International Journal of Modern Physics D

This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge symmetries on the equations of motion. Almost a century has gone since the publication of this work and its applications have permeated modern physics. Our focus will be on some examples that have appeared recently in the literature. This review aims at students, not researchers. The main three topics discussed are (i) global symmetries and conserved charges (ii) local symmetries and gauge structure of a theory (iii) boundary conditions and algebra of asymptotic symmetries. All three topics are discussed through examples.

100 years after the invention of General Relativity (GR) and 110 years after the development of Special Relativity (SR) we have to state that until now no single experiment or observation allows any doubt about the validity of these theories within the accuracy of the available data. Tests of GR can be divided into three categories: (i) test of the foundations of GR, (ii) tests of the consequences of GR, and (iii) test of the interplay between GR and quantum mechanics. In the first category, we have tests of the Einstein Equivalence Principle and the structure of the Newton axioms, in the second category we have effects like the gravitational redshift, light defection, gravitational time delay, the perihelion shift, the gravitomagnetic effects as the Lense–Thirring and Schiff effect, and gravitational waves. Tests of the effects of gravity on quantum systems are a first step towards experiments searching for a quantum gravity theory. In this paper, we also highlight practical applications in positioning, geodesy, and the International Atomic Time. After 100 years, GR can now definitely be regarded also as practical and applied science.

In recent years, significant progress has been made in building new galaxy clusters samples, at low and high redshifts, from wide-area surveys, particularly exploiting the Sunyaev–Zel’dovich (SZ) effect. A large effort is underway to identify and characterize these new systems with optical/NIR and X-ray facilities, thus opening new avenues to constraint cosmological models using structure growth and geometrical tests. A census of galaxy clusters sets constraints on reionization mechanisms and epochs, which need to be reconciled with recent limits on the reionization optical depth from cosmic microwave background (CMB) experiments. Future advances in SZ effect measurements will include the possibility to (unambiguously) measure directly the kinematic SZ effect, to build an even larger catalogue of galaxy clusters able to study the high redshift universe, and to make (spatially-)resolved galaxy cluster maps with even spectral capability to (spectrally-)resolve the relativistic corrections of the SZ effect.

Natures of progenitors of type Ia Supernovae (SNe Ia) have not yet been clarified. There has been long and intensive discussion on whether the so-called single degenerate (SD) scenario or the double degenerate (DD) scenario, or anything else, could explain a major population of SNe Ia, but the conclusion has not yet been reached. With rapidly increasing observational data and new theoretical ideas, the field of studying the SN Ia progenitors has been quickly developing, and various new insights have been obtained in recent years. This paper aims at providing a summary of the current situation regarding the SN Ia progenitors, both in theory and observations. It seems difficult to explain the emerging diversity seen in observations of SNe Ia by a single population, and we emphasize that it is important to clarify links between different progenitor scenarios and different sub-classes of SNe Ia.

After the big bang, production of heavy elements in the early universe takes place starting from the formation of the first (Pop III) stars, their evolution, and explosion. The Pop III supernova (SN) explosions have strong dynamical, thermal, and chemical feedback on the formation of subsequent stars and evolution of galaxies. However, the nature of Pop III stars/supernovae (SNe) have not been well-understood. The signature of nucleosynthesis yields of the first SN can be seen in the elemental abundance patterns observed in extremely metal-poor (EMP) stars. We show that the abundance patterns of EMP stars, e.g. the excess of C, Co, Zn relative to Fe, are in better agreement with the yields of hyper-energetic explosions (Hypernovae, (HNe)) rather than normal supernovae. We note the large variation of the abundance patterns of EMP stars propose that such a variation is related to the diversity of the GRB-SNe and posssibly superluminous supernovae (SLSNe). For example, the carbon-enhanced metal-poor (CEMP) stars may be related to the faint SNe (or dark HNe), which could be the explosions induced by relativistic jets. Finally, we examine the various mechanisms of SLSNe.

We start with a brief introduction to the historical background in the early pioneering days when the first neutron star thermal evolution calculations predicted the presence of neutron stars hot enough to be observable. We then report on the first detection of neutron star temperatures by ROSAT X-ray satellite, which vindicated the earlier prediction of hot neutron stars. We proceed to present subsequent developments, both in theory and observation, up to today. We then discuss the current status and the future prospect, which will offer useful insight to the understanding of basic properties of ultra-high density matter beyond the nuclear density, such as the possible presence of such exotic particles as pion condensates.

We present a time-dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state parameter. In the second part, we generalize the rotating black hole solution to an expanding universe. We derive from the proposed metric the special solutions of the field equations for the dust approximation and the dark energy solution. We show that the presence of a rotating black hole does not modify the scale factor $b(t)=t^{2/3}$ law for dust, nor $b(t)=e^{\lambda t}$ and $p=-\rho$ for dark energy.

We derive the signature for condensed neutrino objects (CNOs) as the primary source of dark matter. Restricting our source data to minimize systematic errors, we find that by just using weak lensing data and Sunyaev–Zel’dovich data, that there may be a weak CNO signature.

We analyze temporal characteristics of signals from the wide field-of-view (WFOV) Cherenkov telescope (CT) detecting extensive air showers (EAS) of cosmic rays (CRs) in coincidence with surface detectors of the Yakutsk array. Our aim is to reveal causal relationships between measured characteristics and physical properties of EAS.

An effective, reliable and time saving numerical method with use of the Pruefer transformation is proposed to calculate eigenvalues of Chandrasekhar–Page angular equations.

Starting off with two distinct initially static stellar cores (i) Florides interior (constant density, vanishing radial pressure) and (ii) Wyman interior (constant density, nonvanishing radial pressure), we explore the dynamics of these two models once hydrostatic equilibrium is lost. We show that although the time of formation of horizon, evolution of the mass and proper radius are independent of the chosen initially static configurations, there is a significant difference in the temperature profiles of the radiating bodies as the collapse proceeds.

We study how galaxy morphology changes the relation among the inner slope $\alpha$ of galactic density profiles and the stellar mass, and rotation velocity.

We find that the slope $\alpha$ flattens monotonically from $\alpha \simeq -1$ to $\alpha \simeq 0$ going from giant galaxies (ellipticals, spirals) to dwarf galaxies ($\simeq 10^8{M}_{*}$). At masses smaller than $\simeq 10^8{M}_{*}$, in the mass range dominated by nonrotational supported galaxies (e.g. dSphs), the slope steepens due to the offset in angular momentum of rotational dominated, and nonrotational dominated galaxies.

A comparison with SPH simulations finds our result in qualitative agreement with them, but the inner slope $\alpha$ at small stellar masses is flatter than that in their simulations. Density profiles become cuspy for $M_{*}$ in the range $10^4$–$10^5{M}_{\odot }$, similarly to Õnorbe.

It has recently been proposed that gamma-ray burst (GRB) events may be modified by the presence of a dark matter sector subcomponent that is charged under an unbroken U(1). This proposal depends upon there being a nontrivial density of charged dark matter in star forming regions of galaxies which host GRBs. We discuss four Wolf–Rayet galaxies (NGC 1614, NGC 3367, NGC 4216 and NGC 5430) which should contain comparable amounts of dark matter gas and visible matter gas in the star forming regions. We show that the ratio of dark jet power to visible jet power depends only on the ratio of particle mass and charge when the densities are equal, allowing for these input parameters to be probed directly by future observations of GRBs.

We consider collision of two geodesic particles near the lightlike surface (black hole horizon or naked singularity) of such an axially symmetric rotating or static metric that the coefficient $g_{\varphi \varphi }\to 0$ on this surface. It is shown that the energy in the center of mass frame $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$ is indefinitely large even without fine-tuning of particles’ parameters. Kinematically, this is the collision between two rapid particles that approach the horizon almost with the speed of light but at different angles (or they align along the normal to the horizon too slowly). The latter is the reason why the relative velocity tends to that of light, hence to high $E_{\mathrm{\text{c}}.\mathrm{\text{m}}.}$. Our approach is model-independent. It relies on general properties of geometry and is insensitive to the details of material source that supports the geometries of the type under consideration. For several particular models (the stringy black hole, the Brans–Dicke analogue of the Schwarzschild metric and the Janis–Newman–Winicour one) we recover the results found in literature previously.

This research aims to develop a new approach towards a consistent coupling of electromagnetic and gravitational fields, by using an electron that couples with a weak gravitational potential by means of its electromagnetic field. To accomplish this, we must first build a new model which provides the electromagnetic nature of both the mass and the energy of the electron, and which is implemented with the idea of $\gamma$-photon decay into an electron–positron pair. After this, we place the electron (or positron) in the presence of a weak gravitational potential given in the intergalactic medium, so that its electromagnetic field undergoes a very small perturbation, thus leading to a slight increase in the field’s electromagnetic energy density. This perturbation takes place by means of a tiny coupling constant $\xi$ because gravity is a very weak interaction compared with the electromagnetic one. Thus, we realize that $\xi$ is a new dimensionless universal constant, which reminds us of the fine structure constant $\alpha$; however, $\xi$ is much smaller than $\alpha$ because $\xi$ takes into account gravity, i.e. $\xi \propto \sqrt{G}$. We find $\xi =V/c\cong 1.5302\times 10^{-22}$, where $c$ is the speed of light and $V\propto \sqrt{G}(\cong 4.5876\times 10^{-14}$m/s) is a universal minimum speed that represents the lowest limit of speed for any particle. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks the Lorentz symmetry. The metric of the flat spacetime shall include the presence of a uniform vacuum energy density, which leads to a negative pressure at cosmological scales (cosmological anti-gravity). The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained in agreement with the observational data.

In this paper, we study the effect of the quantum backreaction on Brans–Dicke cosmology in inflation era. We consider an inflaton field in the $D$-dimensional spacetime in the framework of Brans–Dicke model. We use a new notation for the Brans–Dicke field in terms of the dilaton field. Then we obtain the vacuum expectation value of the full energy–momentum tensor using WKB approximation of the mode functions which satisfy the equations of motion. The obtained vacuum expectation values of energy–momentum tensor are divergent. In order to renormalize it, we introduce a constant cut-off $\mathrm{\Omega }$. The vacuum expectation value of energy–momentum tensor is separated to the UV and IR parts by using $\mathrm{\Omega }$ cut-off. Then, we use the dimensional regularization method to eliminate divergences by introducing a counterterm action. Also, we calculate the IR contribution of the vacuum expectation value of energy–momentum tensor. Thus, we obtain a physically finite result for the quantum energy–momentum tensor. Finally, we find the effect of backreaction on scale factor.

We have studied in this paper, the stability of dynamical system in $f(R)$ gravity. We have considered the $f(R)$ $\gamma$-gravity and explored its dynamical analysis. We found six critical points among which only one describes a universe filled of both matter and dominated dark energy. It is shown that these critical points present specific phase spaces described by the corresponding fluids. Furthermore, we have investigated the stability conditions of these critical points and find that these conditions are dependent of the model parameters. We also study the stability of a new power-law $f_{*}(R)$ model with de Sitter and power law solutions.