Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
Hadamard Regularization
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abstract
Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they admit a power-like singular expansion. We review the concepts of (i) Hadamard ``partie finie'' of such functions at the location of singular points, (ii) the partie finie of their divergent integral. We present and investigate different expressions, useful in applications, for the latter partie finie. To each singular function, we associate a partie-finie (Pf) pseudo-function. The multiplication of pseudo-functions is defined by the ordinary (pointwise) product. We construct a delta-pseudo-function on the class of singular functions, which reduces to the usual notion of Dirac distribution when applied on smooth functions with compact support. We introduce and analyse a new derivative operator acting on pseudo-functions, and generalizing, in this context, the Schwartz distributional derivative. This operator is uniquely defined up to an arbitrary numerical constant. Time derivatives and partial derivatives with respect to the singular points are also investigated. In the course of the paper, all the formulas needed in the application to the physical problem are derived.
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Derives next-to-next-to-leading tidal corrections to flux and phasing in scalar-tensor gravity using adapted post-Newtonian multipolar-post-Minkowskian methods under the adiabatic approximation.
Lorentzian-Euclidean black holes produce excess inner-shadow intensity and accumulate energy at the horizon with backreaction unlike stable light rings.
A review of the MPM-PN approximation scheme that yields equations of motion to 4PN order and gravitational waveforms and fluxes to 4.5PN order for compact binary systems.
citing papers explorer
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Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order
Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
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Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
Derives next-to-next-to-leading tidal corrections to flux and phasing in scalar-tensor gravity using adapted post-Newtonian multipolar-post-Minkowskian methods under the adiabatic approximation.
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Shadow signatures and energy accumulation in Lorentzian-Euclidean black holes
Lorentzian-Euclidean black holes produce excess inner-shadow intensity and accumulate energy at the horizon with backreaction unlike stable light rings.
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Post-Newtonian Theory for Gravitational Waves
A review of the MPM-PN approximation scheme that yields equations of motion to 4PN order and gravitational waveforms and fluxes to 4.5PN order for compact binary systems.