A space-time functional formalism for classical field equations

We start from an O(4) = SU(2) × SU(2) Yang–Mills theory and argue that the O(4) indices can, in fact, be space-time indices. The resulting theory is that of a tensor, Cμαβ = −Cμβα, which is in a reducible representation of the Lorentz group.fj This is a special case of the extended Yang–Mills formalism of Gabrielli. Some special solutions of the classical field equations are found.

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NONEXISTENCE OF IRREVERSIBLE PROCESSES IN COMPACT SPACE–TIME

International Journal of Modern Physics A ◽

10.1142/s0217751x07036798 ◽

2007 ◽

Vol 22 (32) ◽

pp. 6227-6241 ◽

Cited By ~ 4

Author(s):

HOLGER B. NIELSEN ◽

MASAO NINOMIYA

Keyword(s):

Compact Space ◽

Initial Conditions ◽

Physical Space ◽

Second Law Of Thermodynamics ◽

Space Time ◽

Classical Field ◽

Irreversible Processes ◽

Second Law ◽

Field Equations ◽

Time Direction

It is shown that if physical space–time were truly compact there would only be of the order-of-one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a nontrivial second law of thermodynamics. We present a no-go theorem: irreversible processes would be extremely unlikely to occur for the almost unique solution for the intrinsically compact space–time world, although irreversible processes are well known to occur in general. What we assume here — the compact space–time — is that universe could not exist eternally. In other word if universe stays on forever (i.e. noncompact in time direction) our no-go theorem is not applicable.

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Post-Newtonian limit: second-order Jefimenko equations

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8229-7 ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

David Pérez Carlos ◽

Augusto Espinoza ◽

Andrew Chubykalo

Keyword(s):

Linear Equations ◽

Space Time ◽

Second Order ◽

Field Equations ◽

Gravitational Fields ◽

Mass Distributions ◽

Minkowski Space Time ◽

Theory Of Gravitation ◽

Gravity Probe ◽

Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

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SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

The ANZIAM Journal ◽

10.1017/s1446181109000108 ◽

2008 ◽

Vol 50 (2) ◽

pp. 143-176 ◽

Cited By ~ 1

Author(s):

GEORGE SZEKERES ◽

LINDSAY PETERS

Keyword(s):

Cosmological Solution ◽

Space Time ◽

Time Structure ◽

Variation Principle ◽

Field Equations ◽

Covering Group ◽

Space Time Structure ◽

Spinor Geometry ◽

Complete Set ◽

Particle Solution

AbstractThe structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian variation principle is used to derive the field equations for the spinor connection. The result is a complete set of field equations which allow the sources of the gravitational and electromagnetic fields, and the intrinsic spin of a particle, to appear as a manifestation of the space–time structure. A cosmological solution and a simple particle solution are examined. Further extensions to the connection group are proposed.

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DESITTER GAUGE THEORY OF GRAVITATION

International Journal of Modern Physics C ◽

10.1142/s0129183103004188 ◽

2003 ◽

Vol 14 (01) ◽

pp. 41-48 ◽

Cited By ~ 13

Author(s):

G. ZET ◽

V. MANTA ◽

S. BABETI

Keyword(s):

Gauge Theory ◽

Riemann Tensor ◽

Space Time ◽

Point Of View ◽

Field Equations ◽

Minkowski Space Time ◽

Strength Tensor ◽

Group A ◽

Theory Of Gravitation ◽

Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

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A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

International Journal of Modern Physics D ◽

10.1142/s0218271807010547 ◽

2007 ◽

Vol 16 (06) ◽

pp. 1027-1041 ◽

Cited By ~ 8

Author(s):

EDUARDO A. NOTTE-CUELLO ◽

WALDYR A. RODRIGUES

Keyword(s):

Gravitational Field ◽

Minkowski Space ◽

Gravitational Theory ◽

Space Time ◽

Lorentzian Geometry ◽

Field Equations ◽

Yang Mills ◽

Minkowski Space Time ◽

Clifford Bundle ◽

Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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Spinning cosmic strings in conformal gravity

International Journal of Modern Physics A ◽

10.1142/s0217751x20500244 ◽

2020 ◽

Vol 35 (05) ◽

pp. 2050024

Author(s):

Reinoud Jan slagter ◽

Christopher Levi Duston

Keyword(s):

Cosmic String ◽

Energy Condition ◽

Space Time ◽

Special Choice ◽

Mass Relation ◽

Conformal Gravity ◽

Field Equations ◽

Closed Timelike Curves ◽

The Core ◽

Kerr Space

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as [Formula: see text], with [Formula: see text] a dilaton field which contains all the scale dependences. The “unphysical” metric [Formula: see text] is related to the [Formula: see text]-dimensional Kerr space–time. The equation for the angular momentum [Formula: see text] decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, [Formula: see text] falls off as [Formula: see text] and [Formula: see text] close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory.

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Wormhole solutions in embedding class 1 space–time

International Journal of Modern Physics A ◽

10.1142/s0217751x21500159 ◽

2021 ◽

Vol 36 (02) ◽

pp. 2150015

Author(s):

Nayan Sarkar ◽

Susmita Sarkar ◽

Farook Rahaman ◽

Safiqul Islam

Keyword(s):

Dimensional Space ◽

Vacuum Solution ◽

Energy Condition ◽

Radial Distance ◽

Space Time ◽

Exotic Matter ◽

Einstein Field Equations ◽

Field Equations ◽

Asymptotically Flat ◽

Class 1

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an [Formula: see text]-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance [Formula: see text], the Schwarzschild radius, and match to the external vacuum solution.

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Instantons in quantum mechanics (QM)

Quantum Field Theory and Critical Phenomena ◽

10.1093/oso/9780198834625.003.0037 ◽

2021 ◽

pp. 899-918

Author(s):

Jean Zinn-Justin

Keyword(s):

Quantum Mechanics ◽

Saddle Points ◽

Descent Method ◽

Classical Field ◽

Steepest Descent ◽

Steepest Descent Method ◽

Gradient Term ◽

Leading Order ◽

Field Equations ◽

Barrier Penetration

Perturbative expansion can be generated by calculating Euclidean functional integrals by the steepest descent method always looking, in the absence of external sources, for saddle points in the form of constant solutions to the classical field equations. However, classical field equations may have non-constant solutions. In Euclidean stable field theories, non-constant solutions have always a larger action than minimal constant solutions, because the gradient term gives an additional positive contribution. The non-constant solutions whose action is finite, are called instanton solutions and are the saddle points relevant for a calculation, by the steepest descent method, of barrier penetration effects. This chapter is devoted to simple examples of non-relativistic quantum mechanics (QM), where instanton calculus is an alternative to the semi-classical Wentzel–Kramers–Brillouin (WKB) method. The role of instantons in some metastable systems in QM is explained. In particular, instantons determine the decay rate of metastable states in the semi-classical limit initially confined in a relative minimum of a potential and decaying through barrier penetration. The contributions of instantons at leading order for the quartic anharmonic oscillator with negative coupling are calculate explicitly. The method is generalized to a large class of analytic potentials, and explicit expressions, at leading order, for one-dimensional systems are obtained.

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Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

Canadian Journal of Physics ◽

10.1139/cjp-2015-0221 ◽

2016 ◽

Vol 94 (1) ◽

pp. 58-70 ◽

Cited By ~ 4

Author(s):

A. Sheykhi ◽

S.H. Hendi

Keyword(s):

Thermal Stability ◽

Causal Structure ◽

Space Time ◽

Nonlinear Electrodynamics ◽

Thermodynamic Quantities ◽

Black Brane ◽

Dilaton Field ◽

Field Equations ◽

Liouville Type ◽

Counter Term

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.

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