scholarly journals The existence of non-trivial asymptotically flat initial data for vacuum spacetimes

1977 ◽  
Vol 57 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Murray Cantor
Keyword(s):  
Initial Data ◽  
Asymptotically Flat

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

Curvature, causality and completeness in space-times with causally complete spacelike slices

1986 ◽  
Vol 99 (2) ◽  
pp. 367-375 ◽  
Author(s):  
Gregory J. Galloway
Keyword(s):  
Initial Data ◽  
Minkowski Space ◽  
Cauchy Surface ◽  
Space Time ◽  
Finiteness Condition ◽  
Cauchy Horizon ◽  
Asymptotically Flat ◽  
The Future

Let S be a spacelike slice (defined formally in Section 2) in a space-time M. We will say that S is future causally complete in M if for each p ε J+(S) the closure in S of the set J-(p) ∩ S is compact. Define past causal completeness time-dually. Then S is causally complete if it is both future and past causally complete. A compact spacelike slice is necessarily causally complete, as is any Cauchy surface, but the concept of causal completeness is much broader than either of these two conditions. For example the slices t = const. ≠ 0 in the space-time obtained by removing the origin from Minkowski space are causally complete, although they are neither Cauchy nor compact. The slice t = 0 in the previous example and the hyperboloid in Minkowski space (where (t, x1, …, xn) are standard inertial coordinates) are examples of slices which are not causally complete. Physically speaking, an edgeless slice S is future causally complete if the information from S which reaches a point in the future of S comes from a finite nonsingular region in S. The Maximal Reissner-Nordstrom space-time is a well-known example in which this finiteness condition is not fulfilled by any of its asymptotically flat partial Cauchy surfaces. Indeed for any such partial Cauchy surface S, J-(p) ∩ S is non-compact for any p ε H+(S). However, as has been discussed in the literature (e.g. [17], p. 625 f), it is believed that the Cauchy horizon in this situation is unstable with respect to perturbations of the initial data on S.

scholarly journals Spacetime Positive Mass Theorems for Initial Data Sets with Non-Compact Boundary

2020 ◽  
Author(s):  
Sérgio Almaraz ◽  
Levi Lopes de Lima ◽  
Luciano Mari
Keyword(s):  
Initial Data ◽  
Energy Conditions ◽  
Data Sets ◽  
Positive Mass ◽  
Momentum Vector ◽  
Asymptotically Flat ◽  
The Common ◽  
Underlying Manifold ◽  
Asymptotically Hyperbolic ◽  
Compact Boundary

Abstract In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under suitable dominant energy conditions (DECs) imposed both on the interior and along the boundary, we prove the corresponding positive mass inequalities under the assumption that the underlying manifold is spin. In the asymptotically flat case, we also prove a rigidity statement when the energy-momentum vector is light-like. Our treatment aims to underline both the common features and the differences between the asymptotically Euclidean and hyperbolic settings, especially regarding the boundary DECs.

scholarly journals Bartnik mass via vacuum extensions

2019 ◽  
Vol 30 (13) ◽  
pp. 1940006
Author(s):  
Pengzi Miao ◽  
Naqing Xie
Keyword(s):  
Initial Data ◽  
Scalar Curvature ◽  
Apparent Horizon ◽  
Gauss Curvature ◽  
Positive Mass Theorem ◽  
Data Sets ◽  
Penrose Inequality ◽  
Asymptotically Flat ◽  
Apparent Horizons ◽  
Positive Gauss Curvature

We construct asymptotically flat, scalar flat extensions of Bartnik data [Formula: see text], where [Formula: see text] is a metric of positive Gauss curvature on a two-sphere [Formula: see text], and [Formula: see text] is a function that is either positive or identically zero on [Formula: see text], such that the mass of the extension can be made arbitrarily close to the half area radius of [Formula: see text]. In the case of [Formula: see text], the result gives an analog of a theorem of Mantoulidis and Schoen [On the Bartnik mass of apparent horizons, Class. Quantum Grav. 32(20) (2015) 205002, 16 pp.], but with extensions that have vanishing scalar curvature. In the context of initial data sets in general relativity, the result produces asymptotically flat, time-symmetric, vacuum initial data with an apparent horizon [Formula: see text], for any metric [Formula: see text] with positive Gauss curvature, such that the mass of the initial data is arbitrarily close to the optimal value in the Riemannian Penrose inequality. The method we use is the Shi–Tam type metric construction from [Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, J. Differential Geom. 62(1) (2002) 79–125] and a refined Shi–Tam monotonicity, found by the first named author in [On a localized Riemannian Penrose inequality, Commun. Math. Phys. 292(1) (2009) 271–284].

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