Black Holes: Signal Escape Probability

This lecture delves into the scenario of a spacecraft near a black hole with a malfunctioning system that sends signals in random directions, exploring the probability of these signals escaping the black hole. The exercise involves analyzing light signals' trajectories, finding conditions for signal escape, and calculating the probability of signal escape. Additionally, the lecture covers properties of eternal circular orbits near black holes, equations of motion in the Schwarzschild metric, and the impact of space-time dimensions on gravity, particularly in two plus one dimensions. A final exercise addresses signal transmission to a constantly accelerated observer, requiring the application of previously learned formulas.