Horizon State, Hawking Radiation and Boundary Liouville Model

We demonstrate that the near-horizon physics, the Hawking radiation and the reflection off the radial potential barrier, can be understood entirely within a conformal field theory picture in terms of one- and two-point functions in the boundary Liouville theory. An important element in this demonstration is the notion of {\it horizon state}, the Hawking radiation being interpreted as a result of the transition of horizon state to the ordinary states propagating outside black hole horizon.Comment: Revtex, 5pages; final version to appear in Phys.Rev.Let

Remarks on effective action and entanglement entropy of Maxwell field in generic gauge

We analyze the dependence of the effective action and the entanglement entropy in the Maxwell theory on the gauge fixing parameter $a$ in $d$ dimensions. For a generic value of $a$ the corresponding vector operator is nonminimal. The operator can be diagonalized in terms of the transverse and longitudinal modes. Using this factorization we obtain an expression for the heat kernel coefficients of the nonminimal operator in terms of the coefficients of two minimal Beltrami-Laplace operators acting on 0- and 1-forms. This expression agrees with an earlier result by Gilkey et al. Working in a regularization scheme with the dimensionful UV regulators we introduce three different regulators: for transverse, longitudinal and ghost modes, respectively. We then show that the effective action and the entanglement entropy do not depend on the gauge fixing parameter $a$ provided the certain ($a$-dependent) relations are imposed on the regulators. Comparing the entanglement entropy with the black hole entropy expressed in terms of the induced Newton's constant we conclude that their difference, the so-called Kabat's contact term, does not depend on the gauge fixing parameter $a$. We consider this as an indication of gauge invariance of the contact term.Comment: 15 pages; v2: typos in eqs. (31), (32), (34), (36) corrected; discussion in section 6 expande

BTZ Black Hole with Chern-Simons and Higher Derivative Terms

The entropy of a BTZ black hole in the presence of gravitational Chern-Simons terms has previously been analyzed using Euclidean action formalism. In this paper we treat the BTZ solution as a two dimensional black hole by regarding the angular coordinate as a compact direction, and use Wald's Noether charge method to calculate the entropy of this black hole in the presence of higher derivative and gravitational Chern-Simons terms. The parameters labelling the black hole solution can be determined by extremizing an entropy function whose value at the extremum gives the entropy of the black hole.Comment: LaTeX file, 11 page

Entanglement Entropy in Non-Relativistic Field Theories

We calculate entanglement entropy in a non-relativistic field theory described by the Schr\"odinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the relativistic field theory. These observations are further supported by a holographic consideration. We use the non-relativistic symmetry and completely specify entanglement entropy in large class of non-relativistic theories described by the field operators polynomial in derivatives. We suggest that the area law of the entropy can be tested in experiments with condensed matter systems such as liquid helium.Comment: 4 pages; v2: discussion of interacting fields include

Non-minimal coupling and quantum entropy of black hole

Formulating the statistical mechanics for a scalar field with non-minimal $\xi R \phi^2$ coupling in a black hole background we propose modification of the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and allows one to obtain the statistical entropy dependent on the non-minimal coupling. For $\xi<0$ the entropy renormalizes the classical Bekenstein-Hawking entropy in the correct way and agrees with the result previously obtained within the conical singularity approach. For a positive $\xi$, however, the results differ.Comment: 16 pages, latex, no figures; an error in calculation of the entropy corrected, the entropy now is positive for any non-minimal couplin

Quantum entropy of the Kerr black hole arising from gravitational perturbation

The quantum entropy of the Kerr black hole arising from gravitational perturbation is investigated by using Null tetrad and \'t Hooft\'s brick-wall model. It is shown that effect of the graviton\'s spins on the subleading correction is dependent of the square of the spins and the angular momentum per unit mass of the black hole, and contribution of the logarithmic term to the entropy will be positive, zero, and negative for different value of $a/r_+$.Comment: 8 pages, 1 figure, Latex. to appear in Phys. Rev.

PRINCIPIOS DE DESARROLLO DE LA EDUCACIÓN SUPERIOR EN TRABAJOS DE FILOSÓFEROS Y CIENTÍFICOS RUSOS DEL SIGLO XX

Introducción: el artículo está dedicado a la investigación de la educación superior en diversos aspectos, se presentan los resultados de su reconocimiento en el pensamiento científico y filosófico nacional del siglo XX, se detecta la conexión con las tendencias europeas comunes de la escuela superior. Se consideran las opiniones de los filósofos y científicos rusos populares que hicieron su contribución a la base ideológica y los principios de la educación universitaria en Rusia en el siglo XX. Materiales y métodos: los métodos se basan en tradiciones de investigación del conocimiento humano: enfoque filosófico-antropológico de los problemas de la existencia humana, método comparativo de consideración de problemas educativos en relación con diversos contextos culturales e históricos del desarrollo de la existencia humana, método comparativo-histórico. Además de eso se reflejan los métodos de investigación fenomenológica y hermenéutica. Se detectan y comprenden filosóficamente las bases, los contenidos, los objetivos y las metas del sistema educativo, incluida la educación universitaria y la conexión de la educación con las investigaciones reales del ser humano y la sociedad contemporáneos. Resultados de la investigación: se presenta en el artículo que los principales enfoques de la educación y los resultados de su comprensión por parte de los pensadores rusos comprenden la unidad de contenido y resuenan con los problemas reales de su estructura y contenido en términos del mundo moderno, incluida la realidad rusa. Por lo tanto, se confirma la idea de la necesidad de una combinación óptima de conocimiento científico natural, especial y filosófico en el sistema educativo. Tal enfoque permite desarrollar la educación en términos de valores humanitarios, facilita la formación de la personalidad moral y espiritualmente orientada y socialmente responsable del especialista, ejerciendo una visión del mundo razonable. Discusión y conclusión: los resultados recibidos pueden usarse para ejercer los principios del desarrollo de la educación superior en términos de desafíos contemporáneos basados en el principio de sucesión y el mantenimiento de las mayores tradiciones culturales, y también para la planificación estratégica de los programas educativos de la Universidad.Introdução: o artigo é dedicado à pesquisa do ensino superior em vários aspectos, são apresentados os resultados do seu reconhecimento no pensamento científico e filosófico nacional do século XX, sendo detectada conexão com as tendências europeias comuns do ensino superior. Considerações de filósofos e cientistas russos populares que deram sua contribuição à base ideológica e aos princípios do ensino universitário na Rússia no século XX são consideradas.Materiais e métodos: Os métodos são baseados em tradições de pesquisa do conhecimento humano: abordagem filosóficoantropológica dos problemas da existência humana, método comparativo de consideração de problemas educacionais em conexão com vários contextos culturais e históricos do desenvolvimento da existência humana, método histórico-comparativo. Além disso, são refletidos os métodos de pesquisa fenomenológica e hermenêutica. A base, o conteúdo, as metas e os objetivos do sistema educacional, incluindo o ensino universitário e a conexão da educação com investigações reais do ser humano e da sociedade contemporâneos, são detectados e compreendidos filosoficamente.Resultados da pesquisa: É apresentado no artigo que as principais abordagens da educação e os resultados de sua compreensão pelos pensadores russos compreendem a unidade de conteúdo e ressoam com problemas reais de sua estrutura e conteúdo em termos do mundo moderno, incluindo a realidade russa.Portanto, a idéia da necessidade de uma combinação ótima de conhecimentos científicos, especiais e filosóficos naturais no sistema educacional é fundamentada. Essa abordagem permite desenvolver a educação em termos de valores humanitários, facilita a formação de personalidade moral e espiritualmente orientada&nbsp;e socialmente responsável do especialista, exercendo uma visão de mundo razoável. Discussão e conclusão: os resultados recebidos podem ser utilizados para o exercício dos princípios do desenvolvimento do ensino superior em termos de desafios contemporâneos, baseados no princípio da sucessão e na manutenção das maiores tradições culturais, e também no planejamento estratégico dos programas educacionais da Universidade.Introduction: the article is devoted to research of higher education various aspects, results of its recognition in national scientific and philosophical thought of 20th century are presented, connection with common European trends of higher school is detected. Views of popular Russian philosophers and scientists who made their contribution into ideologic basis and principles of University education in Russia in 20th century are considered. Materials and methods: Methods are based on research traditions of humane knowledge: philosophical-anthropologic approach to problems of human existence, comparative method of educational problems consideration in connection with various cultural and historical contexts of human existence development, comparative-historical method. Besides that phenomenological and hermeneutic research methods are reflected. Basis, contents, goals and targets of educational system including University education and connection of education with actual inquiries of contemporary human being and society are detected and philosophically comprehended. Results of research: It is presented in the article that major approaches to education and results of its comprehension by Russian thinkers comprise content unity and resonate with actual problems of its structure and contents in terms of modern world including Russian reality. Therefore the idea of necessity of optimal combination of natural scientific, special and philosophical knowledge in educational system is substantiated. Such approach allows to develop education in terms of humanitarian values, facilitates the formation of morally and spiritually oriented and socially responsible personality of the specialist, exercising reasonable world view. Discussion and conclusion: received results may be used in order to exercising the principles of higher education development in&nbsp;terms of contemporary challenges basing on principle of succession and keeping the greatest cultural traditions, and also for strategical planning of University educational programs

The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a massless scalar field. In vacuum, the volume flow (with respect to cosmological time) asymptotically vanishes if and only if future space-like infinity is 3-manifold of constant curvature. The volume flow thus represents irreversibility of asymptotic evolution in spacetimes with positive cosmological constant.Comment: 15 pages, no figures; v.2: conjecture 1 on p. 11 made more precise; version published in jhe

Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics

Starting from metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the "brick wall" model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with Pauli-Villars regularization scheme, an expression for the statistical-mechanical entropy arising from the nonminimally coupled scalar fields is obtained. Then, by using the conical singularity method Mann and Solodukhin's result for the Kerr-Newman black hole (Phys. Rev. D54, 3932(1996)) is extended to the general stationary black hole and the nonminimally coupled scalar field. We last shown by comparing the two results that the statistical-mechanical entropy and one-loop correction to the thermodynamical entropy are equivalent for coupling $\xi\leq 0$. After renormalization, a relation between the two entropies is given.Comment: 18 pages, Latex, nofigue. Accepted by Phys. Rev.