  I show that several observable properties of bursting neutron stars in metric
theories of gravity can be calculated using only conservation laws, Killing
symmetries, and the Einstein equivalence principle, without requiring the
validity of the general relativistic field equations. I calculate, in
particular, the gravitational redshift of a surface atomic line, the touchdown
luminosity of a radius-expansion burst, which is believed to be equal to the
Eddington critical luminosity, and the apparent surface area of a neutron star
as measured during the cooling tails of bursts. I show that, for a general
metric theory of gravity, the apparent surface area of a neutron star depends
on the coordinate radius of the stellar surface and on its gravitational
redshift in the exact same way as in general relativity. On the other hand, the
Eddington critical luminosity depends also on an additional parameter that
measures the degree to which the general relativistic field equations are
satisfied. These results can be used in conjunction with current and future
high-energy observations of bursting neutron stars to test general relativity
in the strong-field regime.
