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Non-linear general relativistic effects in the observed redshift
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We present the second-order expression for the observed redshift, accounting for all the relativistic effects from the light propagation and from the frame change at the observer and the source positions. We derive the generic gauge-transformation law that any observable quantities should satisfy, and we verify our second-order expression for the observed redshift by explicitly checking its gauge transformation property. This is the first time an explicit verification is made for the second-order calculations of observable quantities. We present our results in popular gauge choices for easy use and discuss the origin of disagreements in previous calculations.
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Cited by 1 Pith paper
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Nonlinear Relativistic Effects on Cosmological Redshift Drift
Second-order relativistic effects on redshift drift are computed, showing distortions appear only at this order with enhanced nonlinear bispectrum contributions at low redshift and large momenta.
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