Year: 2026
Type: preprint
Abstract: We present a fully nonlinear relativistic description of the observed pulsar timing modulations, defined through the ratio of the proper-time intervals between two successive emissions of radio pulses and their observations by a pulsar timing array. Working in the limit of a vanishing emission interval, we derive the observed pulsar timing modulation to second order in relativistic perturbation theory around a Minkowski background, without fixing a gauge and retaining the full scalar, vector, and tensor content of the metric perturbations. Although the derivation naturally introduces several gauge-dependent intermediate quantities, we explicitly demonstrate that they combine into a coordinate-independent expression. Moreover, we explicitly show that the second-order timing modulation from two neighboring radio pulses coincides with the observed redshift, defined as the fractional change in wavelength along a single geodesic. The agreement represents a nontrivial second-order realization of the exact nonlinear equivalence proven in Magi & Yoo 2026.
Source: arXiv (Cornell University)
Authors: Magi, Matteo, Yoo, Jaiyul
Institution: Institute for Basic Science
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Institute for Basic Science
Award: G4487476711
OpenAlex ID: W7213368801