Paper Citation Record · LEDGER

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability

As of 13 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 1 inbound Pith citation observation for arXiv:2606.27016.

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pith.paper-citation-record.v1
2606.27016 v1

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measured 61 of 61 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

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measured 0 of 1 external citation measurements

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Source: pith, observed 2026-08-12T00:46:03.808740Z

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60 of 60 outbound references displayed

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Outbound references

Observation 423a21ce-466f-4479-983f-f1269b0f4842 · outbound

This paper cites occasionally.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability occasionally

Reference 1

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Observation c73d0224-5efe-4a5f-a283-4c63078f09e3 · outbound

This paper cites Integrating ( A1) from xp − ǫ to xp + ǫ and taking the limit ǫ → 0 gives the jump in ∂xu as [u′]p = lim ǫ→ 0 { u′(xp + ǫ) − u′(xp − ǫ) } = s(t).

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Integrating ( A1) from xp − ǫ to xp + ǫ and taking the limit ǫ → 0 gives the jump in ∂xu as [u′]p = lim ǫ→ 0 { u′(xp + ǫ) − u′(xp − ǫ) } = s(t)

Reference 2

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Observation 9f156343-67a1-4e96-94b7-dd6825a62527 · outbound

This paper cites don’t repeat yourself.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability don’t repeat yourself

Reference 3

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Observation b83b216a-e13f-4a82-adae-811b2bb112a8 · outbound

This paper cites I compute these by numerically inverting the tortise-coordinate deﬁni- tion ( 3.2).

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability I compute these by numerically inverting the tortise-coordinate deﬁni- tion ( 3.2)

Reference 4

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Observation 590b3958-8ced-4d0e-90f7-76b40e390e98 · outbound

This paper cites crosses the particle.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability crosses the particle

Reference 5

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Observation 583324a4-a119-49d6-a11b-a1a114a92d5a · outbound

This paper cites (B9) I use 4th order centered ﬁnite diﬀerencing on a uniform-in-r∗ grid to approximate the spatial derivatives in the RHS(vacuum) deﬁnition ( 3.7c) and the M operator.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability (B9) I use 4th order centered ﬁnite diﬀerencing on a uniform-in-r∗ grid to approximate the spatial derivatives in the RHS(vacuum) deﬁnition ( 3.7c) and the M operator

Reference 6

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Observation 2c0bc89e-11ad-4a9f-afff-de9eae361cef · outbound

This paper cites (B10) All the results presented here use the dissipation coeﬃ- cient ǫ = 0.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability (B10) All the results presented here use the dissipation coeﬃ- cient ǫ = 0

Reference 7

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Observation 378c1669-ad46-44ba-b0fb-984caab2f7f8 · outbound

This paper cites adjusted.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability adjusted

Reference 8

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Observation 46a33052-dabe-4b14-a5b1-363ae03a0d46 · outbound

This paper cites 116M instead of P/ 4 ≈ 30.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability 116M instead of P/ 4 ≈ 30

Reference 9

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Observation fbfe73a3-93dd-44a7-b38e-f1a2fe8dde6c · outbound

This paper cites Changing the deﬁnition of λ( occasionally updated ) to be less oscillatory would be useful: 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 |〈– h(ortho), – h(hom)〉| t (M) FIG.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Changing the deﬁnition of λ( occasionally updated ) to be less oscillatory would be useful: 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 |〈– h(ortho), – h(hom)〉| t (M) FIG

Reference 10

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Observation 99840343-34ef-4b25-bb08-c2085a134149 · outbound

This paper cites The scale is the same as that of ﬁgure 9 (which shows the esrc-ortho-P4 evolution).

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability The scale is the same as that of ﬁgure 9 (which shows the esrc-ortho-P4 evolution)

Reference 11

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Observation c8f69a30-eb5d-4aa4-bc8f-d68167e7ed09 · outbound

This paper cites gradual-turnon function.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability gradual-turnon function

Reference 12

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Observation 33b5fcaa-0fbb-450c-8040-d4a8724105d2 · outbound

This paper cites In order for the unstable gauge mode to still be mostly cancelled, λ (ﬁxed) should be fairly close to λ (instantaneous).

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability In order for the unstable gauge mode to still be mostly cancelled, λ (ﬁxed) should be fairly close to λ (instantaneous)

Reference 13

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Observation 87510761-03bb-4246-a0e4-9170c159ed5b · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 14

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Observation 2b17f5e3-4173-4799-9899-deff4e735b03 · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 15

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Observation 7479632a-6d03-445d-abc3-6ccb58534964 · outbound

This paper cites relatively small.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability relatively small

Reference 16

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Observation 66af3960-ea24-4369-ae85-60fa8d8b964f · outbound

This paper cites Parts (a) and (c) show  ¯h(I) (lo) − ¯h(I) (hi)   as a function of time for each evolution and each resolution pair.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Parts (a) and (c) show  ¯h(I) (lo) − ¯h(I) (hi)   as a function of time for each evolution and each resolution pair

Reference 17

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Observation dab6cc05-399c-4e33-8344-5f8442ab2c09 · outbound

This paper cites In each ﬁg- ure, parts (a) and (c) show   ·   as a function of time for each evolution and each resolution.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability In each ﬁg- ure, parts (a) and (c) show   ·   as a function of time for each evolution and each resolution

Reference 18

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Observation 3ce47b8d-e8cd-4e51-aee5-2190b2733f59 · outbound

This paper cites In each ﬁgure, parts (a) and (c) show   ·   as a function of time for each evolution and each resolution.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability In each ﬁgure, parts (a) and (c) show   ·   as a function of time for each evolution and each resolution

Reference 19

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Observation cc3f591f-9001-4590-a133-b37645483191 · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 20

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Observation 71d18eab-7b45-46e9-8f16-c5ada7a6dcd1 · outbound

This paper cites ( bhptoolkit.org), 2026.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability ( bhptoolkit.org), 2026

Reference 21

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Observation 473dbaf4-cd5e-472c-b6d4-8f2c4df6c1e8 · outbound

This paper cites Introduction to 3 + 1 Numerial Rela- tivity.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Introduction to 3 + 1 Numerial Rela- tivity

Reference 22

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This paper cites Self-force eﬀects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Self-force eﬀects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime

Reference 23

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Observation 6f436951-572c-4bed-9019-3d4889d36d71 · outbound

This paper cites Golbourn.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Golbourn

Reference 24

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Observation 5960cfb2-65f1-4d36-8077-e8b5472d74f3 · outbound

This paper cites an unresolved cited work.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 25

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Observation 620a9ab3-d719-4f92-bdcd-58ee826abcd3 · outbound

This paper cites Gravitational self-force on a particle in circular orbit around a Schwarzschild black hole.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Gravitational self-force on a particle in circular orbit around a Schwarzschild black hole

Reference 26

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Observation 36bd80fb-fb84-467c-914a-6dea6f0c8916 · outbound

This paper cites Gravitational self- force correction to the innermost stable circular orbit of a Schwarzschild black hole.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Gravitational self- force correction to the innermost stable circular orbit of a Schwarzschild black hole

Reference 27

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Observation bd603564-fd2f-4868-88a4-b5b655a5815f · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole

Reference 28

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Observation 6d467b92-4e15-4694-a25d-05a82699cd89 · outbound

This paper cites Beyond the geodesic approximation: conservative eﬀects of the gravitational self-force in eccentric orbits around a Schwarzschild blac k hole.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Beyond the geodesic approximation: conservative eﬀects of the gravitational self-force in eccentric orbits around a Schwarzschild blac k hole

Reference 29

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Observation 03e682d9-5fd2-4261-8cdf-00b2c46352fc · outbound

This paper cites Post-Newtonian theory for gravitational waves.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Post-Newtonian theory for gravitational waves

Reference 30

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This paper cites Elements of Numerical Relativity: From Einstein ’s Equations to Black Hole Simulations.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Elements of Numerical Relativity: From Einstein ’s Equations to Black Hole Simulations

Reference 31

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Observation e8ed2e65-8f70-4dc0-a52d-bfbb5b3cc235 · outbound

This paper cites Choptuik.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Choptuik

Reference 32

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Observation 2783b0d5-0e95-4593-8005-a17005d4ddc5 · outbound

This paper cites Low multipole con- tributions to the gravitational self-force.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Low multipole con- tributions to the gravitational self-force

Reference 33

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Observation f7a5235a-6b45-4d6c-a49f-ef648a16e981 · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 34

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Observation 7c486329-4840-436e-b502-e1e78b35ab75 · outbound

This paper cites Dolan and Leor Barack.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Dolan and Leor Barack

Reference 35

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Observation 747bddc5-3ed2-43c6-9fa9-72faf1981f3b · outbound

This paper cites Dolan, Leanne Durkan, Chris Kavanagh, and Barry Wardell.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Dolan, Leanne Durkan, Chris Kavanagh, and Barry Wardell

Reference 36

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Observation a1a6ba58-0865-491d-949e-1075f0f32144 · outbound

This paper cites The Sage project: Unifying free mathematical software to create a viable alternative to Magma, Maple, Mathematica and Matlab.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability The Sage project: Unifying free mathematical software to create a viable alternative to Magma, Maple, Mathematica and Matlab

Reference 37

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Observation 0f99c6d5-566f-4a29-9a61-0f5d87d03ae6 · outbound

This paper cites The post- Newtonian approximation for relativistic compact bina- ries.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability The post- Newtonian approximation for relativistic compact bina- ries

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Observation d09db0a0-d8fd-4beb-b1bf-b830ac9fc9df · outbound

This paper cites What every computer scientist should know about ﬂoating-point arithmetic.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability What every computer scientist should know about ﬂoating-point arithmetic

Reference 39

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Observation d88f4fce-6d53-4f03-95d0-79765582cd9a · outbound

This paper cites Golub and Charles F.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Golub and Charles F

Reference 40

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Observation 04c68d9b-4e63-4288-8083-43baa6534ba6 · outbound

This paper cites Tensor calculus with open-source software: the SageMan- ifolds project.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Tensor calculus with open-source software: the SageMan- ifolds project

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Observation 7f326c48-db87-4273-ac50-93f2fee7702b · outbound

This paper cites Symbolic ten- sor calculus on manifolds: a SageMath implementation , pages 1–54.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Symbolic ten- sor calculus on manifolds: a SageMath implementation , pages 1–54

Reference 42

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Observation 10c66c54-f17b-4cda-8659-659cf2b52b36 · outbound

This paper cites Green, Stefan Hollands, Laura Sberna, Vahid Toomani, and Peter Zimmerman.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Green, Stefan Hollands, Laura Sberna, Vahid Toomani, and Peter Zimmerman

Reference 43

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Observation 7a68173a-2e4d-461b-aaa4-56ce35480bb2 · outbound

This paper cites The Pragmatic Pro- grammer: From Journeyman to Master.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability The Pragmatic Pro- grammer: From Journeyman to Master

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Observation 9dde3901-c64a-452e-838f-ccbf138ec03f · outbound

This paper cites Katz, Alvin J.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Katz, Alvin J

Reference 45

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Observation 70736854-6fe2-4d40-8f85-6b5f74065aa4 · outbound

This paper cites Waveform modelling for the Laser Interferometer Space Antenna.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Waveform modelling for the Laser Interferometer Space Antenna

Reference 46

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Observation 9d6f7baa-4fb4-4295-84c1-66020496edf5 · outbound

This paper cites An axisymmetric evolution code for the Einstein equations on hyperboloidal slices.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability An axisymmetric evolution code for the Einstein equations on hyperboloidal slices

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Observation f486d8d6-f743-4dc4-813c-cec113ee7182 · outbound

This paper cites Hamiltonian formulation of general relativity and post-Newtonian dy- namics of compact binaries.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Hamiltonian formulation of general relativity and post-Newtonian dy- namics of compact binaries

Reference 48

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This paper cites SAGE: System for Algebra and Geometry Experimentation.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability SAGE: System for Algebra and Geometry Experimentation

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Observation cd34bdf0-234d-45dd-93cc-1679a0558190 · outbound

This paper cites Teukolsky.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Teukolsky

Reference 50

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Observation 4b10a095-79fe-434e-8f3d-813d0ddb042c · outbound

This paper cites SageMath, the Sage Math- ematics Software System (Version 10.5.beta0) , 2024.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability SageMath, the Sage Math- ematics Software System (Version 10.5.beta0) , 2024

Reference 51

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Observation dfbcc88f-cc15-4f78-8ff4-42a265029b60 · outbound

This paper cites A 3+1 computational scheme for dynamic spherically symmetric black hole spacetimes – I: Initial data.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability A 3+1 computational scheme for dynamic spherically symmetric black hole spacetimes – I: Initial data

Reference 52

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Observation b52631f2-9ac1-49f9-b976-16dbe869f14f · outbound

This paper cites Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

Reference 53

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Observation fd2ad78e-716c-4501-955c-90704c35e017 · outbound

This paper cites Regularization of ﬁelds for self-force problems in curved spacetime: Foundations and a time-domain application.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Regularization of ﬁelds for self-force problems in curved spacetime: Foundations and a time-domain application

Reference 54

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Observation 76e56ac0-ea03-40c8-abd6-28348e5781cd · outbound

This paper cites an unresolved cited work.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 55

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Observation 01e82127-0460-483f-a1ad-63979bace6a0 · outbound

This paper cites Self-force: Computational strategies.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Self-force: Computational strategies

Reference 56

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Observation 8d9a9a8b-bcd6-4d63-b3f2-a430e13e62fe · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 57

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Observation abdad2a6-42a9-4c0a-86f7-5094c023c245 · outbound

This paper cites LorenzGauge1DEﬀectiveSource: Numeri- cal code to compute a Lorenz-gauge 1-dimensional eﬀec- tive source, 2015.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability LorenzGauge1DEﬀectiveSource: Numeri- cal code to compute a Lorenz-gauge 1-dimensional eﬀec- tive source, 2015

Reference 58

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Observation 10f0448b-71d5-473e-834a-2f3416777645 · outbound

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Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Unresolved cited work

Reference 59

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Observation 22da98b9-9f43-4eea-9ca1-cb67a317fc7f · outbound

This paper cites Metric recon- struction from Weyl scalars.

Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability Metric recon- struction from Weyl scalars

Reference 60

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Pith citing papers

Observation 5062e763-1e7b-4bd4-b86d-d7abbc10d2ee · inbound

Schwarzschild perturbations in Lorenz gauge via elliptic differential equations cites this paper.

Schwarzschild perturbations in Lorenz gauge via elliptic differential equations Time-domain evolution of Lorenz-gauge metric perturbations: taming the $\ell=m=1$ gauge instability

Reference 40

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