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

A complete distribution of redshifts for sub-millimetre galaxies in the SCUBA-2 Cosmology Legacy Survey UDS field

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. Available online at https://doi.org/10.1093/mnras/stx1689. © 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Sub-milllimetre galaxies (SMGs) are some of the most luminous star-forming galaxies in the Universe, however their properties remain hard to determine due to the difficulty of identifying their optical\slash near-infrared counterparts. One of the key steps to determining the nature of SMGs is measuring a redshift distribution representative of the whole population. We do this by applying statistical techniques to a sample of 761 850$\mu$m sources from the SCUBA-2 Cosmology Legacy Survey observations of the UKIDSS Ultra-Deep Survey (UDS) Field. We detect excess galaxies around $> 98.4$ per cent of the 850$\mu$m positions in the deep UDS catalogue, giving us the first 850$\mu$m selected sample to have virtually complete optical\slash near-infrared redshift information. Under the reasonable assumption that the redshifts of the excess galaxies are representative of the SMGs themselves, we derive a median SMG redshift of $z = 2.05 \pm 0.03$, with 68 per cent of SMGs residing between $1.07Peer reviewedFinal Accepted Versio

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

Reply Comment: Comparison of Approaches to Classical Signature Change

We contrast the two approaches to ``classical" signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward's distributional approach is based on a postulated modified form of the field equations. We make an alternative postulate. We point out an important difference between two possible philosophies of signature change --- ours is strictly classical, while Hayward's Lagrangian approach adopts what amounts to an imaginary proper ``time" on one side of the signature change, as is explicitly done in quantum cosmology. We also explain why we chose to use the Darmois-Israel type junction conditions, rather than the Lichnerowicz type junction conditions favoured by Hayward. We show that the difference in results is entirely explained by the difference in philosophy (imaginary versus real Euclidean ``time"), and not by the difference in approach to junction conditions (Lichnerowicz with specific coordinates versus Darmois with general coordinates).Comment: 10 pages, latex, no figures. Replying to - "Comment on `Failure of Standard Conservation Laws at a Classical Change of Signature'", S.A. Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045

(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

A Reverse Hex Solver

We present Solrex,an automated solver for the game of Reverse Hex.Reverse Hex, also known as Rex, or Misere Hex, is the variant of the game of Hex in which the player who joins her two sides loses the game. Solrex performs a mini-max search of the state space using Scalable Parallel Depth First Proof Number Search, enhanced by the pruning of inferior moves and the early detection of certain winning strategies. Solrex is implemented on the same code base as the Hex program Solver, and can solve arbitrary positions on board sizes up to 6x6, with the hardest position taking less than four hours on four threads.Comment: Presented at Computers and Games 2016 Leiden, International Conference on Computers and Games. Springer International Publishing, 201

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

Complex lapse, complex action and path integrals

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.Comment: 12 pages, Te

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

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