Can be possible that a neutron star has a negative gravitational surface redshift?

Question

I am looking for some strange stars that is gravitationally blue shifted. A star surface redshift determines mass-radius relation for chargeless star. Can be possible that a charged neutron star has a negative gravitational surface redshift?

Answer 1

The simple answer is no, though the complicated answer is, well, complicated!

The spacetime outside a charged object is described by the Reissner-Nordstrom metric:

$$ ds^2=-\bigl(1-\frac{r_s}{r}+\frac{r_q^2}{r^2}\bigr)dt^2+\bigl(1-\frac{r_s}{r}+\frac{r_q^2}{r^2}\bigr)^{-1}dr^2+r^2d\Omega^2 $$

where:

$$ r_s = \frac{2GM}{c^2} $$

$$ r_q^2 = \frac{Q^2G}{4 \pi \epsilon_0 c^4} $$

From this we can extract the expression for the time dilation at a radius $r$:

$$ \frac{d\tau}{dt} = \sqrt{1-\frac{r_s}{r}+\frac{r_q^2}{r^2}} $$

For an uncharged neutron star $r_q = 0$ and the right side is always less than one i.e. time always runs slower. However once $r_q^2 \gt 0$ this changes the time dilation and in principle it can become greater than one. This would mean that light would be blue shifted.

The problem is that the charge required is so high the neutron star could never be stable. The charge would cause it to disintegrate. So, sadly, there is no way for a neutron star to have a blue shift in the way you describe.