Relativistic Equations of Motion in Electromagnetic Theory

Wallace, Philip R.

doi:10.2307/2371617

Cited by 12 publications

(36 citation statements)

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“…In the end, this is equivalent to knowing the interactions themselves well enough as to determine the equations of motion of the mass centers, as shown by Einstein et alia, and also of charge centers, as shown by Wallace and Infeld in the interesting but less well known refs. [11][12][13]. 2 This mechanism is, obviously, much more general and explains, for instance, the existence of static multi-D-brane solutions in superstring theory effective field theories (super- 1 In an infinite periodic array of Schwarzschild black holes the total gravitation force over each of them vanishes and the conical singularities disappear [10].…”

Section: Jhep10(2017)066mentioning

confidence: 99%

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Dyonic black holes at arbitrary locations

Meessen

Ortı́n

Ramírez

2017

J. High Energ. Phys.

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We construct and study stationary, asymptotically flat multicenter solutions describing regular black holes with non-Abelian hair (colored magnetic-monopole and dyon fields) in two models of N = 2, d = 4 Super-Einstein-Yang-Mills theories: the quadratic model CP 3 and the cubic model ST [2,6], which can be embedded in 10-dimensional Heterotic Supergravity. These solutions are based on the multicenter dyon recently discovered by one of us, which solves the SU(2) Bogomol'nyi and dyon equations on E 3 . In contrast to the well-known Abelian multicenter solutions, the relative positions of the non-Abelian black-hole centers are unconstrained. We study necessary conditions on the parameters of the solutions that ensure the regularity of the metric. In the case of the CP 3 model we show that it is enough to require the positivity of the "masses" of the individual black holes, the finiteness of each of their entropies and their superadditivity. In the case of the ST [2, 6] model we have not been able to show that analogous conditions are sufficient, but we give an explicit example of a regular solution describing thousands of non-Abelian dyonic black holes in equilibrium at arbitrary relative positions. We also construct non-Abelian solutions that interpolate smoothly between just two aDS 2 ×S 2 vacua with different radii (dumbbell solutions).

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Section: Jhep10(2017)066mentioning

confidence: 99%

“…The equations of motion of the theory can be written in the following form: 11) where G Λ µν is the dual vector field strength…”

Section: Jhep10(2017)066mentioning

confidence: 99%

Dyonic black holes at arbitrary locations

Meessen

Ortı́n

Ramírez

2017

J. High Energ. Phys.

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“…If we assume that charged particles retain f 1 0 ∼ Q/r 2 down to the smallest radii probed by high energy particle physics experiments (10 −17 cm) we have from (35,12),…”

Section: The Einstein Equationsmentioning

confidence: 99%

“…Schrödinger later showed that it could be derived from a very simple Lagrangian density if a cosmological constant was included [6][7][8]. Einstein and Schrödinger suspected that the theory might include electrodynamics, but no Lorentz force was found [9,10] when using the EinsteinInfeld-Hoffmann (EIH) method [11,12]. Here we show that a simple modification of the Einstein-Schrödinger theory closely approximates Einstein-Maxwell theory, and the Lorentz force does result from the EIH method, and in fact the ordinary Lorentz force equation results when sources are included.…”

Section: Introductionmentioning

confidence: 99%

A modification of Einstein–Schrödinger theory that contains both general relativity and electrodynamics

Shifflett¹

2008

Gen Relativ Gravit

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We modify the Einstein-Schrödinger theory to include a cosmological constant Λ z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ z is assumed to be nearly cancelled by Schrödinger's cosmological constant Λ b which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ z + Λ b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |Λ z | → ∞. For |Λ z | ∼ 1/(Planck length) 2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are <10 −16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ∼10 −66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

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“…The question of which tensor represents the physical metric should be answered by the purely affine theory of gravitation and electromagnetism [74,103] extended to the nonsymmetric g µν . The corresponding equations of motion will be contained in the field equations derived from this Lagrangian [104,105,106,107,108,109].…”

Section: The Equations Of Motionmentioning

confidence: 99%