Separability of test fields equations on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-metric background

Kofroň, David

doi:10.1103/physrevd.92.124064

Cited by 19 publications

(21 citation statements)

References 20 publications

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“…In the extremal case (r p = r m ) the point y = −1/Ar p is in general irregular singular point, and, thus, the asymptotic behaviour is difficult to investigate. But, in the case of static and axisymmetric configurations y = −1/Ar p becomes regular singular point, and the exponents then depend on the eigenvalues Λ (S) (l0) , which we found in [3] to be…”

Section: Radial Functionmentioning

confidence: 74%

“…The pioneering work on the separability of the Teukolsky master equation on the C -metric background has been done in [1] and generalized to the rotating case in [2]. In the preceding paper [3] we independently tackled the same problem and provided a separation for the "extreme" Newman -Penrose (NP) field components on the nonrotating C -metric background. To incorporate rotation in the C -metric is a natural generalization as some of the relativistic effects are present in rotating solutions only.…”

Section: Introductionmentioning

confidence: 99%

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Separability of test fields equations on theC-metric background. II. Rotating case and the Meissner effect

Kofroň

2016

Phys. Rev. D

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We present the separation of the Teukolsky master equation for the test field of arbitrary spin on the background of the rotating C -metric. We also summarize and simplify some known results about Debye potentials of these fields on type D background. The equation for the Debye potential is also separated.Solving for the Debye potential of the electromagnetic field we show that on the extremely rotating C -metric no magnetic field can penetrate through the outer black hole horizon -we thus recover the Meissner effect for the C -metric.

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Section: Radial Functionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Separability of test fields equations on theC-metric background. II. Rotating case and the Meissner effect

Kofroň

2016

Phys. Rev. D

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“…Cultures of dissociated DRG neurons represent a suitable in vitro model for the study of nerve regeneration. Several studies have been performed to understand how DRG neurons can survive and extend neurites on different substrates, and the alignment of neurites on physical patterns of micro-/ nano-dimensions have been reported (Thompson and Buettner, 2006;Sørensen et al, 2007;Kofron et al, 2009;Richardson et al, 2011;di Summa et al, 2013). It has been demonstrated that one of the most important requirements for neurons to survive is the presence of glial cells (Richardson et al, 2011;Seggio et al, 2010;Wang et al, 2010).…”

Section: Discussionmentioning

confidence: 99%

Differentiated adipose-derived stem cells act synergistically with RGD-modified surfaces to improve neurite outgrowth in a co-culture model

Luca

Faroni

Downes

et al. 2013

J Tissue Eng Regen Med

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Peripheral nerve damage is a problem encountered after trauma and during surgery and the development of synthetic polymer conduits may offer a promising alternative to autografts. In order to improve the performance of the polymer to be used for nerve conduits, poly-ε-caprolactone (PCL) films were chemically functionalized with RGD moieties, using a chemical reaction previously developed. In vitro cultures of dissociated dorsal root ganglion (DRG) neurons provide a valid model to study different factors affecting axonal growth. In this work, DRG neurons were cultured on RGD-functionalized PCL films. Adult adipose-derived stem cells differentiated to Schwann cells (dASCs) were initially cultured on the functionalized PCL films, resulting in improved attachment and proliferation. dASCs were also co-cultured with DRG neurons on treated and untreated PCL to assess stimulation by dASCs on neurite outgrowth. Neuron response was generally poor on untreated PCL films, but long neurites were observed in the presence of dASCs or RGD moieties. A combination of the two factors enhanced even further neurite outgrowth, acting synergistically. Finally, in order to better understand the extracellular matrix (ECM)-cell interaction, a β1 integrin blocking experiment was carried out. Neurite outgrowth was not affected by the specific antibody blocking, showing that β1 integrin function can be compensated by other molecules present on the cell membrane. Copyright © 2013 John Wiley & Sons, Ltd.

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“…Vieira et al [121] show that for Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry " exact solutions of both angular and radial parts of the covariant Klein-Gordon equation in this background can be obtained, and are given in terms of the confluent Heun functions". In [122] , Kofron separates test fields equations on the non-rotating C-metric background. He finds that the resulting equations are of the Heun or confluent Heun form for the general case.…”

Section: Some Examples Of the Heun Equation In Physical Applicationsmentioning

confidence: 99%

Heun Functions and Some of Their Applications in Physics

Hortaçsu

2018

Advances in High Energy Physics

102

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Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is one of these examples, which recently is often encountered in problems in general relativity and astrophysics. Its special and confluent forms take names as Mathieu, Lamé and Coulomb spheroidal equations. For these equations whenever a power series solution is written, instead of a two way recursion relation between the coefficients in the series, we find one between three or four different ones. An integral transform solution using simpler functions also is not obtainable.The use of this equation in physics and mathematical literature exploded in the later years, more than doubling the number of papers with these solutions in the last decade, compared to time period since this equation was introduced in 1889 up to 2008. We use SCI data to conclude this statement, which is not precise, but in the correct ballpark. Here this equation will be introduced and examples for its use, especially in general relativity literature will be given. * This paper is a revised and many times updated version of the conference talk by the same author, published in

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Separability of test fields equations on theC-metric background

Cited by 19 publications

References 20 publications

Separability of test fields equations on theC-metric background. II. Rotating case and the Meissner effect

Separability of test fields equations on theC-metric background. II. Rotating case and the Meissner effect

Differentiated adipose-derived stem cells act synergistically with RGD-modified surfaces to improve neurite outgrowth in a co-culture model

Heun Functions and Some of Their Applications in Physics

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