Cycles in the chamber homology of GL(3)

Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the existence of parahoric types for GL(N). We construct representative cycles in all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction

Left handed DNA in synthetic and topologically constrained form V DNA and its implications in protein recognition

We have investigated structural transitions in Poly(dG-dC) and Poly(dG-Me5dC) in order to understand the exact role of cations in stabilizing left-handed helical structures in specific sequences and the biological role, if any, of these structures. From a novel temperature dependent Z⇌B transition it has been shown that a minor fluctuation in Na+ concentration at ambient temperature can bring about B to Z transition. For the first time, we have observed a novel Z⇌B⇌Zuble transition in poly(dG-Me5dC) as the Na+ concentration is gradually increased. This suggests that a minor fluctuation in Na+ concentration in conjunction with methylation may transform small stretches of CG sequences from one conformational state to another. These stretches could probably serve as sites for regulation. Supercoiled form V DNA reconstituted from pBR322 and pβG plasmids have been studied as model systems, in order to understand the nature and role of left-handed helical conformation in natural sequences. A large portion of DNA in form V, obtained by reannealing the two complementary singlestranded circles is forced to adopt left-handed double helical structure due to topological constraints (Lk=0). Binding studies with Z-DNA specific antibody and spectroscopic studies confirm the presence of left-handed Z-structure in the pβG and pβR322 form V DNA. Cobalt hexamine chloride, which induces Z-form in Poly(dG-dC) stabilizes the Z-conformation in form V DNA even in the non-alternating purine-pyrimidine sequences. A reverse effect is observed with ethidium bromide. Interestingly, both topoisomerase I and II (from wheat germ) act effectively on form V DNA to give rise to a species having an electrophoretic mobility on agarose gel similar to that of open circular (form II) DNA. Whether this molecule is formed as a result of the left-handed helical segments of form V DNA undergoing a transition to the right-handed B-form during the topoisomerase action remains to be solved

Lorentz-breaking effects in scalar-tensor theories of gravity

In this work, we study the effects of breaking Lorentz symmetry in scalar-tensor theories of gravity taking torsion into account. We show that a space-time with torsion interacting with a Maxwell field by means of a Chern-Simons-like term is able to explain the optical activity in syncrotron radiation emitted by cosmological distant radio sources. Without specifying the source of the dilaton-gravity, we study the dilaton-solution. We analyse the physical implications of this result in the Jordan-Fierz frame. We also analyse the effects of the Lorentz breaking in the cosmic string formation process. We obtain the solution corresponding to a cosmic string in the presence of torsion by keeping track of the effects of the Chern-Simons coupling and calculate the charge induced on this cosmic string in this framework. We also show that the resulting charged cosmic string gives us important effects concerning the background radiation.The optical activity in this case is also worked out and discussed.Comment: 10 pages, no figures, ReVTex forma

Membrane paradigm realized?

Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.Comment: 8 pages, Latex, 3 figures (Essay given second place in Gravity Research Foundation essay competition 2010

The quantum structure of black holes

We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of 2-charge microstates, and explore how `fractionation' can lead to quantum effects over macroscopic length scales of order the horizon radius.Comment: Review article, 58 pages, 2 figures; references added, note about topics covere

Radiation from the non-extremal fuzzball

The fuzzball proposal says that the information of the black hole state is distributed throughout the interior of the horizon in a `quantum fuzz'. There are special microstates where in the dual CFT we have `many excitations in the same state'; these are described by regular classical geometries without horizons. Jejjala et.al constructed non-extremal regular geometries of this type. Cardoso et. al then found that these geometries had a classical instability. In this paper we show that the energy radiated through the unstable modes is exactly the Hawking radiation for these microstates. We do this by (i) starting with the semiclassical Hawking radiation rate (ii) using it to find the emission vertex in the CFT (iii) replacing the Boltzman distributions of the generic CFT state with the ones describing the microstate of interest (iv) observing that the emission now reproduces the classical instability. Because the CFT has `many excitations in the same state' we get the physics of a Bose-Einstein condensate rather than a thermal gas, and the usually slow Hawking emission increases, by Bose enhancement, to a classically radiated field. This system therefore provides a complete gravity description of information-carrying radiation from a special microstate of the nonextremal hole.Comment: corrected typo

Evaporating Black Holes and Entropy

We study the Hawking radiation for the geometry of an evaporating 1+1 dimensional black hole. We compute Bogoliubov coefficients and the stress tensor. We use a recent result of Srednicki to estimate the entropy of entanglement produced in the evaporation process, for the 1+1 dimensional hole and for the 3+1 dimensional hole. It is found that the one space dimensional result of Srednicki is the pertinent one to use, in both cases.Comment: 29 pages, one figure (available from authors), Latex. (Mailer errors removed.

The information paradox: A pedagogical introduction

The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a `theorem': assuming `traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show the the interior of black holes have a `fuzzball' structure. This nontrivial structure of microstates resolves the information paradox, and gives a qualitative picture of how classical intuition can break down in black hole physics.Comment: 38 pages, 7 figures, Latex (Expanded form of lectures given at CERN for the RTN Winter School, Feb 09), typo correcte