General Relativity: An Introduction for Physicists · Problem 8.8

The gravitational field equations — Hobson, Efstathiou & Lasenby

Physics · equation-of-state-parameter-energy-conditions

Problem

The equation-of-state parameter

w

is defined by

w = p/(\rho c^2)

. If one restricts oneself to sources for which

\rho \geq 0

, show that both the weak and strong energy conditions in Exercises 8.6 and 8.7 imply that

w \geq -1