Spherically Symmetric W-Quadratic Metrics

Guo, Enli; Mo, Xiaohuan

doi:10.1007/978-981-13-1598-5_8

Cited by 2 publications

(5 citation statements)

References 16 publications

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“…For the -COOH groups, typical pK A values are reported around 6-7. [40][41][42][43][44] Therefore, at a pH value of 5 the majority of -COOH moieties is protonated, leading to a charge neutral PAA segment and mainly positive charges within the PDha block. This then leads to aggregation at lower pH values (pH < 4), accompanied by increasing turbidity and precipitation at pH 2.3 (see also DLS experiments).…”

Section: Solution Behavior Of Paa 25 -B-pdha 50 and Ps 30 -B-pdha 40mentioning

confidence: 99%

Amphiphilic and double hydrophilic block copolymers containing a polydehydroalanine block

et al. 2017

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We present the synthesis and characterization of amphiphilic and double hydrophilic block copolymers containing a polydehydroalanine (PDha) block. First, polystyrene-block-poly(tert-butoxycarbonylaminomethyl acrylate) (PS-b-PtBAMA) and poly(n-butylacrylate)-block-poly(tert-butoxycarbonylaminomethyl acrylate) (PnBA-b-PtBAMA) were prepared by atom transfer radical polymerization (ATRP). Subsequent deprotection led to the corresponding PS-b-PDha and PnBA-b-PDha block copolymers. All intermediate stages were characterized by 1 H-, 13 C-or solid state MAS 13 C-NMR. Afterwards, the solution behavior of PAA-b-PDha was investigated by a combination of dynamic light scattering, zeta potential measurements, and potentiometric titrationrevealing that aggregation occurs upon reaching pH values of 3 or lower.In case of PS-b-PDha, core-corona micelles are formed in aqueous solution, as revealed by a combination of DLS and cryogenic transmission electron microscopy. † Electronic supplementary information (ESI) available. See

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Section: Solution Behavior Of Paa 25 -B-pdha 50 and Ps 30 -B-pdha 40mentioning

confidence: 99%

Amphiphilic and double hydrophilic block copolymers containing a polydehydroalanine block

et al. 2017

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“…Here we note that in the case of the spherically symmetric background, it always belongs to the type D [9][10][11][12]. However, for the axisymmetric background, that is not always the case.…”

Section: Introductionmentioning

confidence: 75%

“…The case with the general A(r, θ) will be left as the future work. We note that in the case of the spherically symmetric background, the wave equation with the general conformal factor can be derived [11,12], where the different radial coordinate is used. For the comparison of the radial coordinate, see appendix A.…”

Section: Gravitational-wave Equationmentioning

confidence: 99%

“…Finally here we have considered only the gravitational-wave equation. It would be interesting to study the wave equation on this background with the different spin, namely the Klein-Gordon equation, the Dirac equation and the Maxwell equation, as in the case of the spherically symmetric background [12].…”

Section: Jcap02(2024)046mentioning

confidence: 99%

“…In the previous study on the spherically symmetric background, it has been found that the gravitational-wave equation in general depends on the gauge [9][10][11][12], unless the background is vacuum, which is unavoidable due to the gauge-dependence of the source term [12]. In the case of the axisymmetric background, one also has similar problems for the choice the JCAP02(2024)046 gauge [13].…”

Section: Introductionmentioning

confidence: 99%

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Teukolsky-like equations in a non-vacuum axisymmetric type D spacetime

Guo,

Nakajima,

Lin

2024

J. Cosmol. Astropart. Phys.

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We study an axisymmetric metric satisfying the Petrov type D property with some additional ansatze, but without assuming the vacuum condition. We find that our metric in turn becomes conformal to the Kerr metric deformed by one function of the radial coordinate. We then study the gravitational-wave equations on this background metric in the case that the conformal factor is unity. We find that under an appropriate gauge condition, the homogeneous wave equations admit the separation of the variables, which is also helpful for solving the nonhomogeneous equations. The resultant ordinary differential equation for the radial coordinate gives a natural extension of the Teukolsky equation.

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Spherically Symmetric W-Quadratic Metrics

Cited by 2 publications

References 16 publications

Amphiphilic and double hydrophilic block copolymers containing a polydehydroalanine block

Amphiphilic and double hydrophilic block copolymers containing a polydehydroalanine block

Teukolsky-like equations in a non-vacuum axisymmetric type D spacetime

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