Editing Gravitational field (section)

== General relativity ==
{{See also|Gravitational acceleration#General relativity|Gravitational potential#General relativity}}
A freely moving particle in gravitational field has the equations of motion:
<math display="block">\frac{d^2x^\lambda}{d\tau^2} + \Gamma^\lambda_{\mu\nu}\frac{dx^\mu}{d\tau}\frac{dx^\nu}{d\tau} = 0</math>
where <math>\tau</math> is the [[proper time]] for the particle, <math>\Gamma^\lambda_{\mu\nu}</math> are the [[Christoffel symbols]] and repeated indices are summed over.<ref name=Weinberg-1972/>{{rp|70}} 
The proper time can be expressed in terms of the [[metric tensor]]:
<math display="block">d\tau^2 = -g_{\mu\nu} dx^\mu dx^\nu. </math>
The field that determines the gravitational force is the [[Christoffel symbols]] and its derivatives, the [[metric tensor (general relativity)|metric tensor]] plays the role of the gravitational potential.<ref name=Weinberg-1972/>{{rp|73}}

In general relativity, the gravitational field is determined by solving the [[Einstein field equations]]<ref name=Weinberg-1972>{{cite book |last=Weinberg |first=Steven |url=https://archive.org/details/gravitationcosmo00stev_0 |title=Gravitation and cosmology |date=1972 |publisher=John Wiley & Sons |isbn=9780471925675 |author-link=Steven Weinberg |url-access=registration}}</ref>{{rp|157}}
<math display="block"> \mathbf{G} = \kappa \mathbf{T} ,</math>
where {{math|'''T'''}} is the [[stress–energy tensor]], {{math|'''G'''}} is the [[Einstein tensor]], and {{math|''κ''}} is the [[Einstein gravitational constant]].  The latter is defined as {{math|1=''κ'' = 8''πG''/''c''{{sup|4}}}}, where {{math|''G''}} is the [[Newtonian constant of gravitation]] and {{math|''c''}} is the [[speed of light]].

These equations are dependent on the distribution of matter, stress and momentum in a region of space, unlike Newtonian gravity, which is depends on only the distribution of matter.  The fields themselves in general relativity represent the curvature of spacetime.  General relativity states that being in a region of curved space is [[equivalence principle#Einstein equivalence principle|equivalent]] to [[acceleration|accelerating]] up the [[gradient]] of the field.  By [[Newton's laws of motion#Newton's second law|Newton's second law]], this will cause an object to experience a [[fictitious force]] if it is held still with respect to the field.  This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface.  In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable [[General relativity#Consequences of Einstein's theory|differences]], one of the most well known being the [[General relativity#Light deflection and gravitational time delay|deflection of light]] in such fields.