Editing Neutron star (section)

===Gravity===
{{See also|Tolman–Oppenheimer–Volkoff equation|White dwarf#Mass–radius relationship}}

[[File:Neutronstar 2Rs.svg|thumb|Gravitational light deflection at a neutron star. Due to relativistic light deflection over half the surface is visible (each grid patch represents 30 by 30 degrees).<ref name="Zahn" /> In [[Geometrized unit system|natural units]], this star's mass is 1 and its radius is 4, or twice its [[Schwarzschild radius]].<ref name="Zahn" />]]

The gravitational field at a neutron star's surface is about {{val|2|e=11}} times [[Standard gravity|stronger than on Earth]], at around {{val|2.0|e=12|u=m/s2}}.<ref>{{cite book |title=An Introduction to the Sun and Stars |edition=illustrated |first1=Simon F. |last1=Green |first2=Mark H. |last2=Jones |first3=S. Jocelyn |last3=Burnell |publisher=Cambridge University Press |year=2004 |isbn=978-0-521-54622-5 |page=322 |url=https://books.google.com/books?id=lb5owLGIQGsC&pg=PA322 |access-date=2016-06-09 |archive-date=2017-01-31 |archive-url=https://web.archive.org/web/20170131005503/https://books.google.com/books?id=lb5owLGIQGsC&pg=PA322 |url-status=live }}</ref> Such a strong gravitational field acts as a [[gravitational lens]] and bends the radiation emitted by the neutron star such that parts of the normally invisible rear surface become visible.<ref name="Zahn">{{cite web |first=Corvin |last=Zahn |title=Tempolimit Lichtgeschwindigkeit |date=1990-10-09 |url=http://www.tempolimit-lichtgeschwindigkeit.de/galerie/galerie.html |language=de |quote=Durch die gravitative Lichtablenkung ist mehr als die Hälfte der Oberfläche sichtbar. Masse des Neutronensterns: 1, Radius des Neutronensterns: 4, ... dimensionslosen Einheiten (''c'', ''G'' = 1) |access-date=2009-10-09 |archive-date=2021-01-26 |archive-url=https://web.archive.org/web/20210126171353/https://www.tempolimit-lichtgeschwindigkeit.de/galerie/galerie.html |url-status=live }}</ref>
If the radius of the neutron star is 3''GM''/''c''<sup>2</sup> or less, then the photons may be [[photon sphere|trapped in an orbit]], thus making the whole surface of that neutron star visible from a single vantage point, along with destabilizing photon orbits at or below the 1 radius distance of the star.

A fraction of the mass of a star that collapses to form a neutron star is released in the supernova explosion from which it forms (from the law of mass–energy equivalence, {{nowrap|1=''E'' = ''mc''<sup>2</sup>}}). The energy comes from the [[gravitational binding energy]] of a neutron star.

Hence, the gravitational force of a typical neutron star is huge. If an object were to fall from a height of one meter on a neutron star 12 kilometers in radius, it would reach the ground at around 1,400 kilometers per second.<ref>{{cite web |title=Peligroso lugar para jugar tenis |url=http://www.datosfreak.org/datos/slug/Aceleracion-de-superficie-estrella-de-neutrones |website=Datos Freak |access-date=3 June 2016 |language=es |archive-date=11 June 2016 |archive-url=https://web.archive.org/web/20160611022635/http://www.datosfreak.org/datos/slug/Aceleracion-de-superficie-estrella-de-neutrones |url-status=live }}</ref> However, even before impact, the [[tidal force]] would cause [[spaghettification]], breaking any sort of an ordinary object into a stream of material.

Because of the enormous gravity, [[time dilation]] between a neutron star and Earth is significant. For example, eight years could pass on the surface of a neutron star, yet ten years would have passed on Earth, not including the time-dilation effect of the star's very rapid rotation.<ref>{{cite book|author=Marcia Bartusiak | title=Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved| url=https://archive.org/details/blackholehowidea0000bart |url-access=registration |year=2015 | publisher=Yale University Press | isbn=978-0-300-21363-8 |page=[https://archive.org/details/blackholehowidea0000bart/page/130 130]}}</ref>

Neutron star relativistic equations of state describe the relation of radius vs. mass for various models.<ref>[http://www.ns-grb.com/PPT/Lattimer.pdf Neutron Star Masses and Radii] {{Webarchive|url=https://web.archive.org/web/20111217102314/http://www.ns-grb.com/PPT/Lattimer.pdf |date=2011-12-17 }}, p. 9/20, bottom</ref> The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). ''E''<sub>B</sub> is the ratio of gravitational binding energy mass equivalent to the observed neutron star gravitational mass of ''M'' kilograms with radius ''R'' meters,<ref>{{Cite journal |arxiv = astro-ph/0002232|last1 = Hessels|first1 = Jason W. T|title = Neutron Star Structure and the Equation of State | journal = The Astrophysical Journal | volume = 550 | issue = 426|pages = 426–442|last2 = Ransom|first2 = Scott M|last3 = Stairs|first3 = Ingrid H|last4 = Freire | first4 = Paulo C. C | last5 = Kaspi|first5 = Victoria M|last6 = Camilo|first6 = Fernando|year = 2001|doi = 10.1086/319702|bibcode = 2001ApJ...550..426L|s2cid = 14782250}}</ref>
<math display="block">E_\text{B} = \frac{0.60\,\beta}{1 - \frac{\beta}{2}}</math><math display="block">\beta \ = G\,M/R\,{c}^{2}</math>
Given current values
*<math>G = 6.67408\times10^{-11}\, \text{m}^3\text{kg}^{-1}\text{s}^{-2}</math><ref name="CODATA 2014">CODATA 2014</ref>
*<math>c = 2.99792458 \times10^{8}\, \text{m}/\text{s}</math><ref name="CODATA 2014" />
*<math>M_\odot = 1.98855\times10^{30}\, \text{kg}</math>
and star masses "M" commonly reported as multiples of one solar mass,
<math display="block">M_x = \frac{M}{M_\odot}</math>
then the relativistic fractional binding energy of a neutron star is
<math display="block">E_\text{B} = \frac{886.0 \,M_x}{R_{\left[\text{in meters}\right]} - 738.3\,M_x}</math>

A {{Solar mass|2}} neutron star would not be more compact than 10,970 meters radius (AP4 model). Its mass fraction gravitational binding energy would then be 0.187, −18.7% (exothermic). This is not near 0.6/2 = 0.3, −30%.