Angular momentum conservation for uniformly expanding flows

Angular momentum has recently been defined as a surface integral involving an axial vector and a twist 1-form, which measures the twisting around of space-time due to a rotating mass. The axial vector is chosen to be a transverse, divergence-free, coordinate vector, which is compatible with any initial choice of axis and integral curves. Then a conservation equation expresses rate of change of angular momentum along a uniformly expanding flow as a surface integral of angular momentum densities, with the same form as the standard equation for an axial Killing vector, apart from the inclusion of an effective energy tensor for gravitational radiation.Comment: 5 revtex4 pages, 3 eps figure

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

Enabling occupational therapy students to take a fresh approach to psychosis

This practice evaluation describes the implementation of a 2-day workshop on psychosis with third-year undergraduate occupational therapy students at Brunel University. The work was undertaken by the teaching team at Brunel University, a clinical psychologist working in assertive outreach and an occupational therapist working in community mental health. The background to the project and the way in which the 2-day workshop was adapted to accommodate the university timetable are outlined. An evaluation of the workshop, its place in the occupational therapy programme and the feedback from students are presented

Gravitational radiation from dynamical black holes

An effective energy tensor for gravitational radiation is identified for uniformly expanding flows of the Hawking mass-energy. It appears in an energy conservation law expressing the change in mass due to the energy densities of matter and gravitational radiation, with respect to a Killing-like vector encoding a preferred flow of time outside a black hole. In a spin-coefficient formulation, the components of the effective energy tensor can be understood as the energy densities of ingoing and outgoing, transverse and longitudinal gravitational radiation. By anchoring the flow to the trapping horizon of a black hole in a given sequence of spatial hypersurfaces, there is a locally unique flow and a measure of gravitational radiation in the strong-field regime.Comment: 5 revtex4 pages. Additional comment

Dilatonic wormholes: construction, operation, maintenance and collapse to black holes

The CGHS two-dimensional dilaton gravity model is generalized to include a ghost Klein-Gordon field, i.e. with negative gravitational coupling. This exotic radiation supports the existence of static traversible wormhole solutions, analogous to Morris-Thorne wormholes. Since the field equations are explicitly integrable, concrete examples can be given of various dynamic wormhole processes, as follows. (i) Static wormholes are constructed by irradiating an initially static black hole with the ghost field. (ii) The operation of a wormhole to transport matter or radiation between the two universes is described, including the back-reaction on the wormhole, which is found to exhibit a type of neutral stability. (iii) It is shown how to maintain an operating wormhole in a static state, or return it to its original state, by turning up the ghost field. (iv) If the ghost field is turned off, either instantaneously or gradually, the wormhole collapses into a black hole.Comment: 9 pages, 7 figure

Construction and enlargement of traversable wormholes from Schwarzschild black holes

Analytic solutions are presented which describe the construction of a traversable wormhole from a Schwarzschild black hole, and the enlargement of such a wormhole, in Einstein gravity. The matter model is pure radiation which may have negative energy density (phantom or ghost radiation) and the idealization of impulsive radiation (infinitesimally thin null shells) is employed.Comment: 22 pages, 7 figure

Black holes, cosmological singularities and change of signature

There exists a widespread belief that signature type change could be used to avoid spacetime singularities. We show that signature change cannot be utilised to this end unless the Einstein equation is abandoned at the suface of signature type change. We also discuss how to solve the initial value problem and show to which extent smooth and discontinuous signature changing solutions are equivalent.Comment: 14pages, Latex, no figur

On the semiclassical treatment of Hawking radiation

In the context of the semiclassical treatment of Hawking radiation we prove the universality of the reduced canonical momentum for the system of a massive shell self gravitating in a spherical gravitational field within the Painlev\'e family of gauges. We show that one can construct modes which are regular on the horizon both by considering as hamiltonian the exterior boundary term and by using as hamiltonian the interior boundary term. The late time expansion is given in both approaches and their time Fourier expansion computed to reproduce the self reaction correction to the Hawking spectrum.Comment: 18 pages, LaTeX, Corrected typo

The Magnetization of Cu_2(C_5H_{12}N_2)_2Cl_4 : A Heisenberg Spin Ladder System

We study the magnetization of a Heisenberg spin ladder using exact diagonalization techniques, finding three distinct magnetic phases. We consider the results in relation to the experimental behaviour of the new copper compound Cu_2(C_5H_{12}N_2)_2Cl_4 and deduce that the compound is well described by such a model with a ratio of `chain' to `rung' bond strengths (J/J^\prime) of the order of 0.2, consistent with results from the magnetic susceptibility. The effects of temperature, spin impurities and additional diagonal bonds are presented and we give evidence that these diagonal bonds are indeed of a ferromagnetic nature.Comment: Latex file (4 pages), related figures (encapsulated postscript) appende

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