On shear-free motion of charged perfect fluid obeying an equation of state in general relativity

In this note, a spherically symmetric charged perfect fluid executing shear-free motion has been investigated under the assumption of validity of an equation of state. Mashoon and Partovi [4] have studied this problem and have established several theorems giving the properties of such fluid distributions. We find that there is one more solution which is new. It is characterized by three parameters, one of which is the charge parameter. In the limit of vanishing charge the metric goes over to the Wyman metric [2]. It has been shown that the solution does not match with the Reissner-Nordström solution at a boundary and hence it is not suitable to represent a bounded system. We have also discussed the possibility of this solution representing the physical universe. We have found that the solution after a proper choice of constants may satisfy the physical requirements3p,d/dp 1 but will violate the condition /1 wherep, , and represent, respectively, the pressure, matter density, and charge density of the fluid. Therefore, the charged Wyman solution is unsuitable to represent the physical universe. Thus we conclude that for a charged perfect fluid distribution executing shear-free motion the field equations do not admit any physically meaningful solution if we assume the validity of an equation of state.This paper was partially presented at the 12th meeting of Indian Association for General Relativity and Gravitation and the symposium on Applications of General Relativity to Astrophysics and Cosmology held at Puna, India, November 9–12, 1983.     

The equation of motion and gravitational radiation of an ideal fluid sphere moving in a gravitational background

On the basis of an approximation method developed in a previous paper the motion of an ideal fluid sphere in a weak gravitational background is investigated. The sphere is assumed to be small in the sense that its radius is small compared with the change of the background . Furthermore the deformations of the sphere when accelerated by the background are assumed to be small compared with the extension of the sphere in the absence of acceleration. In the lowest mixed order (mixed of the background and the retarded potentials of the sphere in lowest order) the equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world-tube of the sphere. One obtains an equation of motion for the center of the sphere that is identical with the geodesic line linearized in . In the case of a static background of a localized matter distribution it is shown that Einstein's energy-momentum complex formed with the retarded potentials from the accelerated motion of the sphere in lowest order (lowest mixed order) leads to an outgoing radiation of gravitational energy. All radiation terms can be expressed in terms of the background and the world-line of the center of the sphere.     

Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

On the quantum corrections to the virial coefficients of the equation of state of a fluid

The first quantum correction to the virial coefficients of the equation of state of a fluid is derived in the presence of a weak three-body potential ?(i, j, k). Results for the third and fourth virial coefficients are given. Representing the potential energy of interaction of a pair and a triplet, by the Lennard-Jones (12-6) model and the triple dipole dispersion potential model of Axilrod and Teller, the first quantum correction to the third virial coefficient is calculated for many values of T*. The theoretical result is compared with the experimental data of helium.     

The equation of motion and gravitational radiation of a small extended spherically symmetric mass

On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational background is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of rigidity; the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the background . The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the background and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized in . In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given.     

On the final state of spherical gravitational collapse

Following our recent finding [1] that, for the final state of continued spherical gravitational collapse of sufficiently massive bodies, the final gravitational mass of the fluidM _? → 0, we show that for a physical fluid the eventual value of 2M_?/R_? → 1 rather than 2M_?/R_?2M_?/R_? < 1 (the speed of light c = 1 and the gravitational constantG = 1), indicating the approach to a zero-mass black hole. We also point out that, as the final state is approached, the curvature components tend to blow up; also the proper radial distancel and the proper time (measured along a radial worldline) Τ → ∞, indicating that actually the singularity is never attained. We also identify that the final state may correspond to the local 3-speed attaining eitherV = 0 orV → c, even though invariant circumference contraction speedU =dR/dΤ → 0. Nonetheless, at a finite observation epoch, such Eternally Collapsing Objects (ECOs) may have a local speed of collapseV?c and the lab frame speed of collapse may be negligible because of high surface gravitational redshift. However, if quantum back reaction in the strong gravity regime would cause a phase transition of the form pressurep = - ρ, where ρ is the density of the collapsing fluid, it may be possible to have static Ultra Compact Objects (ûCOs) of arbitrary high mass [2]. While supposed Black Holes have no intrinsic magnetic field, ECOs or UCOs are likely to possess strong intrinsic magnetic fields, and we point out that there are already some tentative evidence for existence of such intrinsic magnetic fields in some Black Hole Candidates [3,4]. For the benefit of the readers who may not have gone through Paper I, we also include here the summary of the same. It clearly shows that the central result of Paper I can be derived even without knowing the meaning of the nomenclatureV or without imposing any of property ofV such as whetherV < 1 or not. In addition, we consolidate the same result from other physical considerations too.     

On the gravitational motion of a nonuniformly heated solid particle in a gaseous medium

The steady motion of a nonuniformly heated spherical aerosol particle through a viscous gaseous medium is theoretically studied in the Stokes approximation. It is assumed that the mean temperature of the particle surface may differ appreciably from the ambient temperature. The solution of gasdynamic equations yields an analytical expression for the drag of the medium and the gravitational fall velocity of the nonuniformly heated spherical solid particle with allowance for the temperature dependence of the density of the medium and molecular transfer coefficients (viscosity and thermal conductivity). Numerical estimates show that heating of the particle surface considerably influences the drag force and gravitational fall velocity.     

On the motion of a heavy rigid body in an ideal fluid with circulation

We consider Chaplygin's equations [Izd. Akad. Nauk SSSR 3, 3 (1933)] describing the planar motion of a rigid body in an unbounded volume of an ideal fluid while circulation around the body is not zero. Hamiltonian structures and new integrable cases are revealed; certain remarkable partial solutions are found and their stability is examined. The nonintegrability of the system describing the motion of a body in the field of gravity is proved and the chaotic behavior of the system is illustrated.     

Equation of state of a supercritical fluid based on the Ornstein-Zernike equation

A numerical modeling of the thermodynamic properties of a fluid is performed using the method of integral equations. The predictions are compared with the results of MC and MD simulations. The problem of stability of the numerical solution is examined. The methods for correcting the correlation functions and for estimating their uncertainties are proposed.     

On the motion of test particles in the field of a plane gravitational wave

The motion of test particles in the field of a plane gravitational wave is studied in order to derive some general properties of such motion, especially the possibilities of repeated meetings of two inertially moving particles.The work was done at Moscow State University, Moscow.     

The equation of state of the hard-disc fluid revisited

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.     

Linear response theory for systems obeying the master equation

Linear response theory is developed for systems whose time dependence is described by a master equation. The fluctuation dissipation theorem expressing the linear response of the system in terms of fluctuation properties of the system in equilibrium is derived. The time-dependent Ising spin system in interaction with a heat bath, the Glauber model, is discussed as a particular case of the formalism.The work of one of the authors (D.B.) was supported in part by the National Science Foundation under Contract GP 10536.On leave of absence from the Institute of Physics, Belgrade, Yugoslavia.     

Motion of an ideal fluid in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is found which describes the motion of an initially uniform ideal fluid in the field of a plane gravitational wave of arbitrary amplitude and polarization. For all solutions we find that the pressure and energy density develop singularities on the singular surface, and the velocity of the fluid in the direction of propagation of the gravitational wave approaches the speed of light. In the case of the equation of state =p, the solution becomes intrinsically unstable and describes the generation of sound waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 96–99, November, 1982.     

A FRW dark fluid with a non-linear inhomogeneous equation of state

A dark Friedman–Robertson–Walker fluid governed by a non-linear inhomogeneous equation of state is considered that can be viewed as a conveniently simple paradigm for a whole class of models that exhibit phase transitions from a non-phantom towards a phantom era (superacceleration transition). On the other hand, such dark fluid models may also describe quintessence-like cosmic acceleration. Thermodynamical considerations for the processes involved, which are of great importance in the characterization of the global evolution of the corresponding universe, are given too. Connecting the proposed equation of state with an anisotropic Kasner universe with viscosity, we are led to the plausible conjecture of a dark fluid origin of the anisotropies in the early universe.     

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.