An Introduction to Modern Astrophysics · Problem 16.18

General Relativity and Black Holes — Carroll & Ostlie

Physics — Astrophysics · pulsar-period-evolution

Problem

Consider a pulsar that has a period P0P_0 and period derivative P˙0\dot{P}_0 at t=0t = 0. Assume that the product PP˙P\dot{P} remains constant for the pulsar (cf. Eq. 16.32). (a) Integrate to obtain an expression for the pulsar's period PP at time tt. (b) Imagine that you have constructed a clock that would keep time by counting the radio pulses received from this pulsar. Suppose you also have a perfect clock (P˙=0\dot{P} = 0) that is initially synchronized with the pulsar clock when they both read zero. Show that when the perfect clock displays the characteristic lifetime P0/P˙0P_0/\dot{P}_0, the time displayed by the pulsar clock is (3−1)P0/P˙0(\sqrt{3} - 1)P_0/\dot{P}_0.

Browse the problem library