Abstract
Spacetimes with metrics admitting an expansion in terms of a combination of powers of 1/r and ln r are known as polyhomogeneous spacetimes. The asymptotic behaviour of the Newman-Penrose quantities for the vacuum polyhomogeneous spacetimes is presented under certain gauges. The Bondi mass is revisited via the Iyer-Wald formalism. The memory effect of the gravitational radiation in the vacuum polyhomogeneous spacetimes is also discussed. It is found that the appearance of the logarithmic terms does not affect the balance law and it remains identical to that of spacetimes with metrics admitting an expansion in terms of powers of 1/r.
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