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Thread: Time Dilations for Gravitational Potential and Escape Velocity are Equal?

  1. #1 Time Dilations for Gravitational Potential and Escape Velocity are Equal? 
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    Gravitational potential and escape velocity are of course highly related. In General Relativity, at least for the simple case with one large mass such as the Earth, it seems that the time dilation due to the gravitational potential equals the time dilation that would result from movement at escape velocity.

    escape velocity = [1] for a Lorentz factor of or

    From the Schwarzchild metric for a massive symmetric sphere, not rotating,
    proper time is coordinate time times [2]

    Is that equality obvious, or an obvious result of the kinetic energy to escape equaling the gravitational potential energy, or a result of the Equivalence Principal, or is it something deeper?


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    Quote Originally Posted by mnpguy View Post
    Gravitational potential and escape velocity are of course highly related. In General Relativity, at least for the simple case with one large mass such as the Earth, it seems that the time dilation due to the gravitational potential equals the time dilation that would result from movement at escape velocity.

    escape velocity = [1] for a Lorentz factor of or

    From the Schwarzchild metric for a massive symmetric sphere, not rotating,
    proper time is coordinate time times [2]

    Is that equality obvious, or an obvious result of the kinetic energy to escape equaling the gravitational potential energy, or a result of the Equivalence Principal, or is it something deeper?
    The escape velocity given above is a direct result of the radial velocity/energy condition which is obtained by inserting the Schwarzschild coefficients into the geodesic equations. It can therefore be considered a measure of gravitational potential at a given distance r from the center of gravity; since gravitational time dilation is also a function of gravitational potential, the two are closely related.
    Well spotted.


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