A novel notion of null infinity for c-boundaries and generalized black holes
- 190 Downloads
We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime (M, g). These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general context: if the null infinity is regular (i.e. well behaved in a suitable sense) and (M, g) obeys the null convergence condition, then any closed trapped surface in (M, g) has to be inside the black hole region. As an illustration of this general construction, we apply it to the class of generalized plane waves, where the conformal null infinity is not always well-defined. In particular, it is shown that (generalized) black hole regions do not exist in a large family of these spacetimes.
KeywordsBlack Holes Differential and Algebraic Geometry Spacetime Singularities
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- R. Penrose, Conformal treatment of infinity, in Relativity, Groups and Topology, C.M. de Witt and B. de Witt eds., Gordon and Breach, New York, NY (1964), pp. 566–584 [INSPIRE].
- S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1975) [INSPIRE].
- R. Wald, General Relativity, University of Chicago Press (1984) [INSPIRE].
- H. Friedrich, Smoothness at null infinity and the structure of initial data, in The Einstein Equations and the Large Scale Behavior of Gravitational Fields, P.T. Chrusciel and H. Frierdrich eds., Birkhauser, Basel (2004), pp. 243–275.Google Scholar
- L.B. Szabados, Causal boundary for strongly causal spacetimes. II, Class. Quant. Grav. 6 (1989) 77.Google Scholar
- I.P. Costa e Silva, J. Herrera and J.L. Flores, Hausdorff closed limits and the causal boundary of globally hyperbolic spacetimes with timelike boundary, preprint (2018).Google Scholar
- R. Sachs, Gravitational waves in General Relativity. VI. The outgoing radiation condition, Proc. Roy. Soc. Lond. A 264 (1961) 339.Google Scholar
- J.K. Beem, P.E. Ehrlich and K.L. Easley, Global Lorentzian Geometry, Pure and Applied Mathematics, vol. 202, Marcel Dekker, New York (1996).Google Scholar
- B. O’Neill, Semi-Riemannian Geometry With Applications to Relativity, Pure and Applied Mathematics, vol. 103, Academic Press (1983).Google Scholar
- R. Penrose, Techniques of Differential Topology in Relativity, SIAM, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics (1972) [DOI: https://doi.org/10.1137/1.9781611970609].