Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws

Aakash Palakurthi; Daksh Tamoli; G Keshav; G Prudhvi Raj; Ishaan Singh; Jetain Chetan; K Nanda Kishore; Lakshya Sachdeva; Nanditha Kilari; Pasupuleti Devi

REVIEW 3 major objections 4 minor 1 cited by

Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper argues that the backreaction of emitted radiation on point charges can be captured in a closed canonical framework, and derives analytic inspiral laws for charged binaries, including a crossover scale where dipole emission hands

desk verdict The canonical EM radiation-reaction framework and eccentric/crossover results are solid, but the 2PN inspiral laws in Sec. IX have a sign error that reverses the 1PN/2PN corrections. read the letter →

arxiv 2512.18637 v8 pith:PCY2IPPI submitted 2025-12-21 gr-qc astro-ph.HEhep-th

Suhani Verma , Siddarth Mediratta , Nanditha Kilari , Prakhar Nigam , Ishaan Singh , Daksh Tamoli , Aakash Palakurthi , Valluru Ishaan

show 13 more authors

Tanmay Golchha Sanjay Raghav R Sugapriyan S Yash Narayan Pasupuleti Devi Prathamesh Kapase G Prudhvi Raj Lakshya Sachdeva Shreya Meher K Nanda Kishore G Keshav Jetain Chetan Rickmoy Samanta

This is my paper · ORCID

classification gr-qcastro-ph.HEhep-th MSC 70H0583C2283C25 PACS 04.25.-g04.30.-w

keywords post-NewtonianexpansionradiationreactionLorentz–DiracequationLandau–LifshitzorderreductionDarwinHamiltoniandipoleinspiralchargedcompactbinariesdipole–quadrupolecrossover

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the leading radiation backreaction on a collection of point charges can be written as a canonical, directly implementable 1PN+1.5PN phase-space system: the conservative Darwin Hamiltonian plus a dipole radiation-reaction force obtained by Landau–Lifshitz order reduction of the Lorentz–Dirac equation. If true, the same Hamiltonian-plus-reaction structure that powers gravitational-wave inspiral calculations applies to electromagnetism, and the resulting binaries spiral inward with closed-form circular and eccentric inspiral laws. For charged binaries in Einstein–Maxwell theory, the paper claims a gauge-invariant energy–frequency relation through 2PN order and a dipole–quadrupole crossover scale x_q,cross=(5/48)(η2−η1)^2 that separates electromagnetic from gravitational flux dominance. A sympathetic reader cares because the formulas are ready to use: they turn charge-to-mass asymmetry into concrete chirp and phasing predictions, including the crossover frequency f_cross ≈ 2.2 kHz (M_sun/M)|η2−η1|^3/(1−η1η2).

What carries the argument

The Darwin Hamiltonian, the O(c^{-2}) conservative two-body Hamiltonian with Coulomb plus velocity-dependent interaction, supplies the conservative sector; the Landau–Lifshitz order reduction converts the third-order Lorentz–Dirac self-force into a second-order causal force. In the near zone, its 1.5PN form is the dipole radiation-reaction force, which the paper writes entirely in canonical variables. For binaries the relative acceleration takes the compact form a_RR = K r^{-3}(v − 3(hat r·v)hat r) with K = q1 q2 (m1 q2 − m2 q1)^2/(24π^2 c^3 ε_0^2 m_1^2 m_2^2). The Einstein–Maxwell analysis relies on the gauge-invariant frequency parameter x_q = (GMΩ/c^3)^{2/3}(1−η1η2)^{2/3} and the crossove

What would settle it

An independent first-principles computation of the 2PN Einstein–Maxwell center-of-mass Hamiltonian—without reusing the quoted result—should reproduce E1PN and E2PN in Eqs. (66)–(67); any mismatch in the charge-dependent coefficients shifts the crossover and the 2PN inspiral and phasing laws. On the numerical side, direct integration of the full canonical equations for a moderately charged, mass-asymmetric binary should yield the predicted ⟨dot a⟩ and ⟨dot e⟩ and the invariant I = a(1−e^2)/e^{4/3} to within the stated O(1/c^2) drift; a significant violation would falsify the dipole radiation-re

Watch

Extended reading notes

Core claim

The paper's central claim is that radiating point charges admit a closed canonical N-body description at 1PN+1.5PN order: the Darwin Hamiltonian gives conservative motion through O(c^{-2}), and a Landau–Lifshitz–reduced dipole radiation-reaction force gives dissipation through O(c^{-3}). For binaries this force is proportional to q1 q2 (m1 q2 − m2 q1)^2 times v − 3(hat r·v)hat r, and it vanishes when charge-to-mass ratios are equal. From it the paper derives analytic circular and eccentric inspiral laws (chirp Ωdot = A Ω^3[1 + B Ω^{2/3}/c^2], a(e) relation, finite circularization time) and verifies them numerically. For Einstein–Maxwell binaries it combines a quoted 2PN ADM-type Hamiltonian

Load-bearing premise

The load-bearing premise is that the quoted 2PN ADM-type center-of-mass Hamiltonian for Einstein–Maxwell binaries is correct and complete; every new energy–frequency, inspiral, and crossover result downstream inherits it.

Editorial extensions

If this is right

The 1PN+1.5PN phase-space system is explicit and directly integrable: conservative Darwin dynamics with no secular drift when dissipation is off, and monotonic energy loss with circularization when it is on.
For electromagnetic binaries the circular chirp is Ωdot = A Ω^3[1 + (B/c^2)Ω^{2/3}], giving time-to-coalescence and phase formulas in closed form with a leading Ω^{-1} SPA phase.
Eccentric binaries follow orbit-averaged ⟨dot a⟩ and ⟨dot e⟩ laws that integrate to a(e) = a0 e^{4/3}(1−e0^2)/[(1−e^2)e0^{4/3}] and a finite circularization time.
In Einstein–Maxwell theory, the gauge-invariant binding energy E_b(x_q) through 2PN and the dipole-dominated inspiral phase ∝(t_c−t)^{1/2} differ measurably from the pure-GR quadrupole phase ∝(t_c−t)^{5/8}.
The dipole–quadrupole crossover x_q,cross = 5/48 (η2−η1)^2 translates to f_cross ≈ 2.2 kHz (M_sun/M)|η2−η1|^3/(1−η1η2), so within the leading-order truncation dipole radiation only enters ground-based detector bands for near-unity charge asymmetry.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: because the crossover frequency depends only on the dimensionless charge-to-mass asymmetry and the total mass, a gravitational-wave observation of a chirp whose exponent changes from 3 to 11/3 would directly measure |η2−η1|; within standard astrophysics this asymmetry is expected to be zero, so a detection would point to hidden-sector or exotic charged compact objects.
Editorial inference: the pure electromagnetic part of the construction (Darwin Hamiltonian + 1.5PN force) is independent of the quoted 2PN Einstein–Maxwell Hamiltonian, so the circular and eccentric inspiral laws from the early sections can be tested numerically in Coulomb systems without committing to the charged-black-hole input; such tests would isolate whether any error lives in the conservati
Editorial inference: the eccentric-inspiral invariant I = a(1−e^2)/e^{4/3} is cleaner than the gravitational quadrupole analogue and may be a useful diagnostic in other dipole-driven systems, such as scalar-tensor theories, because it depends only on the leading dipole flux structure.
Editorial inference: a concrete extension would include the 2.5PN electromagnetic quadrupole radiation reaction in the flat-space N-body system to check whether the analytic laws and circularization persist beyond leading order; the paper stops at 1.5PN dissipation, so the higher-order sector is untested.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the paper has a real, useful core—an explicit 1PN+1.5PN canonical N-body phase-space with Landau–Lifshitz dipole radiation reaction—but the headline 2PN Einstein–Maxwell inspiral laws in Sec. IX contain a sign error. I checked the stress-test note against the paper and it holds: Eq. (89) integrates to −(3a1/2)x^{-2} + 3(a1^2−a2)x^{-1} inside the brackets, while Eq. (90) prints +(3a1/2)x^{-2} + 3(a2−a1^2)x^{-1}. Since a1 = E1PN/(6s^2) is positive for small charges, the correct 1PN correction shortens the time to coalescence—matching the flat-space result in Sec. V—while the printed formula lengthens it. This is not a cosmetic slip; the sign error propagates into x_q(τ), Ω(τ), and the phase/SPA formulas (91)–(98). The 2PN-corrected inspiral laws as written are wrong.

What is genuinely good: the explicit canonical double-sum radiation-reaction force (Eq. 20) is new and cleanly derived; the eccentric (a,e) evolution with the invariant I = a(1−e^2)/e^{4/3} integrates nicely; and the dipole–quadrupole crossover scale x_{q,cross} = (5/48)(η2−η1)^2 is a simple, plausible new result. The energy-balance checks in Appendix B give honest numbers and look reproducible. The 1PN circular chirp in Sec. V also checks out.

Softer spots beyond the sign error: κ in Eq. (35) is undefined and α flips sign between Secs. V and VI—both minor but annoying. The 2PN Hamiltonian is quoted from [25] without independent verification; that is standard practice, but given how much of Secs. VII–X rides on it, a cross-check against the published source would have been worth including. The numerics use unphysical small c (c=20) and no error bars; the authors admit these are illustrative, so I don't count it as a hidden flaw.

Who should read this: anyone modeling flat-space EM radiation reaction or speculative charged-binaries. The canonical framework, eccentric results, and crossover formula are usable after fixing notation. Sec. IX needs a careful rewrite before any of the 2PN-corrected formulas can be trusted.

Recommendation: send it to peer review. The core construction deserves referee time, and the sign error is correctable—but the current version should not be accepted as is.

Referee Report

3 major / 4 minor

Summary. The paper constructs an electromagnetic analogue of the post-Newtonian Hamiltonian-plus-radiation-reaction framework used in gravitational-wave physics. It implements Landau–Lifshitz order reduction of the Lorentz–Dirac equation to obtain a 1.5PN dipole radiation-reaction force, combines it with the 1PN Darwin Hamiltonian into an explicit N-body canonical phase-space system, and derives analytic circular and eccentric inspiral laws for binaries. It then extends the analysis to Einstein–Maxwell binaries, quoting a 2PN ADM-type center-of-mass Hamiltonian and combining it with 1.5PN dipole dissipation and 2.5PN quadrupole flux to obtain gauge-invariant energy-frequency relations, closed-form circular inspiral laws, and a dipole-quadrupole crossover scale. The paper includes numerical simulations of the phase-space system and appendices with consistency tests.

Significance. If corrected, the paper would provide a useful, explicit bridge between classical electromagnetic radiation reaction and the PN framework of gravitational-wave physics. The N-body phase-space formulation, the flat-space dipole inspiral laws, and the gauge-invariant crossover x_{q,cross} = (5/48)(η2−η1)^2 are concrete and testable. The derivations are mostly transparent and the numerical checks support the leading-order dissipative dynamics. However, the central 2PN Einstein–Maxwell closed-form inspiral laws contain a sign error in the time-to-coalescence integration, and the quoted 2PN Hamiltonian is not dimensionally consistent as printed. Because these issues affect the paper's main new results, the manuscript requires major revision.

major comments (3)

[Sec. IX, Eqs. (89)–(93)] Equation (90) mis-integrates Eq. (89). Integrating dt/dx_q = (3/2Γ)x_q^{-4}[1 − a1 x_q + (a1^2−a2)x_q^2] from x_q to ∞ gives τ = (1/2Γ)[x_q^{-3} − (3a1/2)x_q^{-2} + 3(a1^2−a2)x_q^{-1}], not the printed expression with + (3a1/2)x_q^{-2} + 3(a2−a1^2)x_q^{-1}. Since a1 = E1PN/(6s^2) is positive for small charges, the sign error reverses the sign of the 1PN correction and contradicts the flat-space result in Eqs. (37)–(38), where the 1PN correction shortens the coalescence time. The error propagates into Eq. (92) (the E1PN term should have a minus sign), Eq. (93) (the E1PN correction in Ω(τ) should be negative), and the subsequent phase/SPA formulas (94)–(98). This is a central closed-form result and must be corrected.
[Sec. VII, Eq. (59)] As printed, the 2PN ADM-type Hamiltonian is not dimensionally consistent. In H2PN, H_N ~ P^2 and G/R, H_1PN ~ P^4 and (G/R)P^2 and (G/R)^2; hence H_2PN must contain P^6, (G/R)P^4, (G/R)^2 P^2, and (G/R)^3. The last line of Eq. (59), however, contains 'G/(4R^3) s(1−12ν)', 'P_R^2/(2R^2)', '−P^2/(4R^2)', and '3ν/R^2(2P_R^2−P^2)' with no G^2 or G^3 factors. Unless one sets G=1 globally, these terms have the wrong dimension and PN order. Since E1PN and E2PN in Eqs. (65)–(67), and therefore all Einstein–Maxwell inspiral laws and the crossover analysis, are derived from this Hamiltonian, the transcription from [25] must be verified and corrected, and the printed expression reconciled with the non-G=1 convention used elsewhere in the paper.
[Sec. IX, Eq. (83) vs. Sec. VIII, Eq. (70)] The dipole luminosity is inconsistent by a factor of 2 between Sec. VIII and Sec. IX. Eq. (70) gives F_dip = 2 c^5 k Δ^2/(3G^2 M^4 s^2) x_q^4, while Eq. (83) gives F_dip = μ^2 c^5 k Δ^2/(3G^2 M^3 m1m2 s^2) x_q^4. Using m1m2 = μM, the latter equals μ c^5 k Δ^2/(3G^2 M^4 s^2) x_q^4, half of Eq. (70). The subsequent balance equation, when combined with Eq. (86)'s definition of Γ, does not reproduce Eq. (88) unless the factor-2 version is used. The reader cannot reproduce the stated 2PN chirp from the printed F_dip. Please correct Eq. (83) or explain the different normalization of Δ.

minor comments (4)

[Sec. V, Eq. (35)] The parameter κ appears in A = 3κμ/(−α) without definition. It should be defined or replaced by the K introduced in Eq. (33). In addition, Sec. VI flips the sign of α relative to Sec. V; although the flip is announced, it would be clearer to rename the parameter (e.g., α̃) to avoid confusion.
[Throughout] There are several typos: 'insiral' in Sec. X.A heading, 'electromagnnetic' in Sec. II, 'avergaed' in Sec. X.A. The caption of Fig. 7 references panels '(d)–(f)' that do not appear in the listed figure. Please proofread carefully.
[Appendix D, Figs. 5–6] The text states that for c=20 the radiation-reaction force is 'suppressed by only ~10^−2 relative to the conservative 1PN corrections'; the actual ratio of O(1/c^3) to O(1/c^2) is 1/c ≈ 0.05, not 0.01. Please correct the statement.
[Sec. VI, Eq. (49)] In the eccentric inspiral section, the sign convention α>0 is adopted after using α<0 earlier. Please verify explicitly that K in Eq. (27) remains negative for opposite charges so that ⟨˙a⟩<0 and ⟨˙e⟩<0 in Eq. (49); the current presentation is easy to misread.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 1.5PN force is obtained by standard order reduction, the inspiral laws follow from energy balance with that same force, and the 2PN Hamiltonian is imported from an external cited source.

full rationale

The paper's derivation chain is not circular. The 1.5PN dipole radiation-reaction force follows from the Landau-Lifshitz order reduction of the Lorentz-Dirac equation, with the third derivative of the dipole expressed through Newtonian accelerations (Eqs. 15-20); no target inspiral result is assumed. The binary specialization reproduces the known q1/m1 = q2/m2 suppression and agrees with the G→0 limit of the external result [25], not with a self-citation. The circular and eccentric inspiral laws (Secs. V-VI, IX-X) are obtained by differentiating the conservative binding energy and imposing energy balance with the explicitly derived dipole (and standard quadrupole) fluxes; no parameter is fitted to data and then renamed as a prediction. The Einstein-Maxwell results import the 2PN ADM-type center-of-mass Hamiltonian from Placidi et al. [25], an external, parameter-free source whose stated assumptions do not include the paper's conclusions, so this is legitimate imported input rather than circular reasoning. The numerical checks integrate the same phase-space equations used for the analytic derivations, so they are self-consistency checks rather than independent verifications, but that is not circularity. Potential concerns such as the correctness of the quoted 2PN Hamiltonian or algebraic sign consistency in a printed integral are accuracy/risk issues, not circularity. No self-definitional reductions, fitted-input-as-prediction steps, load-bearing self-citations, or ansatz smuggling via citation were found.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central derivations use standard classical electrodynamics assumptions (Lorentz-Dirac, Landau-Lifshitz reduction, Larmor balance) and import the 2PN charged-binary Hamiltonian from [25]; no free parameters are fitted. The numerical simulations introduce unphysically small c only to make radiation reaction visible; this is an illustration choice, not a fitted parameter.

assumptions (6)

domain assumption The Landau-Lifshitz order-reduced Lorentz-Dirac equation is the physical causal classical radiation-reaction dynamics.
Adopted in Sec. II as the dissipative input; the paper relies on this rather than the full third-order Lorentz-Dirac equation.
domain assumption At 1.5PN order the near-zone dissipative force is the electric-dipole radiation-reaction force F_a = k q_a (2/(3c^3)) ddd(d), and the mechanical energy loss equals Larmor power up to a Schott total-derivative.
Used in Secs. II-III and in all energy-balance derivations; standard textbook result, not proven in the paper.
standard math The Darwin Hamiltonian (Eq. 14) is the correct 1PN conservative electromagnetic N-body Hamiltonian.
Textbook result; Appendix C re-derives its 1PN force.
domain assumption The 2PN ADM-type center-of-mass Hamiltonian of [25], Eqs. (57)-(59), is correct and complete after the harmonic-to-ADM transformation.
Quoted without independent derivation; all 2PN Einstein-Maxwell results depend on it.
domain assumption Adiabatic energy balance dE/dt = -(F_dip + F_quad) governs quasi-circular inspiral.
Used to convert energy-frequency derivatives into chirp laws in Secs. V and IX-X.
domain assumption Orbit averaging removes oscillatory Schott terms so that secular fluxes are given by the Larmor/Peters-type formulas.
Used in Sec. VI and App. X.A; standard Peters-style averaging.

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Cite this review

Pith. "Pith review of Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws." pith.science (2026). https://pith.science/paper/PCY2IPPI

@misc{pith2026251218637,
  author       = {Pith},
  title        = {Pith review of: Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PCY2IPPI}},
  note         = {Machine review of arXiv:2512.18637}
}

abstract

We revisit an explicit electromagnetic analogue of the Post Newtonian Hamiltonian framework widely used in gravitational wave physics. Starting from the Lorentz Dirac equation, we implement the Landau-Lifshitz order reduction to cast the 1.5PN radiation reaction force in terms of a double sum in canonical variables and incorporate this into the well known 1PN Darwin Hamiltonian system. The resulting phase space is strictly conservative when dissipation is switched off, while in presence of dissipation, it exhibits monotonic energy loss during the inspiral, accompanied by orbit circularization and eccentric bursts in the evolution of the Darwin Hamiltonian. Using this phase space framework we compute the circular and eccentric inspiral laws, including $1$PN conservative corrections. Extending to charged compact binaries in Einstein-Maxwell theory, we combine the known $2$PN ADM-type conservative Hamiltonian with leading $1.5$PN dipole dissipation and $2.5$PN gravitational quadrupole flux, obtaining gauge-invariant energy-frequency relations, closed-form inspiral laws, and a dipole-quadrupole crossover scale that separates electromagnetic and gravitational flux dominated inspirals.

Figures

Figures reproduced from arXiv: 2512.18637 by the authors.

**Figure 2.** FIG. 2: Relativistic trajectory of a charged particle in a uniform magnetic field [PITH_FULL_IMAGE:figures/full_fig_p030_2.png] view at source ↗

**Figure 3.** FIG. 3: More examples: Landau–Lifshitz trajectories for three representative external-field [PITH_FULL_IMAGE:figures/full_fig_p033_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4: Two oppositely charged blobs, each containing ten particles, evolved with the [PITH_FULL_IMAGE:figures/full_fig_p038_4.png]

**Figure 5.** Figure 5: FIG. 5: Charge neutral binary of same mass starting from diametrically opposite locations [PITH_FULL_IMAGE:figures/full_fig_p039_5.png]

**Figure 6.** Figure 6: FIG. 6: Charge neutral binary of extreme mass ratio, one heavy and one light (with [PITH_FULL_IMAGE:figures/full_fig_p040_6.png]

**Figure 7.** Figure 7: FIG. 7: Charge neutral binary, one heavy and one light, with elliptic orbit initial [PITH_FULL_IMAGE:figures/full_fig_p041_7.png]

**Figure 8.** Figure 8: FIG. 8: Three-dimensional trajectories for the conservative Coulomb evolution with [PITH_FULL_IMAGE:figures/full_fig_p042_8.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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X12(η2 2 −η 2 1)(P 2 −2P 2 R)(1−ν) + 2P 2 R(η2 1 +η 2 2 −2) +P 2(η2 1 +η 2 2 + 22) +ν P 2(58 + 7η2 1 −46η 1η2 + 7η2 2 + 2η2 1η2 2)−P 2 R(32 + 10η2 1 + 10η2 2 + 4η1η2) # + G 8R

+ν 23η1η2 −2η 2 1 −2η 2 2 −3η 2 1η2 2 −η 3 1η3 2 −15 # + G2 8R2 " X12(η2 2 −η 2 1)(P 2 −2P 2 R)(1−ν) + 2P 2 R(η2 1 +η 2 2 −2) +P 2(η2 1 +η 2 2 + 22) +ν P 2(58 + 7η2 1 −46η 1η2 + 7η2 2 + 2η2 1η2 2)−P 2 R(32 + 10η2 1 + 10η2 2 + 4η1η2) # + G 8R " 5P 4 + 2νP 2 s P2 R −P 2(11 +η 1η2) −ν 2s(3P 4 + 2P 2P 2 R + 3P 4 R) # + G 4R3 s(1−12ν) + P 2 R 2R2 − P 2 4R2 + 3...

[3] [2]

3 and Table I

More examples To illustrate the structure of radiation–reacting worldlines predicted by the Landau–Lifshitz (LL) equation, we integrate the dynamics for three progressively more complex electromag- netic backgrounds, see Fig. 3 and Table I. In all simulations the four–velocity is initialized relativistically as uµ = (γc, γvx, γvy, γvz), with initial speed...

[4] [3]

The conservative sector As a stringent validation of the conservative sector of our framework, we consider a system of two spatially separated three–dimensional charge blobs of opposite sign, evolved using the Darwin Hamiltonian alone, with all radiation–reaction terms explicitly switched off. Each blob consists of multiple point charges initialized withi...

[5] [4]

hydrogen- like

Dissipative 1.5PN phase space simulations of binary and multicharge systems We now present representative solutions of the dissipative 1.5PN accurateN–body frame- work Eq. (21) described in the main text. Throughout this section we useτto denote the ordinary coordinate time (not the proper time). The conservative interactions are evolved with the Darwin H...

[6] [5]

Charge neutral binary of same mass To validate our construction of the conservative plus dissipative system governed by Eq. (21), we first consider a symmetric charge-neutral bound configuration consisting of two point charges of equal massm= 1 and opposite charge±q, interacting via an attractive Coulomb potentialV(r) =−k/r. The particles are initially pl...

[7] [6]

hydrogen–like

Charge neutral binary of extreme mass ratio As a second application of our N–body framework Eq. (21), we consider an unequal–mass, oppositely charged system designed to mimic a classical “hydrogen–like” configuration. For a pair of point charges (q 1, m1) and (q 2, m2) interacting through the Coulomb potential, a circular orbit may be constructed by impos...

[8] [7]

1 we examine a two–body configuration demonstrating the radiative circulariza- tion predicted by the truncated post-Newtonian scheme Eq

Charge neutral binary of comparable mass showing circularization of initial elliptic orbits In Fig. 1 we examine a two–body configuration demonstrating the radiative circulariza- tion predicted by the truncated post-Newtonian scheme Eq. (21), accompanied by radiative energy loss featuring as eccentric bursts in the evolution of the Darwin Hamiltonian. We ...