abstract

The gravitational sector of classical Lagrangian theories can generally be expressed in the form of a power series \[{\cal L} = \sqrt {-g}\left [-\frac {1}{2} \kappa ^{-2} R+ \sum _{n=2}^{\infty }\left (a_n{\cal R}^n+\tilde {a}_n \partial ^2{\cal R}^n\right )\right ]\,,\] where \(\kappa ^2\) is the gravitational coupling and \(R\) is the Ricci scalar. By means of a metric field-redefinition \(g_{ij}\rightarrow (1+\beta R)g_{ij} + \gamma R_{ij}+ \delta R_{ik}R_j^{k} + \dots \), the quadratic terms \({\cal R}^2\) can be removed completely (due to the Gauss–Bonnet identity) and the cubic and higher-order terms \({\cal R}^n\) partially, only those terms constructed solely from the Riemann tensor \(R_{ijkl}\) remaining invariant. It has been shown by Lawrence, however, that the implementation of this procedure at a specific order \(n\) inevitably gives rise to ghosts at the next and higher orders \(n'\ge n+1\), in the sense that a term \({\cal R}^n\) in \({\cal L}\) is replaced by terms \({\cal R}^{n-m}(\partial ^2{\cal R})^m\), for example. Classically, these ghosts may lead to instabilities, and it is therefore necessary to investigate the stability of the theory to linear perturbations, both before and after the metric has been transformed. In the cosmological Friedmann space-time \(ds^2=dt^2-a_0^2 {\mathrm e}^{2\alpha (t)} d\mathbf {x}^2\) which describes the Universe, where \(t\) is comoving time and \(a_0 {\mathrm e}^{\alpha (t)} \) is the radius function of the three-space \(d \mathbf {x}^2\), assumed flat, we find, by examining the characteristic equation, that the low-energy solution invariably possesses exponentially growing (and decaying) modes, after carrying out the field redefinition, irrespective of whether such modes were present initially. Therefore, it is not expedient to redefine the metric in this background, which, rather, should be considered as fixed. We discuss the relevance of this result for the heterotic superstring theory, particularly with regard to the vacuum solutions obtained previously from the effective Lagrangian including terms \(n \le 4\), and to the terms \({\cal R}^2\).

abstract

In this paper, we investigate the Hawking radiation of the Taub-NUT black hole by Hamilton–Jacobi method. When the unfixed background space-time and self-gravitational interaction are considered, the tunnelling rate is related to the change of Bekenstein–Hawking entropy and the radiation spectrum deviates from the purely thermal one. This result is in accordance with Parikh and Wilczek’s opinion and gives a correction to the Hawking radiation of the black hole.

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In this paper, we investigate higher dimensional spherically symmetric perfect fluid collapse with positive cosmological constant. We take higher dimensional spherically symmetric metric in the interior region and higher dimensional Schwarzschild–de Sitter metric in the exterior region. The junction conditions between interior and exterior space-times are derived. We discuss the apparent horizons and their physical significance and conclude that the cosmological constant slows down the collapse of matter and hence limits the size of the black hole. This analysis gives the generalization of the four-dimensional perfect fluid collapse to higher dimensional perfect fluid collapse. We recover the results of the higher dimensional dust case \((p=0)\).

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In this paper we study the first law of thermodynamics for the (2+1) dimensional charged BTZ black hole considering a pair of thermodynamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the right and left movers of string theory and that the temperature associated with the black hole is the harmonic mean of the temperatures associated with these two systems.

abstract

Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled together during observations of a system travelling through a gravitational field. In the case of a Schwarzschild geometry these two effects are decoupled and in consequence they factorise. Such a factorization is not a universal feature. We define here a necessary and sufficient criterion for time dilation and gravitational red-shift decoupling. This property is manifested in a particular form of the frequency shift in a Schwarzschild geometry.

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This paper considers the effects of space noncommutativity on the thermodynamics of a Reissner–Nordström black hole. In the first step, we extend the ordinary formalism of Bekenstein–Hawking to the case of charged black holes in commutative space. In the second step we investigate the effect of space noncommutativity on the thermodynamics of charged black holes. Finally we compare thermodynamics of charged black holes in commutative space with thermodynamics of Schwarzschild black hole in noncommutative space. In this comparison we explore some conceptual relation between charge and space noncommutativity.

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We propose a modification of the hydrodynamic model of the dynamics in ultrarelativistic nuclear collisions. A modification of the energy-momentum tensor at the initial stage describes the lack of isotropization of the pressure. Subsequently, the pressure is relaxing towards the equilibrium isotropic form in the local comoving frame. Within the Bjorken scaling solution a bound is found on the decay time of the initial anisotropy of the energy-momentum tensor. For the strongest dissipative effect allowed, we find a relative entropy increase of about 30%, a significant hardening of the transverse momentum spectra, and no effect on the HBT radii.

abstract

Superdeformed (SD) bands have been identified in both the \(A \approx 150\) and \(A \approx 60\) regions using the statistical thoery and the configuration dependent cranked Nilsson–Strutinsky (CNS) calculations. A good understanding of SD bands in different mass regions have been obtained using these models and the general features of SD bands in these mass regions are studied. Total energy surfaces (TES) have also been generated for these nuclei with in the CNS formalism to study the shape transition and oblate — prolate coexistence in detail.

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We calculate the equation of state of nuclear matter in the self-consistent \(T\)-matrix scheme including three-body nuclear interactions. We study the effect of the three-body force on the self-energies and spectral functions of nucleons in medium.

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The dipole response function of nuclear matter at zero and finite temperatures is investigated in an extended RPA approach by including collisional damping mechanism and coherent damping due to particle–phonon coupling. Calculations are carried out for nuclear dipole vibrations by employing the Steinwedel–Jensen model and compared with experimental results for \(^{120}\)Sn and \(^{208}\)Pb.

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We present results on the performance of the first prototype of the CASTOR quartz-tungsten sampling calorimeter, to be installed in the very forward region of the CMS experiment at the LHC. This study includes GEANT Monte Carlo simulations of the Cherenkov light transmission efficiency of different types of air-core light guides, as well as analysis of the calorimeter linearity and resolution as a function of energy and impact-point, obtained with 20–200 GeV electron beams from CERN/SPS tests in 2003. Several configurations of the calorimeter have been tested and compared, including different combinations of (i) structures for the active material of the calorimeter (quartz plates and fibres), (ii) various light-guide reflecting materials (glass and foil reflectors) and (iii) photodetector devices (photomultipliers and avalanche photodiodes).

abstract

The method decomposing the molecular electron charge, which facilitates the evaluation of electrostatic potential, is presented. The decomposition is based on the observation, that in a free atom the electron charge distribution in the vicinity of its nucleus does not change, when the atom is incorporated into the molecule. In the decomposed system, the cusp singularity is integrated analytically by the application of the Green’s function of Laplace operator for spherically symmetric systems. It is shown, that the residual charge, which is not treated analytically, is a smooth function and is close to zero in the vicinity of the nuclei. In the second part of the paper, the adaptive numerical integration algorithm is applied to obtain the Dirichlet boundary condition, required to any real space solver of Poisson equation.

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A new luminosity function for galaxies can be built starting from the product of two random variables \(X\) and \(Y\) represented by a gamma variate with argument 2. The mean, the standard deviation and the distribution function of this new distribution are computed. This new probability density function is assumed to describe the mass distribution of galaxies. Through a non linear rule of conversion from mass to luminosity a second new luminosity function for galaxies is derived. The test of reliability of these two luminosity functions was made on the Sloan Digital Sky Survey (SDSS) in five different bands. The Schechter function gives a better fit with respect to the two new luminosity functions for galaxies here derived.

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We present an exact solution around global monopole resulting from the breaking of a global SO(3) symmetry in a five dimensional space time. We have shown that the global monopole in higher dimensional space time exerts gravitational force which is attractive in nature. It is also shown that the space around global monopole has a deficit solid angle. Finally, we study monopole in higher dimensional space-time within the framework of Lyra geometry.

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As an alternative to the Big Bang (the standard model), we present a mathematical theory of cosmological redshift. We show that a fundamental formula of Lobachevskian (hyperbolic) geometry describes cosmological redshift and the Doppler effect as well. As presented here, the cosmological redshift preserves wavelength ratios (it shifts uniformly the whole electromagnetic spectrum), it is scale invariant, it is a monotonically increasing function of distance, and it is source independent. It agrees with all experimental data. The distortion introduced by imaging from hyperbolic into Euclidean space and the limitations of Special Relativity are discussed. Physical observations in Lobachevskian space are discussed and the new formula relating redshift and/or Doppler shift to aberration is given. An analysis is presented of an erroneous origin of Hubble’s so called velocity distance law.