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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 ...
Thus, gravity acts like a fictitious force such as the centrifugal force or the Coriolis force, which result from being in an accelerated reference frame; all fictitious forces are proportional to the inertial mass, just as gravity is. To effect the reconciliation of gravity and special relativity and to incorporate the equivalence principle ...
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse.. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes—from star formation to helioseismology to supernovae—in which gravity plays a dominant ro
In canonical gravity, spacetime is foliated into spacelike submanifolds. The three-metric (i.e., metric on the hypersurface) is and given by = (+) + +. In that equation the Latin indices run over the values 1, 2, 3, and the Greek indices run over the values 1, 2, 3, 4.
Ball falling to the floor in an accelerating rocket (left) and on Earth (right). The effect is identical. Most effects of gravity vanish in free fall, but effects that seem the same as those of gravity can be produced by an accelerated frame of reference. An observer in a closed room cannot tell which of the following two scenarios is true:
The Lie derivative can be defined for type (,) tensor fields and in this respect can be viewed as a map that sends a type (,) to a type (,) tensor. The Lie derivative is usually denoted by L X {\displaystyle {\mathcal {L}}_{X}} , where X {\displaystyle X} is the vector field along whose congruence the Lie derivative is taken.
The value is the total working mass of propellant expended. is the integration over time of the magnitude of the acceleration produced by using the rocket engine (what would be the actual acceleration if external forces were absent). In free space, for the case of acceleration in the direction of the velocity, this is the increase of the speed.
A naive application of Newtonian gravity can yield exactly half this value, where the light ray is assumed as a massed particle and scattered by the gravitational potential well. This approximation is good when 4 G M / c 2 b {\displaystyle 4GM/c^{2}b} is small.