10,767 research outputs found
A critical analysis of prognostic factors for survival in intermediate and high grade non-Hodgkin's lymphoma. Scotland and Newcastle Lymphoma Group Therapy Working Party
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
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
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
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
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
An extreme critical space-time: echoing and black-hole perturbations
A homothetic, static, spherically symmetric solution to the massless
Einstein- Klein-Gordon equations is described. There is a curvature singularity
which is central, null, bifurcate and marginally trapped. The space-time is
therefore extreme in the sense of lying at the threshold between black holes
and naked singularities, just avoiding both. A linear perturbation analysis
reveals two types of dominant mode. One breaks the continuous self-similarity
by periodic terms reminiscent of discrete self-similarity, with echoing period
within a few percent of the value observed numerically in near-critical
gravitational collapse. The other dominant mode explicitly produces a black
hole, white hole, eternally naked singularity or regular dispersal, the latter
indicating that the background is critical. The black hole is not static but
has constant area, the corresponding mass being linear in the perturbation
amplitudes, explicitly determining a unit critical exponent. It is argued that
a central null singularity may be a feature of critical gravitational collapse.Comment: 6 revtex pages, 6 eps figure
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
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