880 research outputs found
Dirty black holes: Entropy versus area
Considerable interest has recently been expressed in the entropy versus area
relationship for ``dirty'' black holes --- black holes in interaction with
various classical matter fields, distorted by higher derivative gravity, or
infested with various forms of quantum hair. In many cases it is found that the
entropy is simply related to the area of the event horizon: S = k
A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for:
Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On
the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of
(Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair.
The pattern underlying these results is less than clear. This paper
systematizes these results by deriving a general formula for the entropy: S =
{k A_H/(4\ell_P^2)}
+ {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu
+ \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector,
V^\mu the four velocity of a co--rotating observer.) If no hair is present the
validity of the ``entropy = (1/4) area'' law reduces to the question of whether
or not the Lorentzian energy density for the system under consideration is
formally equal to the Euclideanized Lagrangian. ****** To appear in Physical
Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references
updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision
A L\'evy input fluid queue with input and workload regulation
We consider a queuing model with the workload evolving between consecutive
i.i.d.\ exponential timers according to a
spectrally positive L\'evy process that is reflected at zero, and
where the environment equals 0 or 1. When the exponential clock
ends, the workload, as well as the L\'evy input process, are modified; this
modification may depend on the current value of the workload, the maximum and
the minimum workload observed during the previous cycle, and the environment
of the L\'evy input process itself during the previous cycle. We analyse
the steady-state workload distribution for this model. The main theme of the
analysis is the systematic application of non-trivial functionals, derived
within the framework of fluctuation theory of L\'evy processes, to workload and
queuing models
Black Holes with a Generalized Gravitational Action
Microscopic black holes are sensitive to higher dimension operators in the
gravitational action. We compute the influence of these operators on the
Schwarzschild solution using perturbation theory. All (time reversal invariant)
operators of dimension six are included (dimension four operators don't alter
the Schwarzschild solution). Corrections to the relation between the Hawking
temperature and the black hole mass are found. The entropy is calculated using
the Gibbons-Hawking prescription for the Euclidean path integral and using
naive thermodynamic reasoning. These two methods agree, however, the entropy is
not equal to 1/4 the area of the horizon.Comment: plain tex(uses phyzzx.tex), 8 pages, CALT-68-185
Quantum Cosmology for a Quadratic Theory of Gravity
For pure fourth order () quantum cosmology the
Wheeler-DeWitt equation is solved exactly for the closed homogeneous and
isotropic model. It is shown that by imposing as boundary condition that at the origin of the universe the wave functions behave as suggested by
Vilenkin.Comment: 13 pages, latex,no figure
Classical and Quantum Solutions and the Problem of Time in Cosmology
We have studied various classical solutions in cosmology. Especially we
have obtained general classical solutions in pure \ cosmology. Even in the
quantum theory, we can solve the Wheeler-DeWitt equation in pure \
cosmology exactly. Comparing these classical and quantum solutions in \
cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte
Cosmological dynamics in six-order gravity
We consider cosmological dynamics in generalized modified gravity theory with
the term added to the action of the form . Influence of term to the known solutions of modified gravity is described. We show
that in particular case of these two non-Einstein terms are equally
important on power-law solutions. These solutions and their stability have been
studied using dynamical system approach. Some results for the case of
(including stability of de Sitter solution in the theory under investigation)
have been found using other methods
Charged Black Holes In Quadratic Theories
We point out that in general the Reissner-Nordstr\"om (RN) charged black
holes of general relativity are not solutions of the four dimensional quadratic
gravitational theories. They are, e.g., exact solutions of the
quadratic theory but not of a theory where a term is present in
the gravitational Lagrangian. In the case where such a non linear curvature
term is present with sufficiently small coupling, we obtain an approximate
solution for a charged black hole of charge and mass . For the
validity of this solution extends down to the horizon. This allows us to
explore the thermodynamic properties of the quadratic charged black hole and we
find that, to our approximation, its thermodynamics is identical to that of a
RN black hole. However our black hole's entropy is not equal to the one fourth
of the horizon area. Finally we extend our analysis to the rotating charged
black hole and qualitatively similar results are obtained.Comment: 11 pages, LaTeX/RevTeX3.
Gravitational Entropy and Global Structure
The underlying reason for the existence of gravitational entropy is traced to
the impossibility of foliating topologically non-trivial Euclidean spacetimes
with a time function to give a unitary Hamiltonian evolution. In dimensions
the entropy can be expressed in terms of the obstructions to foliation,
bolts and Misner strings, by a universal formula. We illustrate with a number
of examples including spaces with nut charge. In these cases, the entropy is
not just a quarter the area of the bolt, as it is for black holes.Comment: 18 pages. References adde
Extended Gravity Theories and the Einstein-Hilbert Action
I discuss the relation between arbitrarily high-order theories of gravity and
scalar-tensor gravity at the level of the field equations and the action. I
show that -order gravity is dynamically equivalent to Brans-Dicke
gravity with an interaction potential for the Brans-Dicke field and further
scalar fields. This scalar-tensor action is then conformally equivalent to the
Einstein-Hilbert action with scalar fields. This clarifies the nature and
extent of the conformal equivalence between extended gravity theories and
general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-
Quantum Cosmology and Higher-Order Lagrangian Theories
In this paper the quantum cosmological consequences of introducing a term
cubic in the Ricci curvature scalar into the Einstein--Hilbert action are
investigated. It is argued that this term represents a more generic
perturbation to the action than the quadratic correction usually considered. A
qualitative argument suggests that there exists a region of parameter space in
which neither the tunneling nor the no-boundary boundary conditions predict an
epoch of inflation that can solve the horizon and flatness problems of the big
bang model. This is in contrast to the --theory.Comment: 13 pages, LaTeX, preprint FERMILAB-Pub-94/XXX-A, March 199
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