Gravitational field of a radiating rotating body

A nonstationary solution of the Einstein field equations, corresponding to the field of a radiating rotating body, is presented. The solution is algebraically special of Petrov type II with a twisting, shear-free, null congruence identical to that of the Kerr metric. The new metric bears the same relation to the Kerr metric as does Vaidya's metric to the Schwarzschild metric, in the sense that in both cases the radiating solution is generated from the nonradiating one by replacing the mass parameter by an arbitrary function of a retarded time coordinate. The energy-momentum tensor in the present case, however, has two terms, a Vaidya type radiative one and an additional nonradiative residual term. Due to the presence of the nonradiative term in this case, however, the energy-momentum tensor becomes Vaidya-like asymptotically only, thus allowing for a geometrical optics interpretation. Asymptotically, part of the radiation field is purely electromagnetic with a Maxwell tensor which admits only one principal null direction corresponding to the undirectional flow of radiation.     

均匀弱磁场中的Kasuya双荷外部引力场

利用Ernst方法,在Harrison变换为线性变换的条件下,得到Kasuya荷电荷磁的外部引力场解,解中所含常量B₀表示一均匀弱磁场,该解不要求q=-2B₀J.当r趋于∞时,度规接近Melvin’s磁宇宙的渐进行为.该度规是非渐近平直的,在均匀外磁场下这是合理的结果. 关键词： Ernst方法 Kasuya双荷 磁场 引力场     

Field equations for gravity quadratic in the curvature

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian—namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type—is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differ from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.     

A rotating homogeneous universe with an electromagnetic field

The field equations of general relativity are solved to describe a gravitational field due to a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field. It turns out that the metric to describe this field is the well-known Robertson-Walker metric with positive space-time curvature or its particular case, the metric of the closed Einstein universe.     

Higher Dimensional Cosmology with Normal Scalar Field and Tachyonic Field

We have considered N-dimensional Einstein field equations in which four-dimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have supposed that the higher dimensional anisotropic universe is filled with only normal scalar field or tachyonic field. Here we have found the nature of potential of normal scalar field or tachyonic field. From graphical representations, we have seen that the potential is always decreases with field φ increases.     

Unified fields in pentadimensional theory

The theory of Jordan-Thiry is investigated by using a five-dimensional Riemannian manifold V₅ which admits a one-parameter group of isometries. The set of trajectories is supposed to represent the space-time of Relativity.The use of the induced metric in the quotient space leads to essential difficulties. It is necessary to consider a conformal metric and to modify the energy tensor in order to obtain the classical results of relativistic celestial mechanics. Moreover, the conformal metric brings out the evident interpretation of the fifteenth potential like a massless scalar field.A mass term referring to the scalar field is introduced; then the gravitational, electromagnetic, and mesonic scalar fields are unified through the metric of V₅. Several results make the new theory very coherent; in particular, the exact relativistic equations of motion are obtained asymptotically when the matter density vanishes.Exact solutions are searched. The classical Schwarzschild solution and neighbouring solutions are valid in the interior of the matter. Special non-static solutions are also obtained; some of these may be interpreted locally as describing the “collapse” of neutron stars; others ones, analogous to Robertson's metric, can be used to build a cosmology of the unified field.     

Euclidean non-vacuum wormholes in Brans－Dicke theory

The Brans－Dicke theory is investigated in which the Pauli metric is identified to be a physical spacetime metric. The solutions of a wormhole are obtained in Brans－Dicke theory with a relativistic radiation field for ω>-3/2. However, it is found that one cannot construct a wormhole in the presence of a 3-form axion field.     

Kerr-Newman metric in deSitter background

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.     

First order formalism off(R) gravity

The first order formalism is applied to study the field equations of a general Lagrangian density for gravity of the form . These field equations correspond to theories which are a subclass of conformally metric theories in which the derivative of the metric is proportional to the metric by a Weyl vector field. The resulting geometrical structure is unique, except whenf(R)=aR ², in the sense that the Weyl field is identifiable in terms of the trace of the energy-momentum tensor and its derivatives. In the casef(R)=aR ² the metric is only defined up to a conformai factor. We discuss the matter conservation equations which are implied by the invariance of the theories under diffeomorphisms. We apply the results to the case of dust and obtain that in general the dust particles will not follow geodesic Unes. We consider the linearized field equations and apply them to obtain the weak field slow motion limit. It is found that the gravitational potential acquires a new term which depends linearly on the mass density. The importance of these new equations is briefly discussed.     

Local and Non-Local Aspects of Quantum Gravity

The analysis of the measurement of gravitational fields leads to the Rosenfeld inequalities. They say that, as an implication of the equivalence of the inertial and passive gravitational masses of the test body, the metric cannot be attributed to an operator that is defined in the frame of a local canonical quantum field theory. This is true for any theory containing a metric, independently of the geometric framework under consideration and the way one introduces the metric in it. Thus, to establish a local quantum field theory of gravity one has to transit to non-Riemann geometry that contains (beside or instead of the metric) other geometric quantities. From this view, we discuss a Riemann–Cartan and an affine model of gravity and show them to be promising candidates of a theory of canonical quantum gravity.     

Gradient properties of the renormalisation group equations in multicomponent systems

The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ⁴ interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed.     

The gravitational field in the wave zone III. Elimination of the gauge condition

The gravitational field of a bounded source is studied as a formal series expansion of powers ofc ^–1 without the use of a gauge condition. The conditions imposed on the metric by the asymptotic flatness and some mathematical properties of the field equations at each step of the expansion are proved to be sufficient for the unique determination of those combinations of the metric components that describe the emission of gravitational radiation.     

Decoherence and Bare Mass Induced by Nonconformal Metric Fluctuations

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case of a nonrelativistic electron in interaction with a quantized electromagnetic field, we may speak of a bare mass, where the observed mass shows a dependence upon the stochastic terms included in the metric. Afterwards, we prove, resorting to the influence functional, that the energy–momentum tensor of the Klein–Gordon field inherites this stochastic behavior, and that this feature provokes decoherence upon a particle immersed in the region where this tensor is present.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.     

A rotating mass embedded in an Einstein-Gödel universe

A metric containing a parameterε(ε ²=1) has been obtained which represents a Kerr metric in the background of a static Einstein universe whenε is put equal to +1. The same metric will represent the external field of a mass embedded in a rotating Gödel universe whenε is set equal to ?1.     

A generalized field theory

Three solutions with spherical symmetry are obtained for the field equations of the generalized field theory established recently by Mikhail and Wanas. The solutions found are in agreement with classical known results. The solution representing a generalized field, outside a spherical symmetric charged body, is found to have an extra term compared with the Reissner-Nordström metric. The space used for application is of type FIGI, so the solutions obtained correspond to a field in a matter-free space. A brief comparison between the solutions obtained and those given by other field theories is given. Two methods have been used to get physical results: the first is the type analysis, and the second is the comparison with classical known results by writing down the metric of the associated Riemannian space.     

Cosmological Models with Rotation

A stationary cosmological model with rotation is constructed for the Ozsvath–Schucking metric where perfect fluid which is not comoving with the system is a source of the gravitational field. A nonstationary cosmological model for the Bianchi metric of type IX is also developed. This is characterized by expansion, rotation and acceleration. A co-moving with the system anisotropic liquid is a source of the gravitational field in this model.     

Gravitation,Electromagnetism and Cosmological Constant in Purely Affine Gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous (ΛCDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-Λ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-ΛCDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.