Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.Comment: 23 pages, 13 figures, submitted to Phys. Rev.

A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity

In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of the conserved quantity is defined to be the value of the Hamiltonian which generates the canonical transformation on phase space corresponding to this symmetry. However, such an approach cannot be employed to define `conserved quantities' in a situation where symplectic current can be radiated away (such as occurs at null infinity in general relativity) because there does not, in general, exist a Hamiltonian which generates the given asymptotic symmetry. (This fact is closely related to the fact that the desired `conserved quantities' are not, in general, conserved!) In this paper we give a prescription for defining `conserved quantities' by proposing a modification of the equation that must be satisfied by a Hamiltonian. Our prescription is a very general one, and is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian, although we have not investigated existence and uniqueness issues in the most general contexts. In the case of general relativity with the standard asymptotic conditions at null infinity, our prescription agrees with the one proposed by Dray and Streubel from entirely different considerations.Comment: 39 pages, no figure

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.Comment: 20 pages, 6 figures; to appear in General Relativity and Gravitatio

Percutaneous Ventricular Restoration (PVR) Therapy Using the Parachute Device in 100 Subjects with Ischaemic Dilated Heart Failure: One-Year Primary Endpoint Results of PARACHUTE III, a European Trial

AIMS: This prospective, non-randomised, observational study conducted in Europe was designed in order to assess the long-term safety and efficacy of the Parachute device in ischaemic heart failure subjects as a result of left ventricle remodelling after anterior wall myocardial infarction. METHODS AND RESULTS: One hundred subjects with New York Heart Association Class II-IV ischaemic heart failure (HF), ejection fraction (EF) between 15% and 40%, and dilated akinetic or dyskinetic anterior-apical wall without the need to be revascularised were enrolled. The primary safety endpoint was procedural- or device-related major adverse cardiac cerebral events (MACCE). The secondary safety endpoint was the composite of mortality and morbidity. Secondary efficacy endpoints included haemodynamic measurements determined by echocardiography, LV volume indices, and assessment of functional improvement measured by a standardised six-minute walk test. Of the 100 subjects enrolled, device implantation was successful in 97 (97%) subjects. The one-year rates of the primary and secondary safety endpoints were 7% and 32.3%, respectively. The secondary endpoints, LV volume reduction (p<0.0001) and six-minute walk distance improvement (p<0.01), were achieved. CONCLUSIONS: The favourable outcomes observed in this high-risk population provide reassuring safety and efficacy data to support adoption of this technology as a therapeutic option for HF subjects.info:eu-repo/semantics/publishedVersio

Future Boundary Conditions in De Sitter Space

We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.Comment: 16 page

High-powered Gravitational News

We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard $N_{+}$ and $N_{\times}$ polarization components. The resulting code is stable and second-order convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about $10^{13}M_{\odot}/sec$.Comment: 24 pages, 4 figures. To appear in Phys. Rev.

Uniqueness of the Trautman--Bondi mass

It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri, are those depending on the metric only through a specific combination of the Bondi `mass aspect' and other next--to--leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman--Bondi energy. It is also shown that this energy remains well-defined for a wide class of `polyhomogeneous' metrics.Comment: latex, 33 page