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- W2907551799 abstract "We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. we do not explicitly deal with conformal rescaling nor the conformal spacetime. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $sigma^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we propose a generalisation to the Bondi mass involving $Lambda$ and obtain a positive-definite mass-loss formula by integrating the Bianchi identity involving $D'Psi_2$ over a compact 2-surface on $mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $Lambda<0$, and yields exactly the known asymptotically flat spacetimes when $Lambda=0$. In other words, our asymptotic vacuum solutions with $Lambdaneq0$ reduce smoothly to those where $Lambda=0$, in spite of the distinct characters of $mathcal{I}$ being spacelike, timelike and null for de Sitter, anti-de Sitter and Minkowski, respectively. Unlike for $Lambda=0$ where no incoming radiation corresponds to setting $Psi^o_0=0$ on some initial null hypersurface, for $Lambdaneq0$, no incoming radiation requires $Psi^o_0=0$ everywhere." @default.
- W2907551799 created "2019-01-11" @default.
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- W2907551799 date "2016-05-17" @default.
- W2907551799 modified "2023-09-27" @default.
- W2907551799 title "Asymptotic behaviour of vacuum spacetimes with non-zero cosmological constant, Bondi mass-loss formula" @default.
- W2907551799 hasPublicationYear "2016" @default.
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