2.3 Stopping time twice
A very
interesting identity is that time dilation effects due
to gravity and time dilation effects due to motion at
the escape velocity are nearly identical for any given
distance. The same formula can be used for
calculating both. This is the result of plugging
the formula for escape velocity
into the Lorentz factor
we get the approximation (formula) for gravitational time dilations
(2015-06-21 Note: This identity was first discovered by Karl Schwarzschild in 1915, and was used to determine the event horizon radius of black holes)
Let’s go back to the imaginary trip to the BH at the center of the Milky Way as described on section 1.3. Let’s say we launch a clock at the BH’s escape velocity of 2.1 Km/s towards the BH. This clock would experience two time dilation effects acting on it: one due to the gravitational field and another one due to the speed. These two effects will get progressively larger as the clock gets closer to the BH and speeds up, but they remain identical to each other. When the clock arrives at the event horizon time will stop twice: both the strength of the gravitational field and the speed of travel will each stop time separately..
we get the approximation (formula) for gravitational time dilations
(2015-06-21 Note: This identity was first discovered by Karl Schwarzschild in 1915, and was used to determine the event horizon radius of black holes)
Let’s go back to the imaginary trip to the BH at the center of the Milky Way as described on section 1.3. Let’s say we launch a clock at the BH’s escape velocity of 2.1 Km/s towards the BH. This clock would experience two time dilation effects acting on it: one due to the gravitational field and another one due to the speed. These two effects will get progressively larger as the clock gets closer to the BH and speeds up, but they remain identical to each other. When the clock arrives at the event horizon time will stop twice: both the strength of the gravitational field and the speed of travel will each stop time separately..
