Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

Balakin, Alexander B.; Zayats, Alexei E.

doi:10.1088/1361-6382/aaaa60

Cited by 13 publications

(18 citation statements)

References 67 publications

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“…We can apply very similar arguments to P gg . First we have where the second equality uses ( 8) and ( 23), the third equality uses (17) and the final equality is (23). From the results that we have obtained, it follows that P µνρσαβ gg vanishes when symmetrized on any three indices.…”

Section: Combining the Symmetriesmentioning

confidence: 99%

Causality in gravitational theories with second order equations of motion

Reall

2021

Preprint

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This paper considers diffeomorphism invariant theories of gravity coupled to matter, with second order equations of motion. This includes Einstein-Maxwell and Einstein-scalar field theory with (after field redefinitions) the most general parity-symmetric four-derivative effective field theory corrections. A gauge-invariant approach is used to study the characteristics associated to the physical degrees of freedom in an arbitrary background solution. The symmetries of the principal symbol arising from diffeomorphism invariance and the action principle are determined. For gravity coupled to a single scalar field (i.e. a Horndeski theory) it is shown that causality is governed by a characteristic polynomial of degree 6 which factorises into a product of quadratic and quartic polynomials. The former is defined in terms of an "effective metric" and is associated with a "purely gravitational" polarisation, whereas the latter generically involves a mixture of gravitational and scalar field polarisations. The "fastest" degrees of freedom are associated with the quartic polynomial, which defines a surface analogous to the Fresnel surface in crystal optics. In contrast with optics, this surface is generically non-singular except on certain surfaces in spacetime. It is shown that a Killing horizon is an example of such a surface. It is also shown that a Killing horizon satisfies the zeroth law of black hole mechanics. The characteristic polynomial defines a cone in the cotangent space and a dual cone in the tangent space. The latter is used to define basic notions of causality and to provide a definition of a dynamical black hole in these theories.

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Section: Combining the Symmetriesmentioning

confidence: 99%

Causality in gravitational theories with second order equations of motion

Reall

2021

Preprint

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“…so that P ab and S ab have 6 independent components each, while Q ab (or, equivalently, R ab ) have the remaining 9 components. Notice that, in the context of electrodynamics in material media, these tensors would be related to the permittivity, permeability and magneto-electric cross terms of the medium [37].…”

Section: B Positive Definitnessmentioning

confidence: 99%

“…follows, which is to be satisfied for any 3-vectors a p and b q , not vanishing simultaneously. Furthermore, since our considerations are essentially algebraic we may restrict to an arbitrary point p ∈ M. In order to complete our symmetric hyperbolization, it suffices to find a specific covector n a ∈ T * p M satisfying inequality (37) since, if this is the case, there will be a unique connected, open and convex cone, S p , containing the initial covector, and this cone will exhaust all possibilities.…”

Section: B Positive Definitnessmentioning

confidence: 99%

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Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure

Goulart,

Bergliaffa

2021

Preprint

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It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant formalism, the general form for the symmetrizer, valid for a general Lagrangian theory, was obtained. When applied to nonlinear electromagnetism linearly coupled to curvature, the inequalities lead to strong constraints on the relevant quantities, which were illustrated with applications to particular cases. The examples show that non-linearity leads to constraints on the field intensities, and non-minimal coupling imposes restrictions on quantities associated to curvature.

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“…Among the multiple consequences of a nonminimal coupling (NMC), we can mention the following. The influence of such a coupling on the dispersion relation for waves was studied in [20]. Exact pp-wave solutions for gravity and electromagnetism in the NMC case were obtained in [21].…”

Section: Introductionmentioning

confidence: 99%

Strong Lensing and Nonminimally Coupled Electromagnetism

Bergliaffa,

Filho,

Maier

2020

Preprint

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The lensing at large deflection angles caused by a Schwarzschild black hole for the case of a nonminimal coupling between gravitation and electromagnetism is examined. We show that photons follow an effective geometry, which displays an effective photon sphere. For the case in which the source, lens and observer are aligned, so that relativistic Einstein rings are formed, the dependence of the angular separation δθ between the first and second ring with the relevant coupling parameter is calculated. We argue that such a separation, which may be measured by telescopes that will be operative in the near future, may set an upper and a lower limit for the coupling parameter.

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Non-minimal Einstein–Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor

Cited by 13 publications

References 67 publications

Causality in gravitational theories with second order equations of motion

Causality in gravitational theories with second order equations of motion

Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure

Strong Lensing and Nonminimally Coupled Electromagnetism

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