Gravitational waves from quasi-spherical black holes

A quasi-spherical approximation scheme, intended to apply to coalescing black holes, allows the waveforms of gravitational radiation to be computed by integrating ordinary differential equations.Comment: 4 revtex pages, 2 eps figure

Generalized inverse mean curvature flows in spacetime

Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is monotone. We focus on a subclass of such flows which we call uniformly expanding, which can be considered for null as well as for spacelike directions. In the null case, local existence of the flow is guaranteed. In the spacelike case, the uniformly expanding condition leaves a 1-parameter freedom, but for the whole family, the embedding functions satisfy a forward-backward parabolic system for which local existence does not hold in general. Nevertheless, we have obtained a generalization of the weak (distributional) formulation of this class of flows, generalizing the corresponding step of Huisken and Ilmanen's proof of the Riemannian Penrose inequality.Comment: 21 pages, 1 figur

Unified first law of black-hole dynamics and relativistic thermodynamics

A unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity. This equation expresses the gradient of the active gravitational energy E according to the Einstein equation, divided into energy-supply and work terms. Projecting the equation along the flow of thermodynamic matter and along the trapping horizon of a blackhole yield, respectively, first laws of relativistic thermodynamics and black-hole dynamics. In the black-hole case, this first law has the same form as the first law of black-hole statics, with static perturbations replaced by the derivative along the horizon. There is the expected term involving the area and surface gravity, where the dynamic surface gravity is defined as in the static case but using the Kodama vector and trapping horizon. This surface gravity vanishes for degenerate trapping horizons and satisfies certain expected inequalities involving the area and energy. In the thermodynamic case, the quasi-local first law has the same form, apart from a relativistic factor, as the classical first law of thermodynamics, involving heat supply and hydrodynamic work, but with E replacing the internal energy. Expanding E in the Newtonian limit shows that it incorporates the Newtonian mass, kinetic energy, gravitational potential energy and thermal energy. There is also a weak type of unified zeroth law: a Gibbs-like definition of thermal equilibrium requires constancy of an effective temperature, generalising the Tolman condition and the particular case of Hawking radiation, while gravithermal equilibrium further requires constancy of surface gravity. Finally, it is suggested that the energy operator of spherically symmetric quantum gravity is determined by the Kodama vector, which encodes a dynamic time related to E.Comment: 18 pages, TeX, expanded somewhat, to appear in Class. Quantum Gra

Quasi-local first law of black-hole dynamics

A property well known as the first law of black hole is a relation among infinitesimal variations of parameters of stationary black holes. We consider a dynamical version of the first law, which may be called the first law of black hole dynamics. The first law of black hole dynamics is derived without assuming any symmetry or any asymptotic conditions. In the derivation, a definition of dynamical surface gravity is proposed. In spherical symmetry it reduces to that defined recently by one of the authors (SAH).Comment: Latex, 8 pages; version to appear in Class. Quantum Gra

Late Miocene to early Pliocene stratigraphic record in northern Taranaki Basin: Condensed sedimentation ahead of Northern Graben extension and progradation of the modern continental margin

The middle Pliocene-Pleistocene progradation of the Giant Foresets Formation in Taranaki Basin built up the modern continental margin offshore from western North Island. The late Miocene to early Pliocene interval preceding this progradation was characterised in northern Taranaki Basin by the accumulation of hemipelagic mudstone (Manganui Formation), volcaniclastic sediments (Mohakatino Formation), and marl (Ariki Formation), all at bathyal depths. The Manganui Formation has generally featureless wireline log signatures and moderate to low amplitude seismic reflection characteristics. Mohakatino Formation is characterised by a sharp decrease in the GR log value at its base, a blocky GR log motif reflecting sandstone packets, and erratic resistivity logs. Seismic profiles show bold laterally continuous reflectors. The Ariki Formation has a distinctive barrel-shaped to blocky GR log motif. This signature is mirrored by the SP log and often by an increase in resistivity values through this interval. The Ariki Formation comprises (calcareous) marl made up of abundant planktic foraminifera, is 109 m thick in Ariki-1, and accumulated over parts of the Western Stable Platform and beneath the fill of the Northern Graben. It indicates condensed sedimentation reflecting the distance of the northern region from the contemporary continental margin to the south

Energy conservation for dynamical black holes

An energy conservation law is described, expressing the increase in mass-energy of a general black hole in terms of the energy densities of the infalling matter and gravitational radiation. For a growing black hole, this first law of black-hole dynamics is equivalent to an equation of Ashtekar & Krishnan, but the new integral and differential forms are regular in the limit where the black hole ceases to grow. An effective gravitational-radiation energy tensor is obtained, providing measures of both ingoing and outgoing, transverse and longitudinal gravitational radiation on and near a black hole. Corresponding energy-tensor forms of the first law involve a preferred time vector which plays the role for dynamical black holes which the stationary Killing vector plays for stationary black holes. Identifying an energy flux, vanishing if and only if the horizon is null, allows a division into energy-supply and work terms, as in the first law of thermodynamics. The energy supply can be expressed in terms of area increase and a newly defined surface gravity, yielding a Gibbs-like equation, with a similar form to the so-called first law for stationary black holes.Comment: 4 revtex4 pages. Many (mostly presentational) changes; emphasizes the definition of gravitational radiation in the strong-field regim

Quasi-spherical approximation for rotating black holes

We numerically implement a quasi-spherical approximation scheme for computing gravitational waveforms for coalescing black holes, testing it against angular momentum by applying it to Kerr black holes. As error measures, we take the conformal strain and specific energy due to spurious gravitational radiation. The strain is found to be monotonic rather than wavelike. The specific energy is found to be at least an order of magnitude smaller than the 1% level expected from typical black-hole collisions, for angular momentum up to at least 70% of the maximum, for an initial surface as close as $r=3m$.Comment: revised version, 8 pages, RevTeX, 8 figures, epsf.sty, psfrag.sty, graphicx.st

(13)C NMR investigation of the superconductor MgCNi_3 up to 800K

We report (13)C NMR characterization of the new superconductor MgCNi_3 (He et al., Nature (411), 54 (2001)). We found that both the uniform spin susceptibility and the spin fluctuations show a strong enhancement with decreasing temperature, and saturate below ~50K and ~20K respectively. The nuclear spin-lattice relaxation rate 1/(13)T_1T exhibits typical behaviour for isotropic s-wave superconductivity with a coherence peak below Tc=7.0K that grows with decreasing magnetic field.Comment: Accepted for publication in Physical Review Letter

Kerr black holes in horizon-generating form

New coordinates are given which describe non-degenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.Comment: 4 revtex4 page