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Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
This equation has two solutions: = (). These concentric event horizons become degenerate for 2 r Q = r s , which corresponds to an extremal black hole . Black holes with 2 r Q > r s cannot exist in nature because if the charge is greater than the mass there can be no physical event horizon (the term under the square root becomes negative). [ 9 ]
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
Equation is a fundamental and much-quoted differential equation for the relation between proper time and coordinate time, i.e. for time dilation. A derivation, starting from the Schwarzschild metric, with further reference sources, is given in Time dilation § Combined effect of velocity and gravitational time dilation.
In particular, the direction of motion with respect to the sense of rotation of the central body is relevant because co-and counter-propagating waves carry a "gravitomagnetic" time delay Δt GM which could be, in principle, be measured [2] [3] if S is known.
Any theory of gravity will predict gravitational time dilation if it respects the principle of equivalence. [ 6 ] : 16 This includes Newtonian gravitation. A standard demonstration in general relativity is to show how, in the " Newtonian limit " (i.e. the particles are moving slowly, the gravitational field is weak, and the field is static ...
where the numerator is the gravitational, and the denominator is the kinematic component of the time dilation. For a particle falling in from infinity the left factor equals the right factor, since the in-falling velocity v {\textstyle v} matches the escape velocity c r s r {\textstyle c{\sqrt {\frac {r_{\text{s}}}{r}}}} in this case.
In a nearly static gravitational field of moderate strength (say, of stars and planets, but not one of a black hole or close binary system of neutron stars) the effect may be considered as a special case of gravitational time dilation. The measured elapsed time of a light signal in a gravitational field is longer than it would be without the ...