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Equation 4 · Part 11 · A Neutron Star Is a Redshift Standard

Numerator: 2GM

zs=(1−2GMRc2)−1/2−1z_s = \left(1 - \frac{2GM}{Rc^2}\right)^{-1/2} - 1
2GM2GM

What this part means

The complete quantity above the fraction bar.

Its job in the formula

2GM occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The relation itself is old and simple. For a spherical, non-rotating exterior, the surface redshift zsz_s follows from the mass M and radius R as zs=(1−2GMRc2)−1/2−1z_s = \left(1 - \frac{2GM}{Rc^2}\right)^{-1/2} - 1. — a function of the star’s compactness alone, so that whatever fraction of a percent of uncertainty NICER puts on M and R propagates directly into the redshift. The paper works through six NICER-mapped pulsars this way, and two of them mark the range worth remembering. PSR J0740+6620, the most massive precisely-timed neutron star known, comes in at roughly 2.07\,M⊙M_\odot with a radio-timing mass fixed independently by Shapiro delay to 2.08±\pm0.07\,M⊙M_\odot [ 4 ] , giving a compactness near 0.25 and a surface redshift zsz_s≃\simeq0.40…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.