Variation of a Signal in Schwarzschild Spacetime

In this paper, the variation of a signal in Schwarzschild spacetime is studied and a general equation for frequency shift parameter (FSP) is presented. It shows that FSP depends on the gravitationally-modified Doppler effects and the gravitational effects of observers. In addition, rates of time of a transmitter and a receiver may be different. When FSP is a function of the time of a receiver, FSP contributed by gravitational effect (GFSP) or gravitationally-modified Doppler effect (GMDFSP) may lead a bandlimited signal to a non-bandlimited signal. Based on the equation, FSP as a function of the time of a receiver is calculated for three scenarios: a) a spaceship moves away from a star with a constant velocity communicating with a transmitter at a fixed position; b) a spaceship moves around a star with different conic trajectories communicating with a transmitter at a fixed position; c) a signal is transmitted at a fixed position in a star system to a receiver moving with an elliptical trajectory in another star system. The studied stars are sun-like star, white dwarf and neutron star, and some numerical examples are presented to illustrate the theory.