Gravitational Casimir Effect at Finite Temperature

Santos, A. F.; Khanna, F. C.

doi:10.1007/s10773-016-3156-y

Cited by 10 publications

(11 citation statements)

References 42 publications

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“…Note that the linearized Christoffel symbols calculated from the metric (20) should be employed in the equation in the (21) above. For further details, we refer the reader to [29].…”

Section: Gem Formalism Of Linearized Gravitymentioning

confidence: 99%

“…The gauge properties and the non-abelian extension of GEM formalism were discussed in [18,19]. The thermalization of the GEM systems and the research of several thermal quantum processes was performed in [20][21][22][23][24]. (For excellent reviews on the topic of the GEM formalism and on its applications see, e.g., [25][26][27][28][29][30][31]).…”

Section: Introductionmentioning

confidence: 99%

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Gravitoelectromagnetic Knot Fields

2021

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We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada–Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the GEM knots are calculated. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the GEM knots are computed.

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“…Note that the linearized Christoffel symbols calculated from the metric (20) should be employed in the equation in the (21) above. For further details, we refer the reader to [29].…”

Section: Gem Formalism Of Linearized Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gravitoelectromagnetic Knot Fields

2021

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“…Using the GEM formulation and considering plates that are made of superconducting material, the gravitational Casimir effect has been analyzed [32]. The Casimir effect for GEM at finite temperature has been calculated [33]. In the present study the Casimir energy and pressure and the Stefan-Boltzmann law for the GEM field with Lorentz-violating corrections at finite temperature are calculated.…”

Section: Introductionmentioning

confidence: 99%

Lorentz violation and gravitoelectromagnetism: Casimir effect and Stefan-Boltzmann law at finite temperature

Santos

Khanna

2019

EPL

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The standard model and general relativity are local Lorentz invariants. However it is possible that at Planck scale there may be a breakdown of Lorentz symmetry. Models with Lorentz violation are constructed using Standard Model Extension (SME). Here gravitational sector of the SME is considered to analyze the Lorentz violation in Gravitoelectromagnetism (GEM). Using the energy-momentum tensor, the Stefan-Boltzmann law and Casimir effect are calculated at finite temperature to ascertain the level of local Lorentz violation. Thermo Field Dynamics (TFD) formalism is used to introduce temperature effects. Lorentz and CPT symmetries play a central role in the Standard Model (SM) and EinsteinGeneral Relativity (GR). GR is a classical theory that describes the gravitational force. The SM describes other three fundamental forces that are defined in a quantum version. There are models that seek to unify the two fundamental theories into a single one. Such a theory is expected to emerge at the Planck scale, ∼ 10 19 GeV, where some new physics may emerge. The new physics may involve different properties, such as the appearance of Lorentz violation effects [1,2]. Studies of Lorentz violation, both theoretical and experimental, are described by an effective field theory called the Standard Model Extension (SME) [3]. The SME includes the SM, GR and all possible operators that break the Lorentz symmetry. A complete description of GR in the framework of the SME has been considered [4][5][6]. In the gravitational sector of the SME [7,8] there are 19 coefficients for Lorentz violation in addition to an unobservable scalar parameter. A similarity between the gravitational sector and the electromagnetic sector of the SME, specifically CPT-even coefficients, has been developed [9]. This would suggest a close relationship between gravitational and CPT-even electromagnetic sectors.The search for analogies between electromagnetism and gravity, for Lorentz invariant theories, started with Faraday [10] and Maxwell [11] and has a long history [12][13][14][15][16][17][18][19][20]. For a review of Gravitoelectromagnetism (GEM) follow references [21]. Experimental efforts to test GEM have been developed [22]. There are three different ways to construct GEM theory: (i) using the similarity between the linearized Einstein and Maxwell equations [21]; (ii) based on an approach using tidal tensors [23] and (iii) the decomposition of the Weyl tensor into gravitomagnetic (B ij = 1 2 ǫ ikl C kl 0j ) and gravitoelectric (E ij = −C 0i0j ) approach [24]. Here Weyl approach is considered. The Weyl tensor is connected with the curvature tensor and it is the trace-less part of the Riemann tensor. The analogy between electromagnetism and General Relativity is based on the correspondence C ασµν ↔ F ασ , where the Weyl tensor is the free gravitational field and F ασ is the electromagnetic tensor. The Weyl tensor gives contributions due to nonlocal sources. In the Weyl tensor approach, a Lagrangian formulation for GEM has been developed [25]. In this formalis...

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“…This force is due entirely to the change, brought about the presence of boundaries, in the energy of the vacuum. The relevance of the Casimir effect is apparent in many branches of physics, ranging from quantum field theory and theories with compactified extra dimensions [12][13][14], to gravitation [15][16][17] and condensed matter [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Casimir effect in Lorentz-violating scalar field theory: a local approach

Escobar,

Medel,

Martín-Ruiz

2020

Preprint

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Gravitational Casimir Effect at Finite Temperature

Cited by 10 publications

References 42 publications

Gravitoelectromagnetic Knot Fields

Gravitoelectromagnetic Knot Fields

Lorentz violation and gravitoelectromagnetism: Casimir effect and Stefan-Boltzmann law at finite temperature

Casimir effect in Lorentz-violating scalar field theory: a local approach

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