17 research outputs found
Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal Coverings
A set of simple rules for constructing the maximal (e.g. analytic) extensions
for any metric with a Killing field in an (effectively) two-dimensional
spacetime is formulated. The application of these rules is extremely
straightforward, as is demonstrated at various examples and illustrated with
numerous figures. Despite the resulting simplicity we also comment on some
subtleties concerning the concept of Penrose diagrams. Most noteworthy among
these, maybe, is that (smooth) spacetimes which have both degenerate and
non-degenerate (Killing) horizons do not allow for globally smooth Penrose
diagrams. Physically speaking this obstruction corresponds to an infinite
relative red/blueshift between observers moving across the two horizons. -- The
present work provides a further step in the classification of all global
solutions of the general class of two-dimensional gravity-Yang-Mills systems
introduced in Part I, comprising, e.g., all generalized (linear and nonlinear)
dilaton theories. In Part I we constructed the local solutions, which were
found to always have a Killing field; in this paper we provide all universal
covering solutions (the simply connected maximally extended spacetimes). A
subsequent Part III will treat the diffeomorphism inequivalent solutions for
all other spacetime topologies. -- Part II is kept entirely self-contained; a
prior reading of Part I is not necessary.Comment: 29 pages, 14 Postscript figures; one figure, some paragraphs, and
references added; to appear in Class. Quantum Gra
Exactly solvable models in 2D semiclassical dilaton gravity and extremal black holes
Previously known exactly solvable models of 2D semiclassical dilaton gravity
admit, in the general case, only non-extreme black holes. It is shown that
there exist exceptional degenerate cases, that can be obtained by some limiting
transitions from the general exact solution, which include, in particular,
extremal and ultraextremal black holes. We also analyze properties of extreme
black holes without demanding exact solvability and show that for such
solutions quantum backreaction forbids the existence of ultraextreme black
holes. The conditions,under which divergencies of quantum stresses in a free
falling frame can disappear, are found. We derive the closed equation with
respect to the metric as a function of the dilaton field that enables one,
choosing the form of the metric, to restore corresponding Lagrangian. It is
demonstrated that exactly solvable models, found earlier, can be extended to
include an electric charge only in two cases: either the dilaton-gravitation
coupling is proportional to the potential term, or the latter vanishes. The
second case leads to the effective potential with a negative amplitude and we
analyze, how this fact affects the structure of spacetime. We also discuss the
role of quantum backreaction in the relationship between extremal horizons and
the branch of solutions with a constant dilaton.Comment: 31 pages. In v.2 typo in Ref. [2] corrected, 4 references added.
Accepted in Class. Quant. Gra
A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field
We present a solvable model of two-dimensional dilaton-gravity coupled to a
massless scalar field. We locally integrate the field equations and briefly
discuss the properties of the solutions. For a particular choice of the
coupling between the dilaton and the scalar field the model can be interpreted
as the two-dimensional effective theory of 2+1 cylindrical gravity minimally
coupled to a massless scalar field.Comment: 6 pages, RevTeX, to be published in Phys. Rev.
Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity
Various studies have explored the possibility of explaining the
Bekenstein-Hawking (black hole) entropy by way of some suitable state-counting
procedure. Notably, many of these treatments have used the well-known Cardy
formula as an intermediate step. Our current interest is a recent calculation
in which Carlip has deduced the leading-order quantum correction to the
(otherwise) classical Cardy formula. In this paper, we apply Carlip's
formulation to the case of a generic model of two-dimensional gravity with
coupling to a dilaton field. We find that the corrected Cardy entropy includes
the anticipated logarithmic ``area'' term. Such a term is also evident when the
entropic correction is derived independently by thermodynamic means. However,
there is an apparent discrepancy between the two calculations with regard to
the factor in front of the logarithm. In fact, the two values of this prefactor
can only agree for very specific two-dimensional models, such as that
describing Jackiw-Teitelboim theory.Comment: 18 pages, Latex; references adde
Quantum-Corrected Entropy for 1+1-Dimensional Gravity Revisited
In this paper, we examine a generic theory of 1+1-dimensional gravity with
coupling to a scalar field. Special attention is paid to a class of models that
have a power-law form of dilaton potential and can capably admit black hole
solutions. The study focuses on the formulation of a Lorentzian partition
function. We incorporate the principles of Hamiltonian thermodynamics, as well
as black hole spectroscopy, and find that the partition function can be
expressed in a well-defined, calculable form. We then go on to extract the
black hole entropy, including the leading-order quantum correction. As
anticipated, this correction can be expressed as the logarithm of the classical
entropy. Interestingly, the prefactor for this logarithmic correction
disagrees, in both magnitude and sign, with the findings from a prior study (on
the very same model). We comment on this discrepancy and provide a possible
rationalization.Comment: 22 pages of Latex; References added and minor change
Spa therapy: can be a valid option for treating knee osteoarthritis?
Osteoarthritis (OA) continues to be one of the leading causes of 'years lived with disability' worldwide. Symptomatic knee OA is highly prevalent among people aged 50Â years and over and is destined to become an ever more important healthcare problem. Current management of knee OA includes non-pharmacological and pharmacological treatments. Spa therapy is one of the most commonly used non-pharmacological approaches for OA in many European countries, as well as in Japan and Israel. Despite its long history and popularity, spa treatment is still the subject of debate and its role in modern medicine continues to be unclear. The objective of this review is to summarize the currently available information on clinical effects and mechanisms of action of spa therapy in knee OA. Various randomized controlled clinical trials (RCTs) were conducted to assess the efficacy and tolerability of balneotherapy and mud-pack therapy in patients with knee OA. Data from these clinical trials support a beneficial effect of spa therapy on pain, function and quality of life in knee OA that lasts over time, until 6-9Â months after the treatment. The mechanisms by which immersion in mineral or thermal water or the application of mud alleviate suffering in OA are not fully understood. The net benefit is probably the result of a combination of factors, among which the mechanical, thermal and chemical effects are most prominent. In conclusion, spa therapy seems to have a role in the treatment of knee OA. Additional RCTs and further studies of mechanisms of action with high methodological quality are necessary to prove the effects of spa therapy