The mergers of two neutron stars are typically accompanied by broad-band electromagnetic emission from either a relativistic jet or a kilonova. It has also been long predicted that coherent radio emission will occur during the merger phase or from a newly formed neutron star remnant, however this emission has not been seen to date. This paper presents the deepest limits for this emission from a neutron star merger folowing triggered LOFAR observations of the short gamma-ray burst (SGRB) 181123B, starting 4.4 minutes after the GRB occurred. During the X-ray plateau phase, a signature of ongoing energy injection, we detect no radio emission to a 3$sigma$ limit of 153 mJy at 144 MHz (image integration time of 136 seconds), which is significantly fainter than the predicted emission from a standard neutron star. At a redshift of 1.8, this corresponds to a luminosity of $2.5 times 10^{44}$ erg s$^{-1}$. Snapshot images were made of the radio observation on a range of timescales, targeting short duration radio flashes similar to fast radio bursts (FRBs). No emission was detected in the snapshot images at the location of GRB 181123B enabling constraints to be placed on the prompt coherent radio emission model and emission predicted to occur when a neutron star collapses to form a black hole. At the putative host redshift of 1.8 for GRB 181123B, the non detection of the prompt radio emission is two orders of magnitude lower than expected for magnetic reconnection models for prompt GRB emission and no magnetar emission is expected.
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