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

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

Using fractals and power laws to predict the location of mineral deposits

Around the world the mineral exploration industry is interested in getting that small increase in probability measure on the earth's surface of where the next large undiscovered deposit might be found. In particular WMC Resources Ltd has operations world wide looking for just that edge in the detection of very large deposits of, for example, gold. Since the pioneering work of Mandelbrot, geologists have been familiar with the concept of fractals and self similarity over a few orders of magnitude for geological features. This includes the location and size of deposits within a particular mineral province. Fractal dimensions have been computed for such provinces and similarities of these aggregated measures between provinces have been noted. This paper explores the possibility of making use of known information to attempt the inverse process. That is, from lesser dimensional measures of a mineral province, for example, fractal dimension or more generally multi-fractal measures, is it possible to infer, even with small increase in probability, where the unknown (preferably large) deposits might be located

Hamilton-Jacobi Method and Gravitation

Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations.Comment: To appear in the proceedings of "Cosmology, the Quantum Vacuum, and Zeta Functions": A workshop with a celebration of Emilio Elizalde's Sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 201

Swimming capabilities of stoats and the threat to inshore sanctuaries

Stoats (Mustela erminea) are small carnivorous mammals which were introduced into New Zealand in the late 19th century, and have now become widespread invasive pests. Stoats have long been known to be capable of swimming to islands 1-1.5 km offshore. Islands further out have usually been assumed to be safe from invasion, therefore routine stoat monitoring on them has been considered un-necessary. Recent incursions, including a stoat found on Rangitoto Island (3 km offshore) in 2010, and another which was deduced to have reached Kapiti (5 km offshore) in 2009, along with distribution modelling and genetic studies, strongly support the proposition that stoats can swim much further than 1.5 km. Acceptance of this hypothesis depends on estimating the probability that such small animals could indeed swim so far unaided. This paper reports the results of a project designed to assist this debate by recording the paddling action, speed and minimal endurance of nine stoats observed (once each) swimming against an endless current in a flume at the Aquatic Research Centre, University of Waikato. Four of the five males and two of the four females could hold a position for at least five minutes against the maximum current available, averaging 1.36 ± 0.336 km/h. In steady swimming against a current of c. 1 km/hr, they all used a rapid quadripedal paddling action (averaging 250 strokes/min, stronger with the spread forepaws). Four of the nine swam strongly for >1 h, including one female who covered 1.8 km in nearly 2 h non- stop. Results from such artificial conditions cannot be conclusive, but support suggestions that wild stoats could indeed swim much further than 1.5 km, hence we conclude that the “risk zone” for stoat reinvasions of inshore islands has been seriously under-estimated

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

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