤ 9, with the (2,2) strain on the right. The near zone is faded out. We thank Mark Ho-Yeuk Cheung for part of the idea behind this animation.

Coverage

Every binary in the catalog, coloured by family as in the tables, with marker area counting the physics tiers held. Choose a projection; click a family in the legend to hide it, or a point to open that binary in the table below. Points outside the current table filters are drawn faint.

Source: vwc_index.json. ι is the tilt of the primary's spin from the orbital angular momentum at the reference time, so cos ι = x0; an aligned primary sits at ±1, and for a precessing binary χ1z = |χ1| cos ι.

Explore

One row per binary; the identifier names the binary, and its physics tiers are alternatives at the same parameters. Select a row for its parameters, tiers and loading code.

· Full index (JSON)

Physics tiers

A tier name states its physical content, and a run is refused if the assembled dynamics disagree with the label it was queued under. Names follow the paper. Columns on the left mark the physics each tier includes; columns on the right count the binaries holding it, by family. Where the secondary spins, every tier carries S, since its spin cannot be switched off while the body has it.

Documentation

Access

The index (parameters, tiers, provenance) is public: data/catalog.json. The waveforms are several gigabytes and are distributed separately; contact the author. They are read through gwModels, once VWC_DATA_ROOT points at the data.

from gwModels.catalogs import vwc

vwc.find(q=15, chi1=0.5)
vwc.tiers("TEUK:BBH:00004")

# one tier; t = 0 at the peak of |h22|
t, h = vwc.waveform("TEUK:BBH:00004", "NRC-C")

# the same binary at two flux contents
for tier in ("0PA", "0PA-H-C-F1"):
    t, h = vwc.waveform("TEUK:BBH:00004", tier)

Conventions

Strain
r h/M in the source frame, spin-weight −2 spherical harmonics
Time
geometric units of M; t = 0 at the peak of |h22|
Modes
ℓ ≤ 9 with the full m = 1…9 band on every aligned run; the precessing survey carries ℓ = 2, 3 with every m from −ℓ to ℓ
Extraction
ψ4 integrated by two-piece fixed-frequency integration, ringdown detrended, record cut at the ψ4 noise floor
Mass unit
total mass M, except 0PA_eps runs, which are in primary mass m1 (a factor 1 + 1/q)
Orbit
quasicircular. The precessing survey is inclined to the primary's equatorial plane, x0 = cos ι, with e = 0; the demonstration set carries e0 up to 0.2 and x0 down to 0.4; every other binary lies in the equatorial plane
Spin
dimensionless; aligned except in the precessing survey, where the primary is tilted from L and χ1z = |χ1| cos(tilt); χ2 = 0 unless a tier models it
Frame
z along the primary's spin. For the precessing survey this is not the NR frame (z along the initial orbital angular momentum): rotate, for example to the co-precessing frame, before comparing

Provenance and versions

Release
Codes
gwTeukolsky (time-domain Teukolsky solver) and gwKerrDynamics (worldlines and fluxes), Islam 2026
Computed on
Identifiers
TEUK:BBH:NNNNN, one per binary, assigned through a registry so a number is never reused. Five digits since 2026-10-11; the earlier four-digit form (TEUK:BBH:0004) names the same binary (TEUK:BBH:00004) and is still accepted by the search and by vwc
Index
data/catalog.json; the page is rebuilt from it on every release, so the two cannot disagree

Limitations

  • Identifiers are provisional until the first numbered release; contact the author before citing one in published work.
  • The precessing survey is computed in the primary's frame, and its primary spin does not precess; compare with NR in a co-precessing frame.
  • 0PA_eps waveforms are in units of the primary mass, the others in the total mass.
  • The numerical-relativity records used for comparison are not redistributed here; they are available from their own catalogs.

Citation

If the catalog supports published work, please cite the paper that presents it and the catalog itself, and contact the author before release.

Islam, T., "The shape of nonlinearity in
  binary-black-hole dynamics", arXiv:XXXX.XXXX.

Islam, T., "Vishveshwara Catalog",
  release 0.1 (2026), TEUK:BBH:NNNNN.
  Generated with gwTeukolsky and gwKerrDynamics.

Tousif Islam · tousifislam24@gmail.com (questions and feedback)

Acknowledgments and references

These simulations are performed with gwTeukolsky and gwKerrDynamics, which are built on work carried out by the black-hole perturbation theory and self-force communities over more than five decades. Almost nothing in the tiers above is new here. The master equation, the Kerr geodesics, the radial and angular solvers, the flux formulae, the first- and second-order self-force, the spinning-secondary dynamics, the transition to plunge, the quasinormal spectrum and the numerical methods that make any of it tractable were all derived, checked and refined by others, often over many years and frequently after false starts that never appear in the published record. What these codes contribute is assembly: putting those results together in one place, in a consistent set of conventions, so that the effect of each term can be turned on and looked at. That is a modest contribution resting on a very large one. The list below is a selection, not a complete bibliography, and it is certainly incomplete in ways that reflect what this implementation happened to need rather than what the field owes. Work that shaped the subject but that these codes did not directly follow is absent. Any errors in what is built on top of this work are ours, not theirs.

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