Back Reaction of Hawking Radiation on Black Hole Geometry

We propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiation results from tunnelling between the two geometries. Using this model, the back reaction correction from Hawking radiation is calculated.Comment: Latex file, 15 pages, 4 figures enclosed, uses eps

Nucleon and nuclear structure functions with non-perturbative and higher order perturbative QCD effects

We have studied the nucleon structure functions $F_{iN}^{EM} (x,Q^2);~i=1,2$, by including contributions due to the higher order perturbative QCD effect up to NNLO and the non-perturbative effects due to the kinematical and dynamical higher twist (HT) effects. The numerical results for $F_{iN}^{EM}(x,Q^2)$ are obtained using Martin, Motylinski, Harland-Lang, Thorne (MMHT) 2014 NLO and NNLO nucleon parton distribution functions (PDFs). The dynamical HT correction has been included following the renormalon approach as well as the phenomenological approach and the kinematical HT effect is incorporated using the works of Schienbein et al. These nucleon structure functions have been used as an input to calculate the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$. In a nucleus, the nuclear corrections arise because of the Fermi motion, binding energy, nucleon correlations, mesonic contribution, shadowing and antishadowing effects. These nuclear corrections are taken into account in the numerical calculations to obtain the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$, for the various nuclear targets like $^{12}C$, $^{27}Al$, $^{56}Fe$, $^{64}Cu$, $^{118}Sn$, $^{197}Au$ and $^{208}Pb$ which are of experimental interest. The effect of isoscalarity correction for nonisoscalar nuclear targets has also been studied. The results for the $F_{iA}^{EM} (x,Q^2)$ are compared with nCTEQ nuclear PDFs parameterization as well as with the experimental results from JLab, SLAC and NMC in the kinematic region of $0.1 \le x \le 0.8$ for several nuclei.Comment: arXiv admin note: text overlap with arXiv:1705.0990

Electromagnetic and Weak Nuclear Structure Functions F1,2(x,Q2)F_{1,2}(x,Q^2) in the Intermediate Region of Q2Q^2

We have studied nuclear structure functions $F_{1A}(x,Q^2)$ and $F_{2A}(x,Q^2)$ for electromagnetic and weak processes in the region of $1 GeV^2 < Q^2 <8 GeV^2$. The nuclear medium effects arising due to Fermi motion, binding energy, nucleon correlations, mesonic contributions and shadowing effects are taken into account using a many body field theoretical approach. The calculations are performed in a local density approximation using a relativistic nucleon spectral function. The results are compared with the available experimental data. Implications of nuclear medium effects on the validity of Callan-Gross relation are also discussed.Comment: Published in Journal of the Physical Society of Japan (NuInt-2015

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

The mathematical principles of tomographic imaging using detected (unscattered) X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field

Scattered Radiation Emission Imaging: Principles and Applications

Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields

On the V-Line Radon Transform and Its Imaging Applications

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results

Cancer Patterns in Karachi Division (1998-1999)

Objective: A minimal cancer incidence data for Karachi, the largest city of Pakistan, is being presented here, for the years 1998-1999. The city has a population of 9,802,134; males 5,261,712 (52.6%) and females 4,540,422 (47.4%); census 19981. Methodology: A predominantly mixed (passive and active) registration system has evolved in Karachi, the data sources being the hospitals within the Karachi Division. The reported/retrieved cancer data sets at the Karachi Cancer Registry are checked, coded, computerised in an analytical format and analysed. Results: The incident cancer cases registered in Karachi, during the 2-year period, 1st January 1998 to 31st December 1999 were analysed. The age-standardised incidence rate (ASR) of cancer, all sites was 132.4/100,000 for the males. Cancer of the lung 10.8%; ASR 17.3 was the most frequently recorded malignancy, followed by oral cavity 10.5%; ASR 13.2 and larynx 5.0%; ASR 7.4. The age-standardised incidence rate (ASR) of cancer, all sites was 133.0/100,000 in the females. Cancer of the breast, 32.0%; ASR 40.7 was the most frequently recorded malignancy, followed by oral cavity 8.1%; ASR 11.7 and gall bladder 3.6%; ASR 5.5. Conclusion: The present data has been calculated with an estimated 15-20% probable under ascertainment. Tobacco-associated cancers in Karachi were responsible for 38.3% of the tumours diagnosed amongst the males. Two principal cancers, breast and oral cavity were responsible for 40.1% of the cancers in females. A rare finding was the high incidence of gall bladder cancer in the females. At present it is difficult to determine whether this indicates a genuine high risk or a selection bias. A continuous process of cancer registration to study the trends in the incidence and an adequate cancer control program are possible and essential for Pakistan and can be based on the pattern being practiced in Karachi