scholarly journals Asymptotically simple spacetimes and mass loss due to gravitational waves

2017 ◽  
Vol 27 (01) ◽  
pp. 1730027 ◽  
Author(s):  
Vee-Liem Saw
Keyword(s):  
Mass Loss ◽  
Gravitational Waves ◽  
Hamiltonian Formulation ◽  
Conformal Structure ◽  
De Sitter ◽  
Research Activity ◽  
Null Infinity ◽  
Open Problems ◽  
Timelike Hypersurface ◽  
Bondi Mass

The cosmological constant [Formula: see text] used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of [Formula: see text] or [Formula: see text] being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on [Formula: see text]: null infinity [Formula: see text] is a spacelike, null, or timelike hypersurface, if [Formula: see text], [Formula: see text], or [Formula: see text], respectively. Recent observations of distant supernovae have taught us that our universe expands at an accelerated rate, and this can be accounted for by choosing [Formula: see text] in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of [Formula: see text], is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with [Formula: see text] has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.

scholarly journals Null infinity as an open Hamiltonian system

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Wolfgang Wieland
Keyword(s):  
Free Energy ◽  
Phase Space ◽  
Hamiltonian Formulation ◽  
Time Dependent ◽  
Null Infinity ◽  
Null Tetrad ◽  
Bondi Mass ◽  
New Interpretation ◽  
Background Fields ◽  
Bondi Energy

Abstract When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time-dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our derivation starts from the Hamiltonian formulation in domains with boundaries that are null. We introduce the most general boundary conditions on a generic such null boundary, and compute quasi-local charges for boosts, energy and angular momentum. Initially, these domains are at finite distance, such that there is a natural IR regulator. To remove the IR regulator, we introduce a double null foliation together with an adapted Newman-Penrose null tetrad. Both null directions are surface orthogonal. We study the falloff conditions for such specific null foliations and take the limit to null infinity. At null infinity, we recover the Bondi mass and the usual covariant phase space for the two radiative modes at the full non-perturbative level. Apart from technical results, the framework gives two important physical insights. First of all, it explains the physical significance of the corner term that is added in the Wald-Zoupas framework to render the quasi-conserved charges integrable. The term to be added is simply the derivative of the Hamiltonian with respect to the background fields that drive the time-dependence of the Hamiltonian. Secondly, we propose a new interpretation of the Bondi mass as the thermodynamical free energy of gravitational edge modes at future null infinity. The Bondi mass law is then simply the statement that the free energy always decreases on its way towards thermal equilibrium.

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+.

scholarly journals De Sitter braneworld and gravitational waves

2021 ◽  
Author(s):  
Dong-Yu Li ◽  
Zhao-Xiang Wu ◽  
Hao Hu ◽  
Bao-Min Gu
Keyword(s):  
Gravitational Waves ◽  
Scalar Fields ◽  
Background Solution ◽  
De Sitter ◽  
Dimensional Theory ◽  
Massive Mode ◽  
Large Extra Dimension ◽  
Mass Gap ◽  
Massless Mode ◽  
Background Fields

We study the braneworld theory constructed by multi scalar fields. The model contains a smooth and infinitely large extra dimension, allowing the background fields propagating in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of massless mode evolve the same as the four dimensional theory, while that of the massive modes evolve greatly different from the massless mode.

scholarly journals Gravitational waves in a spatially closed de Sitter spacetime

2013 ◽  
Vol 73 (10) ◽  
Author(s):  
Amir H. Abbassi ◽  
J. Khodagholizadeh ◽  
Amir M. Abbassi
Keyword(s):  
Gravitational Waves ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime

scholarly journals An Upper Limit to the Mass Loss from the Centre of the Galaxy

1974 ◽  
Vol 64 ◽  
pp. 36-36
Author(s):  
Arcadio Poveda ◽  
Christine Allen
Keyword(s):  
Mass Loss ◽  
Gravitational Waves ◽  
Mass Distribution ◽  
Globular Clusters ◽  
Loss Rate ◽  
Galactic Centre ◽  
Isotropic Source ◽  
The Past ◽  
Upper Limit ◽  
The Galaxy

A mass loss of 200 M⊙ per year, as conservatively suggested if Weber is detecting gravitational waves from an isotropic source at the galactic centre, is shown to be incompatible with the existence of (a) globular clusters, (b) old wide binaries, if this loss rate has been constant over the past 1010 yr.From the orbit of ω Centauri in the galactic field and its observed mass distribution and tidal radius an upper limit to the mass loss from the galactic centre is found to be 1 M⊙ yr-1 over the past 1010 yr.

scholarly journals A possible new cosmological redshift effect due to Λ on traveling gravitational waves in Friedmann universes

2017 ◽  
Vol 26 (14) ◽  
pp. 1750168
Author(s):  
Stefano Viaggiu
Keyword(s):  
Laplace Transform ◽  
Gravitational Waves ◽  
Einstein Condensation ◽  
De Sitter ◽  
Expansion Factor ◽  
Cosmological Redshift ◽  
Bose Einstein Condensation ◽  
Abscissa Of Convergence ◽  
Physical Consequences ◽  
Bose Einstein

In this paper, we continue the investigation concerning the propagation of gravitational waves in a cosmological background using Laplace transform. a We analyze the possible physical consequences of the result present in Ref. 19 where it is argued that a nonvanishing positive abscissa of convergence caused by the de Sitter expansion factor [Formula: see text] implies a shift in the frequencies domain of a traveling gravitational wave as measured by a comoving observer. In particular, we show that in a generic asymptotically de Sitter cosmological universe, this redshift effect does also arise. Conversely, in a universe expanding with, for example, a power law expansion, this phenomenon does not happen. This physically possible new redshift effect, although negligible for the actual very low value of [Formula: see text], can have interesting physical consequences concerning for example its relation with Bose–Einstein condensation or more speculatively with the nature of the cosmological constant in terms of gravitons, as recently suggested in Ref. 21 near a Bose–Einstein condensation phase.

scholarly journals Conformal scattering of the Maxwell-scalar field system on de Sitter space

2019 ◽  
Vol 16 (04) ◽  
pp. 743-791
Author(s):  
Grigalius Taujanskas
Keyword(s):  
Scalar Field ◽  
De Sitter Space ◽  
Decay Rates ◽  
Energy Estimates ◽  
Small Data ◽  
De Sitter ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Field System ◽  
Gauge Fixing

We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. Using these, we construct bounded and invertible, but nonlinear, scattering operators taking past asymptotic data to future asymptotic data. We deduce exponential decay rates for solutions with data having at least two derivatives, and for more regular solutions discover an asymptotic decoupling of the scalar field from the charge. The construction involves a carefully chosen complete gauge fixing condition which allows us to control all components of the Maxwell potential, and a nonlinear Grönwall inequality for higher-order estimates.

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