Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant

作者：Saw Vee Liem

来源：PHYSICAL REVIEW D, 2016, 94(10): 104004.

DOI：10.1103/PhysRevD.94.104004

We derive the asymptotic solutions for vacuum spacetimes with nonzero 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 falloffs 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 nonzero. After solving the vacuum Newman-Penrose equations asymptotically, we propose a generalization to the Bondi mass involving A and obtain a positive-definite mass-loss formula by integrating the Bianchi identity involving D'Psi(2) over a compact 2-surface on 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 Lambda not equal 0 reduce smoothly to those where. Lambda = 0, in spite of the distinct characters of 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(0)(0) = 0 on some initial null hypersurface, for Lambda not equal 0, no incoming radiation requires Psi(o)(0) = 0 everywhere.

• 出版日期2016-11-2