Comment on the Brans-Dicke-Bianchi type-I solution

We should like to point out that the Brans-Dicke-Bianchi type-I vacuum solution recently given by Ram and Singh is wrong. The correct solution is nothing but a special case of the general BDT-Bianchi type-I solutions given by us recently (Lorenz-Petzold, 1984). It is the aim of this comment to rediscuss the corresponding field equations and to disprove the statement that the (correct) solution has no analogy in Einstein's theory.     

A bianchi type-III cosmological model in Brans-Dicke theory for vacuum field

An exact solution of Brans-Dicke (B-D) field equations for the metric tensor of a spatially homogeneous Bianchi type-III configuration has been obtained for vacuum field. It is shown that in the limiting case the solution reduces to that of Einstein field equations in vacuum.     

Axisymmetric stationary vacuum fields in the general scalar tensor theory

It is show that axisymmetric stationary vacuum solutions of the general scalar tensor theory of gravitation proposed by Nordvedt and later discussed by Barker and others can be obtained from the solutions of the axisymmetric stationary Einstein vacuum fields and also from the axisymmetric static vacuum fields of the general scalar tensor theory. The scalar tensor analogue of the Kerr solution has been obtained.     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.     

A tilted Bianchi type-V perfect fluid solution for stiff matter

We present a solution to the Einstein field equations for a massless scalar field in a Bianchi type-V spacetime, which can be interpreted as a solution for a perfect fluid with the equation of state of stiff matter. This solution complements a solution previously given by us for an anisotropic fluid.     

Thermodynamics of the universe filled with perfect fluid having variable equation of state

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Hor̃ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein’s general relativity at large distances. Subsequently Lü et al. have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences have been analyzed. Also the thermodynamics of the FRW universe has been studied.     

Non-static cylindrically symmetric fields in general projective relativity

Exact solutions for the vacuum field equations of General Projective Relativity of Arcidiacono (1986) are obtained for the non-static Einstein-Rosen metric (Einstein and Rosen, 1937). The nature of singularities in these solutions is discussed.     

Comment on the vacuum Bianchi type I solution in the Brans-Dicke theory

We wish to point out that the axialsymmetric Bianchi type I vacuum solution recently given by Ram, is wrong. Moreover, the correct solution is only a special case of the general triaxial Bianchi type I solution given by Ruban and Finkelstein.     

Dark energy as space-time curvature induced by quantum vacuum fluctuations

It is shown that quantum vacuum fluctuations give rise to a curvature of space-time equivalent to a cosmological constant, that is a homogeneous energy density ρ and pressure p fulfilling −p=ρ>0. The fact that the fluctuations produce curvature, even if the vacuum expectation of the energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature. Arguments are given which suggest that the density ρ might be of order the “dark energy” density currently assumed to explain the observed accelerated expansion of the universe.     

Particles,space, and time

Our Universe consistes of particles, space and time. Ever since Descartes we have known that true emptiness cannot exist; ever since Einstein we have known that space and time are part of the stuff of our world. Efforts to determine the structure of particles go in parallel with the search for the structure of spacetime. Einstein gave us a geometrical answer regarding the structure of spacetime: a distance recipe (Lorentz-Minkowski) suffices. The theory boils down to a patching together of local Lorentz frames into a global whole, which gives it the form of a gauge field theory based on local Lorentz symmetry. On large scales, the Einstein Equation seems to work well. The structure of particles is described by a gauge field. too. On small scales the Standard Model seems to work very well.However, we know from Newtonian gravity that the presence of particles must be related to the structure of spacetime. Einstein made a conjecture for the form of this connection using the Newtonian limit of small speeds and weak fields. The right hand side of his equation for the bulk theory of matter (the energy-momentum tensor), is equated to the Einstein tensor from non-Euclidian geometry.But that connection is wrong. The structure of spacetime cannot be equated to the density of particles if we include the Standard Model in the matter tensor. In field theory a potential is not something that can be freely changed by adding an arbitrary scalar term; due to the local (as opposed to global) character of the fields, a potential becomes an entity in itself. Einstein's conjecture runs into profound trouble because the reality of potentials implies that the zero point energy of the vacuum must be included in the Einstein equation. The net result is the appearance of a term equivalent to a cosmological constant A of stupendous size, some 10¹¹⁸ times the critical cosmic density.The crisis due to the zero point fluctuations in the energy-momentum tensor is a clash of titans: Einstein's geometrical ideas on spacetime structure vs the behaviour of particles and the vacuum discribed by Dirac and followers. Someone, or everyone, is wrong. In my opinion the straightforward quantization of spacetime will always be impossible because the usual particle symmetries (U(1), SU(2), SU(3) and relatives) connect fermions and bosons, whereas relativistic analogies of these symmetries (the Lorentz symmetry) says something about spacetime and not about particles.     

A new class of relativistic stellar models

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.     

Exact five-dimensional cosmological solutions

We derive some new perfect solutions in five dimensions. The solutions given are the generalizations of theL(4, 7) vacuum solution given recently by Demaret and Hanquin (1985) in an incorrect form only.     

Conformally symmetric Abelian Higgs sunspot and non-metricity of the Sun's spacetime

A U(1)-symmetric Yang-Mills-Higgs (i.e., an Abelian Higgs) sunspot's model is recognized to originate from a massless, complex-valued scalar field coupled minimally to electromagnetic gauge potentials in the background of a (globally)conformally symmetric semi-metric spacetime, whose metric structure is described by the generalized Einstein equations with nonvanishing (positive-valued) cosmological constant. It is shown, in particular, that non-linearity (selfcoupling) of the scalar field appears due to a non-zeroness of the cosmological term, whereas its non-zero vacuum amplitude is induced by the (Ricci scalar) curvature of the Sun's spacetime manifold.     

Nodal and periastron precession of inclined orbits in the field of a rapidly rotating neutron star

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates.     

Comment on the LRS-BDT-Bianchi type-V vacuum solution

We wish to point out that the anisotropic LRS-BDT-Bianchi type-V vacuum solution recently given by Ram and Singh is wrong. Moreover, the correct solution is nothing but an isotropic FRW (k=–1) solution given by us previously.     

Massless scalar static spheres

It is known that the requirement of asymptotic flatness places restrictions on spherically-symmetric solutions to field equations. Here it is shown that the most general solution to the static spherically-symmetric massless scalar Einstein equations with zero cosmological constant is asymptotically flat; furthermore, the general solution is derived and shown to be identical to a solution previusly found by M. Wyman.     

Some Robertson-Walker models with time dependent <Emphasis Type="Italic">G</Emphasis> and Λ

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for Robertson-Walker universe by assuming the cosmological term proportional to the Hubble parameter. This variation law for vacuum density has recently been proposed by Schützhold on the basis of quantum field estimations in the curved and expanding background. The cosmological term tends asymptotically to a genuine cosmological constant and the model tends to a deSitter universe. We obtain that the present universe is accelerating with a large fraction of cosmological density in the form of cosmological term.     

Higher dimensional dust collapse with a cosmological constant

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman–Bondi metrics embedded in a de Sitter background. The solution is then matched to exterior HD Schwarzschild–de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.      

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

Self-consistent solutions of the semi-classical back-reaction equations with cosmological constant spatial curvature and perfect fluid

Exact solutions of the semi-classical Einstein equations with cosmological constant for conformally invariant free quantum fields in a general Robertson-Walker metric are found when a classical perfect fluid is present. There exist a one-parameter family of time-symmetric bouncing solutions that avoid the singularity and a one-parameter family which does not have particles horizons. The de Sitter solution is found to be stable, while the Einstein universe is unstable.