GRAVITATIONAL MASS IN ASYMPTOTICALLY DESITTER SPACETIMES

The Abbott-Deser (AD) mass in asymptotically de Sitter spacetime is a conserved Killing 'energy'. We show that the AD mass can be negative in some situations but may still deserve the title of 'gravitational mass'. In order to see the property of negative AD mass we consider the Tolman-Bondi dust sphere solution. The negative AD mass prevents the dust sphere's gravitational collapse. Rather it causes cosmic expansion, resulting in isotropic and homogeneous de Sitter spacetime locally. As a result, the cosmic no hair conjecture holds even though the AD mass may be negative.