Passage of Time for an Astronaut Rotating Around a Schwarzschild Black Hole - An Application of General Theory of Relativity

The General Theory of Relativity (GTR) is a fundamental framework that describes the gravitational interaction between matter and spacetime, formulated by Albert Einstein in 1916. Within the scope of GTR, the Schwarzschild Black Hole is a notable solution, representing a non-rotating, uncharged, spherically symmetric black hole. Time dilation, a concept intrinsic to GTR, manifests as a relativistic effect, where time progresses at different rates in different regions for different observers. The time elapsed in the astronaut clock is the proper time, and the time passed in any other frame of reference is the improper time. Time dilation is a function of the distance of the astronaut to the radius of the black hole factor (DTRF). This paper calculates the time dilation factor for DTRF 1.1 to 7. It is observed that the DTRF increases as the time dilation factor increases. For instance, for DTRF 1.1, the time dilation factor is 0.9258, and when the DTRF is 7, the time dilation factor is 0.3015. It is also observed that the time dilation factor increases rapidly and non-linearly for DTRF 1.1 to 4 and increases approximately linearly thereafter.