Gravitational and movement related time dilation

serp777
Messages
117
Reaction score
6
Consider a massive object moving close to the speed of light. Imagine it travels close to a black hole, but does not enter the black hole. How do you calculate the exact time dilation experienced by the massive object's reference frame? How does time dilation due to movement stack with gravitational time dilation?
 
Physics news on Phys.org
Imagine a distant static observer that observes a local static observer's clock at the same place that the massive object is moving. According to the distant observer, the local observer's clock is ticking at a rate that is sqrt(1 - 2 m / r) slower due to gravitational time dilation. Locally SR is valid so the static observer also measures the time of the massive object be kinematically sqrt(1 - (v/c)^2) slower. Since there is no relativity of simultaneity between the static observers, the distant observer will also agree that the rate of time of the moving massive object is sqrt(1 - (v/c)^2) slower than the local clock, while the local clock is sqrt(1 - 2 m / r) slower than the distant observer's own clock, so according to the distant observer that is static to the black hole, the total time dilation of the massive object is sqrt(1 - 2 m / r) sqrt(1 - (v/c)^2), where v is the locally measured speed of the object.
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...

Similar threads

Replies
9
Views
381
Replies
103
Views
6K
Replies
16
Views
4K
Replies
58
Views
4K
Replies
36
Views
4K
Replies
31
Views
607
Replies
21
Views
2K
Back
Top