Abstract

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.

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