Data Lake

Documentations:

We recommend starting with this manual (ver. 2021-12-11), which describes the naming conventions used throughout the BHPC datasets below. 

Post-Newtonian results:

!! INFORMATION !! (Update: 2025-09-01)  We have corrected a few minor errors and typos in the previously released 5PNe10 generic-orbit data. Please use the updated datasets containing '250407' (for fluxes) and '250822' (for Teukolsky amplitudes) in their filenames. We apologize for any inconvenience this may have caused; please note that the results in arXiv:2008.13554 and arXiv:2111.05288 have basically stayed the same. If you have any questions regarding our datasets, please get in touch with bhpc1996_at_gmail.com and we will be happy to help!

Gravitational wave fluxes 

1. Secular evolution of orbital parameters for general bound orbits in Kerr spacetime
   Prog. Theor. Exp. Phys. 2026, 073E04 (2026), arXiv:2603.27941
   6PNe16 (but arbitrary inclination) generic fluxes in Kerr (last updated on April 8, 2026): Maple data, Mathematica data (coming soon!)

2. Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
   Phys. Rev. D 102, 064005 (2020), arXiv:2008.13554
   5PNe10 (but arbitrary inclination) generic fluxes in Kerr (last updated on April 7, 2025): Maple data, Mathematica data

3. Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
   Prog. Theor. Exp. Phys. 2015, 073E03 (2015) , arXiv:1505.01600
   4PNe6 (but arbitrary inclination) generic fluxes in Kerr (last updated on August 21, 2020): Maple data, Mathematica data

4. Gravitational waves from a particle in circular orbits around a rotating black hole to the 11th post-Newtonian order
   Prog. Theor. Exp. Phys. 2015, Issue 3, 033E01 (2015), arXiv:1412.5689
   11PN equatorial-circular fluxes in Kerr (last updated on March 11, 2015): Maple data, Mathematica data

5. Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order
   Prog.Theor.Phys.128, 971-992 (2012), arXiv:1211.5535
   22PN circular fluxes in Schwarzschild (last updated on November 19, 2012): Maple data, Mathematica data

Teukolsky data (the Spheroidal harmonics, mode amplitudes etc.)

NOTE: For circular and equatorial orbits, the asymptotic mode amplitude "Zlm"  can also be reconstructed from  `rho[l, m]' and `delta[l, m]' of (so named) PN factorized multipolar waveforms. These are presented up to 22PN order (Schwarzschild) and 11PN order (Kerr) in the Maple/Mathematica flux files above.  Please refer to the README file therein for details, sa well as Sec.4.2.1. and 4.2.2. of Fujita's 11PN paper [arXiv:1412.5689] for BHPC convention. 

1.  Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
   Phys. Rev. Lett 128 (2021) 23, 231101, arXiv:2111.05288
   (a omega)^3  Spheroidal harmonics (s = -2), and 5PNe10 (but arbitrary inclination) generic mode amplitudes in Kerr (last updated on September 1,  2025): Maple data, Mathematica data (18MB).

Taylor Templates for adiabatic inspirals

1. Post-Newtonian templates for phase evolution of spherical extreme mass ratio inspirals
   Phys.Rev.D 111 (2025) 6, 064043, arXiv:2411.09147
   12PN (but arbitrary inclination) spherical fluxes in Kerr, TaylorT families and TaylorF2 templates for Kerr spherical inspirals (last updated on November 15, 2024): Maple data

Numerical results: 

Gravitational wave fluxes

1.  Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
   Phys. Rev. D 102, 064005 (2020), arXiv:2008.13554
   Equatorial fluxes in Kerr (last updated on August 31, 2020): Numerical data  (17MB)

Teukolsky data (the Spheroidal harmonics, mode amplitudes etc.)

Coming soon! [If you are interested in the generic data (fluxes and amplitudes), please contact us at  bhpc1996_at_gmail.com, and we will be happy to assist you!]

Fitting formulas: 

The averaged rate of change of the orbital angular momentum and Carter constant due to tidal resonances

1. Importance of tidal resonances in extreme-mass-ratio inspirals
   Phys.Rev.D 104, 044056 (2021), arXiv:2104.03422  
   For (n : k : m) = (3 : 0 : -2), (3 : -4 : 2), (3 : 0 : 2) and (3 : -4 : -2) (last updated on July 26, 2021):  Fittings Tidal Resonances.wl (Mathematica)

2. Modeling transient resonances in extreme-mass-ratio inspirals
   Phys.Rev.D 106 (2022) 10, 104001 arXiv:2205.04808  
   For (n : k : m) = (-3 : 1 : 1), (-3 : 2 : 0), (-3 : 3 : -1),  (-4 : 1 : 1), (-4 : 2 : 0) and (-4 : 3 : -1) (last updated on August 14, 2022): Fittings Tidal Resonances-m01.wl (Mathematica)