If consistent with the principle of scientific method, we can’t perform testing general relativity in any way, including tests using a massive neutron star, because the hypothesis of general relativity is not valid.
In 1993 Joseph Taylor and Russell Hulse were awarded the Nobel Prize in Physics for discovery the Binary Pulsar-PSR B1913+16- and it was said that massive objects in short binary orbits should emit gravitational waves precisely as general relativity predicts.
In 2013, John Antoniadis and colleagues measured the mass of PSR J0348+0432, it also was said testing general relativity using a massive neutron star.
More surprising, in his book A Brief History of Time Stephen Hawking wrote (may be a joke):”This confirmation of general relativity won J. H. Taylor and R. A. Hulse the Nobel Prize in 1993".
But, actually, nothing to do with general relativity. 1993 Nobel Prize in Physics “for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation”