On the Entropy of a Quantum Field in the Rotating Black Holes

By using the brick wall method we calculate the free energy and the entropy of the scalar field in the rotating black holes. As one approaches the stationary limit surface rather than the event horizon in comoving frame, those become divergent. Only when the field is comoving with the black hole (i.e. $\Omega_0 = \Omega_H$) those become divergent at the event horizon. In the Hartle-Hawking state the leading terms of the entropy are $A \frac{1}{h} + B \ln(h) + finite$, where $h$ is the cut-off in the radial coordnate near the horizon. In term of the proper distance cut-off $\epsilon$ it is written as $S = N A_H/\epsilon^2$. The origin of the divergence is that the density of state on the stationary surface and beyond it diverges.Comment: Latex, 23 pages, 7 eps figure

Remarks on 't Hooft's Brick Wall Model

A semi-classical reasoning leads to the non-commutativity of the space and time coordinates near the horizon of Schwarzschild black hole. This non-commutativity in turn provides a mechanism to interpret the brick wall thickness hypothesis in 't Hooft's brick wall model as well as the boundary condition imposed for the field considered. For concreteness, we consider a noncommutative scalar field model near the horizon and derive the effective metric via the equation of motion of noncommutative scalar field. This metric displays a new horizon in addition to the original one associated with the Schwarzschild black hole. The infinite red-shifting of the scalar field on the new horizon determines the range of the noncommutativ space and explains the relevant boundary condition for the field. This range enables us to calculate the entropy of black hole as proportional to the area of its original horizon along the same line as in 't Hooft's model, and the thickness of the brick wall is found to be proportional to the thermal average of the noncommutative space-time range. The Hawking temperature has been derived in this formalism. The study here represents an attempt to reveal some physics beyond the brick wall model.Comment: RevTeX, 5 pages, no figure

Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture

The axial anomaly equation in 1+1 dimensional QED is obtained on the lattice for fermions obeying the Ginsparg-Wilson relation. We make use of the properties of the Lattice Dirac sea to investigate the connection between the anomaly and the Ginsparg-Wilson operator in the Hamiltonian picture. The correct anomaly is reproduced for gauge fields whose characteristic time is much larger than the lattice spacing, which is the regime where the adiabatic approximation applies. A non-zero Wilson $r$ parameter is necessary to get the correct anomaly. The anomaly is shown to be independent of $r$ for $r>0.5$. The generalization to 3+1 dimensions is also discussed.Comment: 19 pages latex,12 figures; manuscript revised, references adde

World experience in management and development of transport and logistics systems

1. Масенко Т.Є. Проблеми управління транспортно-логістичними системами України та перспективи розвитку в контексті європейської інтеграції / Т.Є. Масенко, С.Г. Шевченко // Науковий вісник НЛТУУ. – 2007. –№ 17.2. – 301–305. 2. Гринів Л.В. Шляхи підвищення конкурентоспроможності міжнародних транспортних перевезень / Л.В. Гринів, С.М. Синиця // Наука й економіка. – 2010. – № 3 (19). – С.115–121. 3. Кузьменко А. В. Досвід та закономірності формування світової транспортно-логістичної інфраструктури / А. В. Кузьменко // Журнал науковий огляд. – 2015. – № 7 (17). – С. 1-14. 4. Питуляк Н. С. Зарубіжний досвід функціонування логістичних центрів. Маркетинг інновацій і інновації в маркетингу: збірник тез доповідей Четвертої міжнародної науково- практичної конференції (29 вересня – 1 жовтня 2010 року). Суми: Сумський державний університет. – 2010. –С. 175–177. 5. Транспортно-логістичні центри: світовий досвід. URL: http://www.elc-ua.com/ru/news/60. 6. Кирлик Н.Ю. Європейський досвід розвитку транспортно-логістичних центрів URL: https://dspace.uzhnu.edu.ua/jspui/bitstream/lib/31122/1.pdf. 7. Тарнавська Н.П. Організаційні та інфраструктурні передумови створення міжнародного логістичного центру / Тарнавська Н.П., Сивак Р.Б. // Бізнес–Інформ. – 2013. – № 13. – С. 29–35. 8. Китай: транспортна мережа. [Електронний ресурс]. – Режим доступу: https://dovidka.biz.ua/kitay-transportna-merezha. 9. Пасічник А.М., Кутирєв В.В. Світовий досвід створення транспортно-логістичної Інфраструктури: стан та перспективи застосування в Україні. [Електронний ресурс]. – Режим доступу: http://biblio.umsf.dp.ua/jspui/bitstream/123456789/1986/1.pdf. 10. Китай продовжує вливати інвестиції у транспортну інфраструктуру. [Електронний ресурс]. – Режим доступу: https://logist.today/uk/dnevnik_logista/2017-12-27/kitaj-prodolzhaet-vlivat-investicii-v-transportnuju-infrastrukturu.Розглянуто світовий досвід управління та розвитку транспортно-логістичних систем. Показано, що постійні інвестиції у розвиток транспортно-логістичних систем та їх модернізація є вирішальним фактором зростання.The world experience of management and development of transport and logistics systems is considered. It is shown that constant investment in the development of transport and logistics systems and their modernization is a decisive factor in growth

Unruh Radiation, Holography and Boundary Cosmology

A uniformly acclerated observer in anti-deSitter space-time is known to detect thermal radiation when the acceleration exceeds a critical value. We investigate the holographic interpretation of this phenomenon. For uniformly accelerated trajectories transverse to the boundary of the AdS space, the hologram is a blob which expands along the boundary. Observers on the boundary co-moving with the hologram become observers in cosmological space-times. For supercritical accelerations one gets a Milne universe when the holographic screen is the boundary in Poincare coordinates, while for the boundary in hyperspherical coordinates one gets deSitter spacetimes. The presence or absence of thermality is then interpreted in terms of specific classes of observers in these cosmologies.Comment: LaTeX, 35 pages, 3 figures. A reference is added and typos are correcte

Tachyon Dynamics and the Effective Action Approximation

Recently effective actions have been extensively used to describe tachyon condensation in string theory. While the various effective actions which have appeared in the literature have very similar properties for static configurations, they differ for time-dependent tachyons. In this paper we discuss general properties of non-linear effective Lagrangians which are first order in derivatives. In particular we show that some observed properties, such as asymptotically vanishing pressure, are rather generic features, although the quantative features differ. On the other hand we argue that certain features of marginal tachyon profiles are beyond the reach of any first order Lagrangian description. We also point out that an effective action, proposed earlier, captures the dynamics of tachyons well.Comment: References added and confusing reference clarifie

Metric Fluctuation Corrections to Hawking Radiation

We study how fluctuations of the black hole geometry affect the properties of Hawking radiation. Even though we treat the fluctuations classically, we believe that the results so obtained indicate what might be the effects induced by quantum fluctuations in a self consistent treatment. To characterize the fluctuations, we use the model introduced by York in which they are described by an advanced Vaidya metric with a fluctuating mass. Under the assumption of spherical symmetry, we solve the equation of null outgoing rays. Then, by neglecting the greybody factor, we calculate the late time corrections to the s-wave contributions of the energy flux and the asymptotic spectrum. We find three kind of modifications. Firstly, the energy flux fluctuates around its average value with amplitudes and frequencies determined by those of the metric fluctuations. Secondly, this average value receives two positive contributions one of which can be reinterpreted as due to the `renormalisation' of the surface gravity induced by the metric fluctuations. Finally, the asymptotic spectrum is modified by the addition of terms containing thermal factors in which the frequency of the metric fluctuations acts as a chemical potential.Comment: 27 pages, 2 figures, LaTeX. Revised versio

Thermal partition function of photons and gravitons in a Rindler wedge

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order temperature dependence $T^4$ is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded. It is argued that similar terms could appear dealing with any integer spin $s\geq 1$ in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.

Does the generalized second law hold in the form of time derivative expression?

We investigate whether the generalized second law is valid, using two dimensional black hole spacetime, irrespective of models. A time derivative form of the generalized second law is formulated and it is shown that the law might become invalid. The way to resolve this difficulty is also presented and discussed.Comment: 12 pages, 3 figures, revte

Hawking Radiation as Tunneling for Extremal and Rotating Black Holes

The issue concerning semi-classical methods recently developed in deriving the conditions for Hawking radiation as tunneling, is revisited and applied also to rotating black hole solutions as well as to the extremal cases. It is noticed how the tunneling method fixes the temperature of extremal black hole to be zero, unlike the Euclidean regularity method that allows an arbitrary compactification period. A comparison with other approaches is presented.Comment: 17 pages, Latex document, typos corrected, four more references, improved discussion in section