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At present, 19 double neutron star (DNS) systems are detected by radio timingand 2 merging DNS systems are detected by kilo-hertz gravitational waves.Because of selection effects, none of them has an orbital period $P_b$ in therange of a few tens of minutes. In this paper we consider a multimessengerstrategy proposed by Kyutoku et al. (2019), jointly using the LaserInterferometer Space Antenna (LISA) and the Square Kilometre Array (SKA) todetect and study Galactic pulsar-neutron star (PSR-NS) systems with $P_b \sim$10-100 min. We assume that we will detect PSR-NS systems by this strategy. Weuse standard pulsar timing software to simulate times of arrival of pulsesignals from these binary pulsars. We obtain the precision of timing parametersof short-orbital-period PSR-NS systems whose orbital period $P_b \in(8,120)\,$min. We use the simulated uncertainty of the orbital decay,$\dot{P}_{b}$, to predict future tests for a variety of alternative theories ofgravity. We show quantitatively that highly relativistic PSR-NS systems willsignificantly improve the constraint on parameters of specific gravity theoriesin the strong field regime. We also investigate the orbital periastron advancecaused by the Lense-Thirring effect in a PSR-NS system with $P_b = 8\,$min, andshow that the Lense-Thirring effect will be detectable to a good precision.

Stringent Tests of Gravity with Highly Relativistic Binary Pulsars in the Era of LISA and SKA