3,459 research outputs found
Entropy of eternal black holes
The entropy of a quantum-statistical system which is classically approximated
by a general stationary eternal black hole is studied by means of a
microcanonical functional integral. This approach opens the possibility of
including explicitly the internal degrees of freedom of a physical black hole
in path integral descriptions of its thermodynamical properties. If the
functional integral is interpreted as the density of states of the system, the
corresponding entropy equals in the semiclassical
approximation, where is the area of the black hole horizon. The
functional integral reflects the properties of a pure state.Comment: To appear in the proceedings of the Sixth Canadian Conference on
General Relativiy and Relativistic Astrophysics, 7 pages, Late
Grand canonical ensemble in generalized thermostatistics
We study the grand-canonical ensemble with a fluctuating number of degrees of
freedom in the context of generalized thermostatistics. Several choices of
grand-canonical entropy functional are considered. The ideal gas is taken as an
example.Comment: 14 pages, no figure
On critical behaviour in gravitational collapse
We give an approach to studying the critical behaviour that has been observed
in numerical studies of gravitational collapse. These studies suggest, among
other things, that black holes initially form with infinitesimal mass. We show
generally how a black hole mass formula can be extracted from a transcendental
equation.
Using our approach, we give an explicit one parameter set of metrics that are
asymptotically flat and describe the collapse of apriori unspecified but
physical matter fields. The black hole mass formula obtained from this metric
exhibits a mass gap - that is, at the onset of black hole formation, the mass
is finite and non-zero.Comment: 11 pages, RevTex, 2 figures (available from VH
Phase imaging with intermodulation atomic force microscopy
Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic
force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever
in close proximity to a surface experiences the nonlinear tip-sample force
which mixes the drive tones and generates new frequency components in the
cantilever response known as intermodulation products (IMPs). We present a
procedure for extracting the phase at each IMP and demonstrate phase images
made by recording this phase while scanning. Amplitude and phase images at
intermodulation frequencies exhibit enhanced topographic and material contrast.Comment: 6 pages, 6 page
Exact solution for scalar field collapse
We give an exact spherically symmetric solution for the Einstein-scalar field
system. The solution may be interpreted as an inhomogeneous dynamical scalar
field cosmology. The spacetime has a timelike conformal Killing vector field
and is asymptotically conformally flat. It also has black or white hole-like
regions containing trapped surfaces. We describe the properties of the apparent
horizon and comment on the relevance of the solution to the recently discovered
critical behaviour in scalar field collapse.Comment: 10 pages(Latex) (2 figures available upon request), Alberta-Thy-4-9
Quasilocal Energy for a Kerr black hole
The quasilocal energy associated with a constant stationary time slice of the
Kerr spacetime is presented. The calculations are based on a recent proposal
\cite{by} in which quasilocal energy is derived from the Hamiltonian of
spatially bounded gravitational systems. Three different classes of boundary
surfaces for the Kerr slice are considered (constant radius surfaces, round
spheres, and the ergosurface). Their embeddings in both the Kerr slice and flat
three-dimensional space (required as a normalization of the energy) are
analyzed. The energy contained within each surface is explicitly calculated in
the slow rotation regime and its properties discussed in detail. The energy is
a positive, monotonically decreasing function of the boundary surface radius.
It approaches the Arnowitt-Deser-Misner (ADM) mass at spatial infinity and
reduces to (twice) the irreducible mass at the horizon of the Kerr black hole.
The expressions possess the correct static limit and include negative
contributions due to gravitational binding. The energy at the ergosurface is
compared with the energies at other surfaces. Finally, the difficulties
involved in an estimation of the energy in the fast rotation regime are
discussed.Comment: 22 pages, Revtex, Alberta-Thy-18-94. (the approximations in Section
IV have been improved. To appear in Phys. Rev. D
Action and Hamiltonian for eternal black holes
We present the Hamiltonian, quasilocal energy, and angular momentum for a
spacetime region spatially bounded by two timelike surfaces. The results are
applied to the particular case of a spacetime representing an eternal black
hole. It is shown that in the case when the boundaries are located in two
different wedges of the Kruskal diagram, the Hamiltonian is of the form , where and are the Hamiltonian functions for the right
and left wedges respectively. The application of the obtained results to the
thermofield dynamics description of quantum effects in black holes is briefly
discussed.Comment: 24 pages, Revtex, 5 figures (available upon request
The postulates of gravitational thermodynamics
The general principles and logical structure of a thermodynamic formalism
that incorporates strongly self-gravitating systems are presented. This
framework generalizes and simplifies the formulation of thermodynamics
developed by Callen. The definition of extensive variables, the homogeneity
properties of intensive parameters, and the fundamental problem of
gravitational thermodynamics are discussed in detail. In particular, extensive
parameters include quasilocal quantities and are naturally incorporated into a
set of basic general postulates for thermodynamics. These include additivity of
entropies (Massieu functions) and the generalized second law. Fundamental
equations are no longer homogeneous first-order functions of their extensive
variables. It is shown that the postulates lead to a formal resolution of the
fundamental problem despite non-additivity of extensive parameters and
thermodynamic potentials. Therefore, all the results of (gravitational)
thermodynamics are an outgrowth of these postulates. The origin and nature of
the differences with ordinary thermodynamics are analyzed. Consequences of the
formalism include the (spatially) inhomogeneous character of thermodynamic
equilibrium states, a reformulation of the Euler equation, and the absence of a
Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor
corrections included. To appear in Physical Review
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