The definition of mass in asymptotically de Sitter space-times

Physical Review D, 1999

to be published in Phys. Rev. D

Physical Review D, 1994

We perform numerical computations to investigate the dynamical evolution of axisymmetric gravitational waves in asymptotically de Sitter spacetime. The final fates of such spacetimes are classified into two types: (1) de Sitter spacetime with small perturbations, and (2) Schwarzschild-de Sitter-like spacetime with both black-hole and cosmological apparent horizons. We also Gnd that if the mass of gravitational waves is larger than the critical value, M";, =-(3&A), then the black hole is not formed even in the case that there exist highly nonlinear localized gravitational waves. In such a case, the Universe is initially dominated by gravitational waves rather than a cosmological constant A and eventually approaches a de Sitter universe. These results are consistent with the previous analysis by use of initial data.

Physical Review D, 2005

The boundary stress tensor approach has proven extremely useful in defining mass and angular momentum in asymptotically anti-de Sitter spaces with CFT duals. An integral part of this method is the use of boundary counterterms to regulate the gravitational action and stress tensor. In addition to the standard gravitational counterterms, in the presence of matter we advocate the use of a finite counterterm proportional to φ 2 (in five dimensions). We demonstrate that this finite shift is necessary to properly reproduce the expected mass/charge relation for R-charged black holes in AdS 5 .

Eprint Arxiv 0807 3176, 2008

It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at nonrelativistic momenta and large distances). We consider a quantum-mechanical description of systems of two free particles in de Sitter invariant quantum theory (i.e. the paper contains nothing but the two-body de Sitter kinematics). In our pure algebraic approach the cosmological constant problem does not arise. It is shown that a system can be simultaneously quasiclassical in relative momentum and energy only if the cosmological constant is not anomalously small. We explicitly construct the relative distance operator. The corresponding eigenvectors differ from standard ones at both, large and small momenta. At large momenta they ensure fast convergence of quasiclassical wave functions. There also exists an anomalously large (but finite) contribution from small momenta, which is a consequence of the fact that the cosmological constant is finite. We argue that gravity might be a manifestation of this contribution.

Classical and Quantum Gravity, 2015

The general structure of the conformal boundary I + of asymptotically de Sitter spacetimes is investigated. First we show that Penrose's quasi-local mass, associated with a cut S of the conformal boundary, can be zero even in the presence of outgoing gravitational radiation. On the other hand, following a Witten-type spinorial proof, we show that an analogous expression based on the Nester-Witten form is finite only if the Witten spinor field solves the 2-surface twistor equation on S, and it yields a positive functional on the 2-surface twistor space on S, provided the matter fields satisfy the dominant energy condition. Moreover, this functional is vanishing if and only if the domain of dependence of the spacelike hypersurface which intersects I + in the cut S is locally isometric to the de Sitter spacetime. For non-contorted cuts this functional yields an invariant analogous to the Bondi mass.

2001

We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter (dS) spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/CFT correspondence, our methods compute the (Euclidean) stress tensor of the dual. We compute the masses of Schwarzschild-de Sitter black

2010

In this paper we discuss massive gravity in de Sitter space via gravitational Higgs mechanism, which provides a nonlinear definition thereof. The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. Using the aforesaid non-perturbative definition, we address appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. By studying full non-perturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. We argue that this is indeed the case by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. In particular, we argue that no negative norm state is present in the full nonlinear theory. 1

Physical review, 2016

The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.

Classical and Quantum Gravity, 2018

This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area boundsà la Boucher-Gibbons-Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild-de Sitter spacetime.

Journal of Mathematical Physics, 2008

In the present work the massless vector field in the de Sitter (dS) space has been quantized. "Massless" is used here by reference to conformal invariance and propagation on the dS light-cone whereas "massive" refers to those dS fields which contract at zero curvature unambiguously to massive fields in Minkowski space. Due to the gauge invariance of the massless vector field, its covariant quantization requires an indecomposable representation of the de Sitter group and an indefinite metric quantization. We will work with a specific gauge fixing which leads to the simplest one among all possible related Gupta-Bleuler structures. The field operator will be defined with the help of coordinate independent de Sitter waves (the modes) which are simple to manipulate and most adapted to group theoretical matters. The physical states characterized by the divergencelessness condition will for instance be easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemanian manifold for the modes and the two-point function.