Metric conditions for clusters in hierarchical cosmologies

Algebraic conditions on the continuity of the components of the metric tensor are employed to get an approximate metric in four limiting forms relevant to a condensation in an expanding Einstein/de Sitter substratum. The metric of the condensation is in general spherically-symmetric, nonstatic and asymptotically flat, passing over into the usual Friedmann solution at large distances and late times. The line-element derived supersedes an earlier incorrect formulation of the problem by Einstein and Straus. The metric is applicable in particular to clusters of galaxies, wich cannot avoid being involved in the expansion of the Universe for the density-distributions relevant to average loose clusters as presently observed. It is likely that all clusters, including compact ones, are in a state of dynamical evolution, a conclusion which may remove the missing mass problem. The results found agree, in this respect, with recent work by Noerdlinger and Petrosian, and give effective Hubble parmeters for systems in an expanding substratum.     

Second post-Minkowskian order harmonic metric for a moving Kerr-Newman black hole

We apply the Lorentz boosting method to the Kerr-Newman metric in harmonic coordinates, and obtain the second post-Minkowskian order harmonic metric for a moving Kerr-Newman black hole with an arbitrary constant speed. This metric may be useful for investigating observable relativistic effects due to the motion of the moving source. As an application, the post-Newtonian equations of motion for a particle and a photon in the far field of this black hole are calculated.     

On the election of the flat metric in the bimetric theory of gravitation

The problem of the form of the flat metric in the Rosen bimetric theory is examined in the following work.It is shown, on concrete examples, how necessary it is to write down the flat metric and solve the problem of finding the gravitational field in arbitrary non-inertial frame. It is shown also how to separate the pure gravitational effects from those connected with non-inertiality of the frame by way of comparing both metrics.     

Solutions for Massless Bosons in the Mannheim-Kazanas Space-Time

Astrophysics - The present paper deals with the Mannheim-Kazanas metric which is supposed to offer a reliable explanation on the observed galaxy rotation curves. The effective potential and the...     

Predicting the maximum sunspot number and the associated geomagnetic activity indices a a $aa$ and A p $Ap$ for solar cycle 25

We are considering the spacetime described by the metric proposed by Mannheim and Kazanas. The effective potential and the circular orbits are discussed. The rotational velocity derived from the geodesics equation agrees with the observed flat galactic rotation curves. Finally, solutions to the Gordon equation for massless bosons evolving in this spacetime are obtained in terms of Heun general functions.

     

The effects of a minimal length on the Kerr metric

The effects of a minimal length on the Kerr metric are studied within the pseudo-complex General Relativity (pcGR), which has a minimal length parameter and also depends on a $r$-dependent metric, allowing for the accumulation of dark energy around a star. The relevant parameters are the rotational Kerr parameter $a$, the mass of a black hole, and a parameter measuring the amount of dark energy accumulated. It is found that the metric is modified by a factor, depending on $r$, resulting in a maximal acceleration. This factor shows several singularities. For small black holes, the corresponding effective potentials exhibit potential barriers, avoiding the increase of the black hole's mass. It is found that the effects of a minimal length are only of importance for very small mass black holes and vanish for macroscopic black holes.     

Natural entropy production in an inflationary model for a polarized vacuum

Though entropy production is forbidden in standard FRW Cosmology, Berman and Som presented a simple inflationary model where entropy production by bulk viscosity, during standard inflation without ad hoc pressure terms can be accommodated with Robertson–Walker’s metric, so the requirement that the early Universe be anisotropic is not essential in order to have entropy growth during inflationary phase, as we show. Entropy also grows due to shear viscosity, for the anisotropic case. The intrinsically inflationary metric that we propose can be thought of as defining a polarized vacuum, and leads directly to the desired effects without the need of introducing extra pressure terms.     

Affinely invariant field theory

If we require the effective field equations for a local system to be second order partial differential equations, an affinely invariant theory (not presuming the existence of a metric tensor beforehand) has to be non-local, the action being a multiple integral over the manifold considered.     

Kerr — Newman metric in cosmological background

A new solution of Einstein-Maxwell field equations is presented. The material content of the field described by this solution is a perfect fluid plus sourceless electromagnetic fields. The metric of the solution is explicitly written. This metric is examined as a possible representation of Kerr-Newman metric embedded in Einstein static universe. The Kerr-Newman metric in the background of Robertson-Walker universe is also briefly described.     

Effective sound speed in relativistic accretion discs around Schwarzschild black holes

For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that the introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.     

On the Envelope Soliton – Like Fine Structure in Solar Radio Emission

Several quasi-periodic, milliseconds fine structures in the metric wave band occurring during the evolution of solar type IV bursts have been observed by Yunnan Radio Telescope, Trieste Radio Telescope and IZMIRAN dynamic spectrometer. The envelope of these quasi-period modulational fine structures have a soliton pattern, so it is called an envelope soliton-like fine structure. A modulational instability model of electromagnetic wave has been adopted here. It is found that the longitudinal modulational instability can occur only in the solar coronal region of low magnetic field and high temperature, as well as high density plasma, which will give rise to the envelope soliton-like fine structures in the solar metric and decimetric radio emission. The propagation effects of envelope soliton-like fine structure from corona to the observer on the Earth have been briefly considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cosmological viscous fluid universe in slow rotation

The problem of slowly rotating cosmological viscous fluid universe in a homogeneous and isotropic models has been investigated by considering the perturbation in the metric rotation function to the first order of smallness associated with certain physical restrictions imposed on the metric rotation function and matter angular velocity. Some more general solutions for the metric rotation function have been obtained and physical interpretation of the solutions have been investigated.     

A general relativistic model for magnetic monopole-infused compact objects

Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused with magnetic monopoles produced by proton-proton collisions within the intense dipolar magnetic fields generated by these objects during their collapse. It is found that the effective mass of such an object’s acquired monopolar magnetic field is three times greater than the mass of its native fluid and monopoles combined, necessitating that the interior matter undergo a transition to a state of negative pressure in order to attain equilibrium. Assuming full symmetry between the electric and magnetic Maxwell equations yields expressions for the monopole charge density and magnetic field by direct analogy with their electrostatic equivalents; inserting these into the Einstein equations then leads to an interior metric which is well-behaved from the origin to the surface, where it matches smoothly to an exterior magnetic Reissner-Nordström metric free of any coordinate pathologies. The source fields comprising the model are all described by simple, well-behaved polynomial functions of the radial coordinate, and are combined with straightforward regularity conditions to yield expressions delimiting several fundamental physical parameters pertaining to this hypothetical astrophysical object.     

A further generalization of Vaidya''s star metric

In this paper, a metric containing five arbitrary functions of time is obtained which describes the gravitational field of an arbitrary accelerated and charged point-mass (star). It is a further generalization of Vaidya's star metric, [1]. In particular cases, it reduces to the Reissner-Nortström metric and the Kinnersley metric [2]. Since the various parameters of the source can vary arbitrarily in time, this metric is of wide applicability and may prove to be useful for various specific astronomical objects.     

Photometric Solution of the O-type Eclipsing Binary V1007 Sco

A Cosmological model with a viscous fluid in Kaluza-Klein metric is obtained assuming a time-dependent equation of state. The solution is in fact a generalization of an earlier work by Hajj and Boutros for a perfect fluid. It is also found that dimensional reduction of the extra space takes place such that the five-dimensional universe naturally evolves into an effective four-dimensional one. The dynamical behavior of the model is examined and it is also found that with a decrease in extra space the observable 3D space entropy increases thus accounting for the large value of entropy observable at present.     

Cosmological Model with a Time-Dependent Equation of State in a Kaluza–Klein Metric

A homogeneous cosmological model in Kaluza–Klein metric is obtained assuming a time-dependent equation of state. The solution is in fact generalization of an earlier work by Hajj and Boutros for a perfect fluid. It is also found that dimensional reduction of the extra space takes place such that the five-dimensional universe naturally evolves into an effective four-dimensional one. The dynamical behaviour of the model is examined and it is also found that with a decrease in extra space the observable three-dimensional space entropy increase thus accounting for the large value of entropy observable at present.     

The deviation of light path in Einstein–Brans–Dicke theory

Both Jordan–Brans–Dicke (shortened JBD) theory and Brans–Dicke theory in the Einstein’s frame (shortened EBD) are treated as Brans–Dicke theory. However, we learn that only Pauli metric represents the massless spin-two graviton and thus, should be identified as physical. If one just considers the weak field approximation and Newtonian limit, EBD theory gives the same results with Einstein’s general relativity. So, it is necessary to consider strong field effects and cosmological model. The purpose of this paper is to find the exact spherically symmetric metric in the strong field situation, and deduce the deviation of light path in EBD theory.     

Gravitational sources of purely electromagnetic origin

The Einstein-Maxwell field equations for charged dust corresponding to static axially-symmetric metric of Levi-Civita have been studied. It has been shown that when the metric potentialsg _ij are functions of only one of the coordinates, viz.,r, the interior charged dust becomes purely of electromagnetic origin, in the sense that the physical quantities like the energy density, the effective gravitational mass, etc., are dependent only on the charge density and vanish when this charge density vanishes. Such models are known as electromagnetic mass models in the classical electrodynamics. An interior charged dust solution corresponding to this case has been obtained which, in a sense, represents an infinite dust distribution of electromagnetic origin. In the second case, viz., when the metric potentials are functions of the coordinatesr andz both, it has been shown that some of the situations correspond to electromagnetic mass models. An example to illustrate this case has been obtained. This represents the source of the Reissner-Nordström-Curzon field (an analogue of the Reissner-Nordström solution obtained by Curzon) which according to Curzon describes the exterior field of an electron.     

Generalized uncertainty principle and quantum gravitational effects on tunneling rate of Reissner-Nordström black hole

It is shown that the Bekenstein-Hawking entropy of black holes can accept a correction that effects on the radiation tunneling probability. By assumption of a spatially flat universe accompanied with expansion of metric, we could obtain an expression for entropy of black hole that is changing with respect to time and Bekenstein-Hawking temperature.     

Some Cosmological Models in Scalar-Tensor Theory of Gravitation

Field equations in a scalar-tensor theory of gravitation proposed by Saezand Ballester (1985) are obtained with the aid of (i) Friedmann-type metric (ii) a non static plane symmetric metric and (iii) spatially homogeneous Bianchi type – III metric. Some cosmological models corresponding to perfect fluid and bulk viscous fluid are presented. Physical and kinematical properties of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.