Pulsar Timing Response and Spatial Correlations of Shear Modes in Torsionless Palatini Spacetime
Abstract
In the nanohertz band, spatial correlations between pulsar timing residuals provide a key observable for characterizing stochastic gravitational-wave backgrounds and probing their polarization content. In torsionless Palatini spacetime, nonmetricity can generate two additional shear modes, referred to as the shear-x and shear-y modes. In this work, we investigate the pulsar timing response produced by the shear-induced motions of the emitting pulsar and the receiving Earth. Assuming that the electromagnetic field is minimally coupled to the physical metric and that the Earth and pulsar possess non-negligible effective hypermomentum responses, we derive the single-pulsar redshift, the frequency-domain two-point correlation function, and the corresponding spatial correlation. For a stationary and isotropic stochastic shear background, the normalized overlap reduction function (ORF) for distinct pulsars reduces in the short-wavelength limit to the pure dipolar form Γabsh(ζ)=cosζ, where ζ is the angular separation between the two pulsars. The same dipolar correlation can also be produced by isotropic Solar System ephemeris errors, leading to a spatial degeneracy between the two signals. This degeneracy highlights the importance of information beyond the angular correlation for identifying Palatini shear signatures in PTA data.
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BibTeX
@misc{li2026pulsar,
title = {{Pulsar Timing Response and Spatial Correlations of Shear Modes in Torsionless Palatini Spacetime}},
author = {Tian-Shi Li and Yu-Mei Wu and Chang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10251},
eprint = {2609.10251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pulsar Timing Response and Spatial Correlations of Shear Modes in Torsionless Palatini Spacetime
AU - Tian-Shi Li
AU - Yu-Mei Wu
AU - Chang Liu
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10251
UR - https://arxiv.org/abs/2609.10251
AB - In the nanohertz band, spatial correlations between pulsar timing residuals provide a key observable for characterizing stochastic gravitational-wave backgrounds and probing their polarization content. In torsionless Palatini spacetime, nonmetricity can generate two additional shear modes, referred to as the shear-x and shear-y modes. In this work, we investigate the pulsar timing response produced by the shear-induced motions of the emitting pulsar and the receiving Earth. Assuming that the electromagnetic field is minimally coupled to the physical metric and that the Earth and pulsar possess non-negligible effective hypermomentum responses, we derive the single-pulsar redshift, the frequency-domain two-point correlation function, and the corresponding spatial correlation. For a stationary and isotropic stochastic shear background, the normalized overlap reduction function (ORF) for distinct pulsars reduces in the short-wavelength limit to the pure dipolar form Γ_ab^sh(ζ)=cosζ, where ζ is the angular separation between the two pulsars. The same dipolar correlation can also be produced by isotropic Solar System ephemeris errors, leading to a spatial degeneracy between the two signals. This degeneracy highlights the importance of information beyond the angular correlation for identifying Palatini shear signatures in PTA data.
ER -