Eleven Spherically Symmetric Constant Density Solutions with Cosmological Constant

Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.     

SPHERICALLY SYMMETRIC AND STATIC FIELDS IN LINEARIZED GAUGE THEORIES OF GRAVITATION

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational sourtion are obtained by maens of Green's function for the five Lagrangians with out ghosts and tachyons. In cases of four Lagrangians,the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-older, while in the case of the fifth hagrangian the space-time metric differs from the Schwarzschild one. Under both,Newtonian and-weak gravitational field approximations,the motion of a test particle without span should therefore be different from Newton's second law. As a result of the exchanged particles of spin o⁺ the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational "constant" G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant G_∞ is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).     

The gravitational field of a homogeneous plate with a non-zero cosmological constant

A static interior solution of Einstein gravitational equations with λ ≠ 0 generated by a plane plate of a constant mass density is found. It is shown how to join this interior solution with the exterior metric as well     

A charged interior solution with cosmological constant Λ in general relativity

A new interior solution of the field equation of general relativity with cosmological constant Λ has been obtained for a static and spherically symmetric charged body. Recent charged generalizations of a class of solutions by Florides are discussed here as special cases of our solution. Robson's junction condition is extended to discuss the smooth joint of the interior solution to the Reissner-Nordström solution with nonzero Λ.     

Equilibrium of charged,spinning, magnetic particles

An unsymmetrical, stationary solution of the Einstein-Maxwell equations is given. The solution corresponds to the exterior field of two massive, charged, magnetised, spinning particles. In general line singularities are present in the solution. The field ofN such particles is then considered and necessary and sufficient conditions for the equilibrium of the system are given.     

The gravitational and electrostatic fields far from an isolated Einstein-Maxwell source

The exterior solution for an arbitrary charged, massive source is studied as a static deviation from the Reissner-Nordström metric This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic potential functions. The homogeneous equations are explicitly solved in the particular caseq ²=m ², obtaining a multipole expansion with radial hypergeometric dependence for both potentials. In the limiting case of a neutral source, the equations are shown to coincide with recent results by Bondi and Rindler.     

Analytic solution of gauge field equations for Lorentz gravity

The exterior analytic solution for a static, spherically symmetric system is given by means of a set of gauge field equations from Lorentz gravity in the curvature coordinate. The correction contributed by the gravitational gauge field in the exterior of a static sphere is obtained for the gravity.     

ON THE EXTERIOR SOLUTIONS OF A CHARGED MASS POINT IN GAUGE THEORIES OF GRAVITATION

In a case of spherically symtric and static field, exterior solutions of a charged mass point for the nine-parameter R+R² gravitational theories are investigated. We obtain results as follows: in the case of coupling constant (zP-2r+s)=0, solution without torsion is the Reissner-Nordstrom metric; otherwise there is no solution with vanishing torsion.     

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

Outline of a classical theory of quantum physics and gravitation

It is argued that in the manner in which the Galilean-Newtonian physics may be said to have explained the Ptolemaic-Copernican theories in terms which have since been called classical, so also Milner's theories of the structure of matter may be said to explain present day quantum and relativistic theory. In both cases the former employ the concept of force and the latter, by contrast, are geometrical theories. Milner envisaged space as being stressed, whereas Einstein thought of it as strained. Development of Milner's theory from criticisms and suggestions made by Kilmister has taken it further into the realms of quantum and gravitational physics, where it is found to give a more physically comprehensible explanation of the phenomena. Further, it shows why present day quantum theory is cast in a statistical form. The theory is supported by many predictions such as the ratio of Planck's constant to the mass of the electron, the value of the fine structure constant and reason for apparent variations in past measurements, the magnetic moment of the electron and proton of the stable particles such as the neutron Λ and Σ together with the kaon, and a relation between the universal gravitational constant and Hubble's constant—all within published experimental accuracy. The latest results to be accounted for by the theory are the masses of the newly discovered ψ particles and confirmation of the value of the decay of Newton's gravitational constant obtained from lunar measurements. While this paper is being typed, new particles are rapidly being discovered—the latest being a neutral ψ particle. A short Appendix discusses the significance of these.     

Perfect fluid metrics conformal to the Schwarzschild exterior spacetime

We construct perfect fluid spacetimes by performing a conformal transformation on a non-conformally flat vacuum solution, namely the Schwarzschild exterior metric. It should be noted that conformally Ricci flat perfect fluid solutions, except those that are conformally flat, are rarely reported explicitly. In this article it is demonstrated that perfect fluid metrics conformal to the Schwarzschild exterior line element are necessarily static. The Einstein field equations for the static case reduce to a fully determined system of three differential equations in three unknowns and the conformal factor is uniquely determined in closed form. The solution is analysed for physical plausibility by establishing the positivity of the energy density and pressure profiles graphically. Additionally, the solution is observed to be causal in an appropriate limit and both the energy density and pressure is shown to be decreasing outwards towards the boundary. Finally, the weak, strong and dominant energy conditions are found to be satisfied in the region under investigation. Accordingly, the most common elementary physical conditions are met and the model is seen to be suitable for a core-envelope stellar model.     

Stars in five-dimensional Kaluza–Klein gravity

In the five-dimensional Kaluza–Klein (KK) theory there is a well known class of static and electromagnetic-free KK-equations characterized by a naked singularity behavior, namely the Generalized Schwarzschild solution (GSS). We present here a set of interior solutions of five-dimensional KK-equations. These equations have been numerically integrated to match the GSS in the vacuum. The solutions are candidates to describe the possible interior perfect fluid source of the exterior GSS metric and thus they can be models for stars for static, neutral astrophysical objects in the ordinary (four-dimensional) spacetime.     

Semiclassical gravitational effects near cosmic strings

The vacuum expectation value of the stress-energy tensor of an arbitrary collection of conformal massless free quantum fields (scalar, spinor, and vector) in the presence of a static, cylindrically symmetric cosmic string is found, up to an undetermined numerical constant. This quantum stress-energy tensor is then used as a source in the linearized semiclassical Einstein equations, which are solved to find the first-order (in Ł) corrections to the exterior metric of a static, cylindrically symmetric cosmic string. The main result is that, at first-order in Ł, the (r, ø) two-space is no longer a simple flat cone; to this order the (r, ø) two- space is a (linearized) hyperboloid, which asymptotically approaches the classical conical surface at large values of r. The asymptotic value of the deficit angle of the cone is unchanged, still being precisely 8πμ.     

An approximate global solution of Einstein’s equations for a rotating finite body

We obtain an approximate global stationary and axisymmetric solution of Einstein’s equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find second-order approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to check that Kerr’s metric cannot be the exterior part of that metric.     

Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

Particle-like solutions of the Einstein–Dirac–Maxwell equations

We consider the coupled Einstein–Dirac–Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.     

The cosmological constant as a thermodynamic black hole parameter

One may consider the cosmological constant Λ as a dynamical variable in general relativity. The simplest way of doing this is to couple the gravitational field to a three-index tensor. In a black hole solution Λ appears then as an integration constant (“hair”) in a similar footing with the total mass and charges of the hole. There is a quantum process of radiation of bubbles, analogous to particle emission, which spontaneously reduces Λ. The general laws of black hole thermodynamics still appear to hold.     

电磁场存在时宇宙因子不为零的高维类Vaidya时空

本文求出了在宇宙因子不为零时,由高维球对称电磁场和球对称辐射产生的高维类Vaidya时空,并探讨了在高维时空中电磁场能量动量张量的可能表示式。