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Register a new userMass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
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Added by
Piotr T. Chru\\'sciel
Publication date
2008
fields
Physics
and research's language is
English
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We extend the validity of Dains angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential.
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We extend the validity of Brills axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.
Angular momentum at null infinity has a supertranslation ambiguity from the lack of a preferred Poincare group and a similar ambiguity when the center-of-mass position changes as linear momentum is radiated. Recently, we noted there is an additional one-parameter ambiguity in the possible definitions of angular momentum and center-of-mass charge. We argue that this one-parameter ambiguity can be resolved by considering the generalized BMS charges that are constructed from local 2-sphere-covariant tensors near null infinity; these supertranslation-covariant charges differ from several expressions currently used. Quantizing angular momentum requires a supertranslation-invariant angular momentum in the center-of-mass frame. We propose one such definition of angular momentum involving nonlocal quantities on the 2-sphere, which could be used to define a quantum notion of general-relativistic angular momentum.
This paper proposes a strategy for detecting the presence of a gravito-magnetic field due to the rotation of the galactic dark halo. Visible matter in galaxies rotates and dark matter, supposed to form a halo incorporating barionic matter, rotates also, since it interacts gravitationally with the rest. Pursuing the same line of reasoning, dark matter should produce all gravitational effects predicted by general relativity, including a gravito-magnetic field. I discuss a possible strategy for measuring that field. The idea recovers the old Sagnac effect and proposes to use a triangle having three Lagrange points of the Sun-Earth pair at its vertices. The asymmetry in the times of flight along the loop in opposite directions is proportional to the gravito-magnetic galactic field.
The anticipated enhancements in detector sensitivity and the corresponding increase in the number of gravitational wave detections will make it possible to estimate parameters of compact binaries with greater accuracy assuming general relativity(GR), and also to carry out sharper tests of GR itself. Crucial to these procedures are accurate gravitational waveform models. The systematic errors of the models must stay below statistical errors to prevent biases in parameter estimation and to carry out meaningful tests of GR. Comparisons of the models against numerical relativity (NR) waveforms provide an excellent measure of systematic errors. A complementary approach is to use balance laws provided by Einsteins equations to measure faithfulness of a candidate waveform against exact GR. Each balance law focuses on a physical observable and measures the accuracy of the candidate waveform vis a vis that observable. Therefore, this analysis can provide new physical insights into sources of errors. In this paper we focus on the angular momentum balance law, using post-Newtonian theory to calculate the initial angular momentum, surrogate fits to obtain the remnant spin and waveforms from models to calculate the flux. The consistency check provided by the angular momentum balance law brings out the marked improvement in the passage from texttt{IMRPhenomPv2} to texttt{IMRPhenomXPHM} and from texttt{SEOBNRv3} to texttt{SEOBNRv4PHM} and shows that the most rece
We prove an inequality relating the trace of the extrinsic curvature, the total angular momentum, the centre of mass, and the Trautman-Bondi mass for a class of gravitational initial data sets with constant mean curvature extending to null infinity. As an application we obtain non-existence results for the asymptotic Dirichlet problem for CMC hypersurfaces in stationary space-times.
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