Quantum Information Paradox: Real or Fictitious?

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of Black Hole (BH) evaporation or accretion. Let us recall that Quantum Mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH would exist, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction of QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an INTEGRATION CONSTANT of Einstein equations. And it has been shown that the value of this integration constant is actually zero. Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an "Eternally Collapsing Object" which is a ball of hot plasma and which is asymptotically approaching the true BH state with M=0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by highest QM acceleration. In any case no EH is ever formed and in reality, there is no quantum information paradox.Comment: 8 pages in Pramana Style, 6 in Revtex styl

A note on the entropy of charged multi - black - holes

Majumdar--Papapetrou multi--black-hole solutions of the Einstein--Maxwell equations are considered in four and higher dimensions. The Euclidean action with boundary conditions appropriate to the canonical ensemble is shown to lead to zero entropy.Comment: LaTeX, 8 page

Regime switching volatility calibration by the Baum-Welch method

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample

Ordinary atom-mirror atom bound states: A new window on the mirror world

Mirror symmetry is a plausible candidate for a fundamental symmetry of particle interactions which can be exactly conserved if a set of mirror particles exist. The properties of the mirror particles seem to provide an excellent candidate to explain the inferred dark matter of the Universe and might also be responsible for a variety of other puzzles in particle physics, astrophysics, meteoritics and planetary science. One such puzzle -- the orthopositronium lifetime problem -- can be explained if there is a small kinetic mixing of ordinary and mirror photons. We show that this kinetic mixing implies the existence of ordinary atom - mirror atom bound states with interesting terrestrial and astrophysical implications. We suggest that sensitive mass spectroscopic studies of ordinary samples containing heavy elements such as lead might reveal the presence of these bound states, as they would appear as anomalously heavy elements. In addition to the effects of single mirror atoms, collective effects from embedded fragments of mirror matter (such as mirror iron microparticles) are also possible. We speculate that such mirror matter fragments might explain a mysterious UV photon burst observed coming from a laser irradiated lead target in a recent experiment.Comment: about 8 pages, couple of change

The evolution of unstable black holes in anti-de Sitter space

We examine the thermodynamic stability of large black holes in four-dimensional anti-de Sitter space, and we demonstrate numerically that black holes which lack local thermodynamic stability often also lack stability against small perturbations. This shows that no-hair theorems do not apply in anti-de Sitter space. A heuristic argument, based on thermodynamics only, suggests that if there are any violations of Cosmic Censorship in the evolution of unstable black holes in anti-de Sitter space, they are beyond the reach of a perturbative analysis.Comment: 29 pages, latex, four figures. For problems printing the figures, see http://viper.princeton.edu/~ssgubser/tachyon/README . v2: minor additions, JHEP versio

Dreibein as prepotential for three-dimensional Yang-Mills theory

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically non-trivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.Comment: 13 pages, improved version, section on Jacobian remove