23,944 research outputs found
Charge Loss (or the Lack Thereof) for AdS Black Holes
The evolution of evaporating charged black holes is complicated to model in
general, but is nevertheless important since the hints to the Information Loss
Paradox and its recent firewall incarnation may lie in understanding more
generic geometries than that of Schwarzschild spacetime. Fortunately, for
sufficiently large asymptotically flat Reissner-Nordstrom black holes, the
evaporation process can be modeled via a system of coupled linear ordinary
differential equations, with charge loss rate governed by Schwinger
pair-production process. The same model can be generalized to study the
evaporation of AdS Reissner-Nordstrom black holes with flat horizon. It was
recently found that such black holes always evolve towards extremality since
charge loss is inefficient. This property is completely opposite to the
asymptotically flat case in which the black hole eventually loses its charges
and tends towards Schwarzschild limit. We clarify the underlying reason for
this different behavior.Comment: References updated. Published in JHE
The Fate of Monsters in Anti-de Sitter Spacetime
Black hole entropy remains a deep puzzle: where does such enormous amount of
entropy come from? Curiously, there exist gravitational configurations that
possess even larger entropy than a black hole of the same mass, in fact,
arbitrarily high entropy. These are the so-called monsters, which are
problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT)
correspondence paradigm since there is far insufficient degrees of freedom on
the field theory side to account for the enormous entropy of monsters in AdS
bulk. The physics of the bulk however may be considerably modified at
semi-classical level due to the presence of branes. We show that this is
especially so since monster spacetimes are unstable due to brane nucleation. As
a consequence, it is not clear what the final fate of monsters is. We argue
that in some cases there is no real threat from monsters since although they
are solutions to Einstein's Field Equations, they are very likely to be
completely unstable when embedded in string theory, and thus probably are not
solutions to the full quantum theory of gravity. Our analysis, while suggestive
and supportive of the claim that such pathological objects are not allowed in
the final theory, by itself does not rule out all monsters. We comment on
various kin of monsters such as the bag-of-gold spacetime, and also discuss
briefly the implications of our work to some puzzles related to black hole
entropy.Comment: Version accepted by JHE
Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schr\"odinger Equation
We show that the method of splitting the operator
to fourth order with purely positive coefficients produces excellent algorithms
for solving the time-dependent Schr\"odinger equation. These algorithms require
knowing the potential and the gradient of the potential. One 4th order
algorithm only requires four Fast Fourier Transformations per iteration. In a
one dimensional scattering problem, the 4th order error coefficients of these
new algorithms are roughly 500 times smaller than fourth order algorithms with
negative coefficient, such as those based on the traditional Ruth-Forest
symplectic integrator. These algorithms can produce converged results of
conventional second or fourth order algorithms using time steps 5 to 10 times
as large. Iterating these positive coefficient algorithms to 6th order also
produced better converged algorithms than iterating the Ruth-Forest algorithm
to 6th order or using Yoshida's 6th order algorithm A directly.Comment: 11 pages, 2 figures, submitted to J. Chem. Phy
Adaptive Learning and Monetary Policy: Lessons from Japan
Motivated by Japan's economic experiences and policy debates over the past two decades, this paper uses a dynamic general equilibrium open economy model to examine the volatility and welfare impact of alternative monetary policies. To capture the dynamic effects of likely structural breaks in the Japanese economy, we model agents’ expectation formation process with an adaptive learning framework, and compare four Taylor-styled policy rules that reflect concerns commonly raised in Japan's actual monetary policy debate. We first show that imperfect knowledge and the associated learning process induce higher volatility in the economy, while still retaining some of the policy conclusions from rational-expectations setups. In particular, explicit exchange rate stabilization is unwarranted; moreover, under volatile foreign disturbances, policymakers should consider targeting domestic price inflation rather than consumer price inflation. However, contrary to results based on rational expectations, we show that even though highly inflation-sensitive rules do raise output volatility, they may nevertheless improve overall welfare in an adaptive learning setting by smoothing inflation fluctuations. Our findings suggest that previous policy conclusions that are based on partial equilibrium analyses, or that ignore likely deviations from rational expectations, may not be robust.
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