De Sitter Holography with a Finite Number of States

We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hilbert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representations, we show that it is possible to construct an S-matrix that is finite-dimensional, unitary, and de Sitter-invariant. We present a class of examples that realize this idea holographically in terms of spinor fields on the boundary sphere. The finite dimensionality is due to Fermi statistics and an `exclusion principle' that truncates the orthonormal basis in which the spinor fields can be expanded.Comment: 23 pages, 1 eps figure, LaTe

Generalised Separable Solution of Double Phase Flow through Homogeneous Porous Medium in Vertical Downward Direction Due to Difference in Viscosity

In this paper the instability (fingering) phenomenon in a double phase immiscible (oil and water) flow through the homogeneous porous medium with mean capillary pressure in the vertical downward direction is discussed. The mathematical formulation of this problem yields a nonlinear partial differential equation and the generalised separable solution is given in the exponential form. The numerical solution and graphical presentation is given using MAT LAB coding

A strongly changing accretion morphology during the outburst decay of the neutron star X-ray binary 4U 1608−52

It is commonly assumed that the properties and geometry of the accretion flow in transient low-mass X-ray binaries (LMXBs) significantly change when the X-ray luminosity decays below ∼10⁻² of the Eddington limit (L_(Edd)). However, there are few observational cases where the evolution of the accretion flow is tracked in a single X-ray binary over a wide dynamic range. In this work, we use NuSTAR and NICER observations obtained during the 2018 accretion outburst of the neutron star LMXB 4U 1608−52, to study changes in the reflection spectrum. We find that the broad Fe–Kα line and Compton hump, clearly seen during the peak of the outburst when the X-ray luminosity is ∼10³⁷ erg s⁻¹ (∼0.05 L_(Edd)), disappear during the decay of the outburst when the source luminosity drops to ∼4.5 × 10³⁵ erg s⁻¹ (∼0.002 L_(Edd)). We show that this non-detection of the reflection features cannot be explained by the lower signal-to-noise ratio at lower flux, but is instead caused by physical changes in the accretion flow. Simulating synthetic NuSTAR observations on a grid of inner disc radius, disc ionization, and reflection fraction, we find that the disappearance of the reflection features can be explained by either increased disc ionization (log ξ ≳ 4.1) or a much decreased reflection fraction. A changing disc truncation alone, however, cannot account for the lack of reprocessed Fe–Kα emission. The required increase in ionization parameter could occur if the inner accretion flow evaporates from a thin disc into a geometrically thicker flow, such as the commonly assumed formation of a radiatively inefficient accretion flow at lower mass accretion rates

Effective temperature for black holes

The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes are natural candidates for an interpretation in terms of quantum levels. The spectrum of black hole's quasinormal modes can be re-analysed by introducing a black hole's effective temperature which takes into account the fact that, as shown by Parikh and Wilczek, the radiation spectrum cannot be strictly thermal. This issue changes in a fundamental way the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area result modified becoming functions of the quantum "overtone" number n. Consequently, the famous formula of Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates are also modified. Black hole's entropy results a function of the quantum overtone number too. We emphasize that this is the first time that black hole's entropy is directly connected with a quantum number. Previous results in the literature are re-obtained in the limit n \to \infty.Comment: 10 pages,accepted for publication in Journal of High Energy Physics. Comments are welcom

An overview of municipal solid waste management in Jaipur city, India - Current status, challenges and recommendations

In developing countries, urbanization and rapid population growth has resulted in a substantial increase in generation of Municipal Solid Waste (MSW). Safe collection, transportation and treatment of MSW are among the major issues for Indian cities. Poor MSW management practices have negative impact on public health, environment and climate change. India currently only treats 21% of MSW while the remainder disposed in unsanitary landfill sites with no recycling and treatment technologies. This paper reviews the existing MSW management practices, challenges and provides recommendations for improving MSW management for the city of Jaipur in Rajasthan, India. Despite being the state capital as well as the top tourist destination in northern part of India, there is no detailed study which reviews the waste management strategies of this city along with identifying the key challenges. The study reveals that the major challenges for MSW management in Jaipur include uncontrolled landfilling, inadequate public participation as well as failings of implementation of MSW legislation and waste conversion. Recommendations for improvement include public awareness campaigns, public-private partnership, investment in lined landfills, recycling and waste to energy techniques. Optimization models and life cycle assessment tools should be employed to minimize cost and the environmental impact of MSW management. This study will provide policy makers and private sector stakeholders to develop strategies for future planning, investment and execution of improved MSW management in Indian cities

A Study on Google Classroom for Mobile Edification at University level by Using AHP Model for Initial Perceptions – A Case Study of Sankalchand Patel University

In India, many online teaching platforms are being used in universities, colleges, and schools at all levels in the context of COVID-19. This research provides an online teaching platform evaluation system in order to systematically investigate the elements that influence the selection of online teaching platforms. Following a review of a series of factors that have significant influences on the selection of online teaching platforms, eight major factors are identified. Based on the Analytic Hierarchy Process, a hierarchical structure model for online teaching platform selection is constructed. Based on the questionnaire, the rank was the same with both methods for the most preferred question and the least important question, which were derived from Performance Expectancy (PE) and Use Behaviour, respectively (UB). These findings revealed that both techniques produced the same rank for the five likert scale alternatives, with "Agree" being the most important and "Strongly disagree" being the least important. In specifically, the weights of the indicators are calculated and evaluated for each layer in order to achieve the overall ranking and, as a result, the optimal scheme. The following is the order of priority for assessment indicators of online teaching platforms, according to the findings: Google Classroom is useful in this course since it is simple to use and has all of the materials that are required to participate in Google Classroom (internet, Smartphone, laptop, etc.)

Triple-horizon spherically symmetric spacetime and holographic principle

We present a family of spherically symmetric spacetimes, specified by the density profile of a vacuum dark energy, which have the same global structure as the de Sitter spacetime but the reduced symmetry which leads to a time-evolving and spatially inhomogeneous cosmological term. It connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. This family contains a special class distinguished by dynamics of evaporation of a cosmological horizon which evolves to the triple horizon with the finite entropy, zero temperature, zero curvature, infinite positive specific heat, and infinite scrambling time. Non-zero value of the cosmological constant in the triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of the cosmological horizon.Comment: Honorable Mentioned Essay - Gravity Research Foundation 2012; submitted to Int. J. Mod. Phys.

Maternal and fetal outcome in cases of eclampsia

Background: Eclampsia refers to occurrence of generalized tonic clonic convulsions (GTCS) followed by confusion or coma during pregnancy or puerperium in patients with preeclampsia excluding other neurological conditions. Purpose of this study was to evaluate the risk factors, management protocols and determine maternal and perinatal morbidity and mortality in patients of eclampsia.Methods: This is retrospective study of 180 cases of eclampsia carried out from June 2017 to December 2019 including all the antepartum, intrapartum and postpartum cases at tertiary care centre. Immediate management was focused to control the convulsion and lower the blood pressure followed by NST and USG foetus with Doppler study.Results: In this study, 72.2% cases reported antepartum eclampsia while 27.8% cases were postpartum and overall incidence was 0.91% of total deliveries conducted during the study period. Incidence was higher in primigravida (74.4%) and below 25 years age (68.8%). Magnesium sulphate was effective in 94.4% cases. Study reports 63 normal vaginal delivery, 5 assisted vaginal delivery, 110 caesarean section and 2 women expired undelivered. There were 10 maternal deaths.Conclusions: Time interval between eclamptic seizures and initiation of therapy is an important prognostic factor affecting maternal and perinatal outcome. Public awareness regarding the importance of regular antenatal visits can help in reducing chances of development of eclampsia. Even though various drugs and methods have been tried for the treatment of eclampsia, the definitive management is the delivery of foetus after control of convulsion, hypertension and should be managed at tertiary care hospital