Separable metrics and radiating stars

Abebe, G. Z.; Maharaj, S. D.

doi:10.1007/s12043-016-1329-0

Cited by 6 publications

(4 citation statements)

References 22 publications

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“…The various possible models with equation of state are given in Table 1. It is interesting to note that separable metric potentials also yield an equation of state as shown by Abebe and Maharaj [34]…”

Section: Equation Of Statementioning

confidence: 87%

Charged radiating stars with Lie symmetries

Abebe

Maharaj

2019

Eur. Phys. J. C

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We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

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Section: Equation Of Statementioning

confidence: 87%

Charged radiating stars with Lie symmetries

Abebe

Maharaj

2019

Eur. Phys. J. C

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“…The n dimensional solution reduces to the four dimensional solution by Naidoo et al [42] when n = 4 in (56). It is still necessary to show that the condition ( 51) is integrable, as will be demonstrated below.…”

Section: Transformed Riccati Equationmentioning

confidence: 92%

“…Some results in this regard are presented in Naidoo et al [42]. In the absence of or Q particular models of the boundary condition were obtained by Govinder and Govender [31], Abebe et al [34] and Abebe and Maharaj [28,56] with a barotropic equation of state. The presence of Q and leads to more complex gravitational interactions.…”

Section: Equation Of Statementioning

confidence: 96%

Radiating stars and Riccati equations in higher dimensions

2023

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The objective of this study is to investigate spherically symmetric radiating stars undergoing gravitational collapse, in higher dimensional general relativity, inclusive of acceleration, expansion, shear, an electromagnetic field and a cosmological constant. Methods that can be used to obtain exact solutions to the boundary condition with/without a linear equation state are studied. Two distinct approaches are investigated. In the first approach, the boundary condition is expressed as a Riccati equation in terms of one of the dependent variables, and restrictions are placed to obtain new exact solutions. In the second approach, transformations that map the boundary condition into a new Riccati equation are investigated. The resulting new transformed equation is solved, by placing restrictions on the coefficients, to obtain new exact models. Special properties of the transformation are shown when appropriate restrictions on the parameters of the transformation are placed. This allows the order of the boundary condition to be reduced from a second order partial differential equation into a first order partial differential equation. The versatility of the transformation on other equations is exhibited when new solutions to the system of equations consisting of both the boundary condition and equation of state are obtained. When the dimension is set to four, some known solutions are recovered. It is shown that horizons can be identified by using a special case of the transformation. Our results elucidates the importance of the use of transformations that map the coordinates of differential equations into new and different coordinate systems.

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“…It also reduces to the integrable Bernoulli or linear equation when some of its coefficients vanish. Analytic solutions were found also by using the Lie symmetry group analysis [29] or separation of variables [30].…”

Section: Introductionmentioning

confidence: 99%

On general spherical fluid collapse

Иванов

2019

Eur. Phys. J. C

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A rather general form of spherical fluid collapse is formulated. The fluid is anisotropic, has shear, bulk and shear viscosities and is charged. It radiates energy through a heat flow or null radiation. The exterior solution is the charged Vaidya shining star solution. The general junction conditions are given. The main one represents a Riccati equation for the horizon function. We present a simple neutral solution, where the equation becomes a linear one. The whole mass of the star is radiated away without a remnant and the result is flat spacetime.

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Separable metrics and radiating stars

Cited by 6 publications

References 22 publications

Charged radiating stars with Lie symmetries

Charged radiating stars with Lie symmetries

Radiating stars and Riccati equations in higher dimensions

On general spherical fluid collapse

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