Narrow Results

The paper aims to explore the impact of composite operators containing a few physical quantities on the gravitational and electromagnetic fields, studying the influencing factors and physical properties of octonion field equations. Maxwell first utilized the quaternions and vector terminology to describe the electromagnetic fields. The octonions can be used to simultaneously describe the physical quantities of electromagnetic and gravitational fields, including the octonion field potential, field strength, field source, linear momentum, angular momentum, torque and force. In the octonion spaces, the field strength and quaternion operator are able to combine together to become one composite operator, making an important contribution to the field equations. Similarly, the field potential can also form some composite operators with the quaternion operator, and they have a certain impact on the field equations. Furthermore, other physical quantities can also be combined with the quaternion operator to form several composite operators. In these composite operators, multiple physical quantities can also have a certain impact on the field equations. In other words, the field strength does not occupy a unique central position, compared to other physical quantities in these composite operators. In the field theories described by the octonions, various field equations can be derived from the application of different composite operators. According to different composite operators, it is able to infer the field equations when the field strength or/and field potential make a certain contribution, and it is also possible to deduce several new field equations when the remaining physical quantities play a certain role. This further deepens the understanding of the physical properties of field equations.

We provide a general framework of global behavior of static solutions of spherically symmetric objects for the modeling of compact objects, making it an ideal fluid to study, analytically and numerically. We demonstrate that every single conceivable solution can be acquired by means of a solitary creating function characterized as far as one of the gravitational possibilities. We demonstrate that our answers can be used to display specific object applicants, for example, RX J 186-37, Her X-1, SAX J11808.4-3658 (SS1), SAX J11808.4-3658 (SS2) and PSR J1614-2230.

This paper provides a simplified description for simulating the coupling of dark energy with baryonic matter by considering a super-dense pulsar PSRJ1614-2230 as the model star. The starting equation of state for modeling the dark energy is motivated by the MIT Bag model for spherically confined hadrons and the observational evidences of its repulsive nature. Einstein field equations are solved in the stellar interior using the generalized framework of Tolman–Kuchowicz spacetime metric. The solutions are then analyzed for various physical parameters such as metric potential, pressure, density, energy conditions, etc. The physical analysis of multiple parameters indicates stable star formation. The proposed stellar model is free from all singularities and also meets the requisite stability criteria. The numerical results obtained for relativistic adiabatic index indicate that the model star is stiff and stable against radially induced adiabatic perturbations.

We show that the Einstein field equations for a Friedmann-Robertson-Walker(FRW) universe are completely equivalent to a generalized Ermakov-Milne-Pinney system. This extends recent work of R. Hawkins and J. Lidsey, and provides an alternate method for deriving exact solutions of the field equations.

The first law of thermodynamics at black hole horizons is known to be obtainable from the gravitational field equations. A recent study claims that the contributions at inner horizons should be considered in order to give the conventional first law of black hole thermodynamics. Following this method, we revisit the thermodynamic aspects of field equations in the Lovelock gravity and f(R) gravity by focusing on two typical classes of charged black holes in the two theories.

In the literature, several spherically symmetric static solutions of the Einstein–Maxwell field equations (EMFEs) have been obtained by taking assumptions/ansatz on the parameters involved, like electric field intensity, gravitational potential, equation of state, etc. In this paper, using the Segre classification, we present a systematic scheme that limits the number of assumptions/ansatz required to be taken. It is found that the static spherically symmetric solutions of the EMFEs can only be of Segre types $[(1111)]$, $[(11)(11)]$, $[1(111)]$, or $[1(11)1]$. It is also shown that the type $[(1111)]$ leads to the Schwarzschild de-Sitter/anti de-Sitter solutions.

There are at least two ways to deduce Einstein’s field equations from the principle of maximum force $c^4/4G$ or from the equivalent principle of maximum power $c^5/4G$. Tests in gravitational wave astronomy, cosmology, and numerical gravitation confirm the two principles. Apparent paradoxes about the limits can all be resolved. Several related bounds arise. The limits illuminate the beauty, consistency and simplicity of general relativity from an unusual perspective.

In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry.

The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector fields (of special form) defined globally on TM defining the parallelization. Four different d-connections are used to explore the properties of this geometry. Simple and compact formulae for the curvature tensors and the W-tensors of the four defined d-connections are obtained, expressed in terms of the torsion and the contortion tensors of the EAP-space.

Further conditions are imposed on the canonical d-connection assuming that it is of Cartan type (resp. Berwald type). Important consequences of these assumptions are investigated. Finally, a special form of the canonical d-connection is studied under which the classical AP-geometry is recovered naturally from the EAP-geometry. Physical aspects of some of the geometric objects investigated are pointed out and possible physical implications of the EAP-space are discussed, including an outline of a generalized field theory on the tangent bundle TM of M.

Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further developments, with the search for the unification of the gravitation and the electromagnetism on a single unified theory. Some attempts to the geometrization of the electromagnetism emerged in this context, where these first models resided strictly on a classical basis. Posteriorly, they were followed by more complete and embracing quantum field theories. The present work reconsiders the classical viewpoint, with the purpose of showing that at first-order of approximation the electromagnetism constitutes a geometric structure aside other phenomena as gravitation, and that magnetic monopoles do not exist at least up to this order of approximation. Even though being limited, the model is consistent and offers the possibility of an experimental test of validity.

An analysis of the Schwinger’s action principle in Lagrangian quantum field theory is presented. A solution of a problem contained in it is proposed via a suitable definition of a derivative with respect to operator variables. This results in a preservation of Euler-Lagrange equations and a change in the operator structure of conserved quantities. Besides, it entails certain relation between the field operators and their variations (which is identically valid for some fields, e.g. for the free ones). The general theory is illustrated on a number of particular examples.