Generalized geodesic radiating models

Mahomed, A. B.; Maharaj, S. D.; Narain, R.

doi:10.1140/epjp/i2019-12905-6

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…A useful transformation, for Riccati equations, was suggested by Ivanov [27][28][29] called the horizon function as it is related to the formations of horizons. Other treatments related to the horizon function are contained in the works of Mahomed et al [30][31][32]. A transformation related to that of Ivanov was considered by Thirukkanesh and Maharaj [33].…”

Section: Introductionmentioning

confidence: 99%

New Riccati equations for radiating matter

2022

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The relationship between radiating stars in general relativity and Riccati equations is investigated for a general matter distribution including the electromagnetic field and the cosmological constant. A generalised transformation relating the gravitational potentials for a spherically symmetric relativistic gravitating fluid is introduced. This generates a new Riccati equation at the surface of the radiating star. Exact solutions to the boundary condition are found and the gravitational potentials are given explicitly. Some of the consistency conditions can be reduced to Bernoulli equations which admit exact solutions. We also demonstrate that the reduction of order allows us to write the boundary condition as a first order equation utilising the generalised transformation. Solutions obtained using the generalised transformation also admit a linear equation of state.

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Section: Introductionmentioning

confidence: 99%

New Riccati equations for radiating matter

2022

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“…The interior matter distribution is heat conducting and the exterior spacetime is given by the conventional Vaidya metric. For comprehensive treatments of recent exact solutions for radiating stellar models see Abebe and Maharaj [52], Mohanlal et al [53] and Mohamed et al [54][55][56]. The generalized Vaidya spacetime may also be used to model a radiating star in general relativity.…”

Section: Radiating Starsmentioning

confidence: 99%

“…arises in the matching process, that governs the evolution of the radiating star is given by (p −q) = ρ . (55) This fundamental equation relates the external null string density ρ to the internal pressurep and the heat fluxq. at the surface of a star with a generalized atmosphere.…”

Section: Radiating Starsmentioning

confidence: 99%

Embedding with Vaidya geometry

Николаев

Maharaj

2020

Eur. Phys. J. C

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The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.

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“…Years later, with the solution of the field equations for a null fluid presented by Vaidya (1951) and with the junction conditions deduced by Santos (1985), it was possible to build more realistic gravitational collapse scenarios for isotropic fluids including dissipative fluxes such as heat flow (de Oliveira et al 1985;Herrera et al 1989;Bonnor et al 1989;Herrera et al 2006;Ivanov 2012) and shear and bulk viscosities (Chan et al 1994). In addition, models of gravitational collapse for anisotropic fluids with dissipative processes (Chan 2001;Govender et al 2019) and even with electric charge (Pinheiro & Chan 2013;Ivanov 2019a,b;Mahomed et al 2019) have been developed in recent years.…”

Section: Introductionmentioning

confidence: 99%

Stability and gravitational collapse of neutron stars with realistic equations of state

Pretel,

da Silva

2020

Preprint

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We discuss the stability and construct dynamical configurations describing the gravitational collapse of unstable neutron stars with realistic equations of state compatible with the recent LIGO-Virgo constraints. Unlike other works that consider the collapse of a stellar configuration without a priori knowledge if it is stable or unstable, we first perform a complete analysis on stellar stability for such equations of state. Negative values of the squared frequency of the fundamental mode indicate us radial instability with respect to the collapse of the unstable star to a black hole. We find numerical solutions corresponding to the temporal and radial behavior during the evolution of the collapse for certain relevant physical quantities such as mass, luminosity, energy density, pressure, heat flow, temperature and quantities that describe bulk viscous processes. Our results show that the equation of state undergoes abrupt changes close to the moment of event horizon formation as a consequence of dissipative effects. During the collapse process all energy conditions are respected, which implies that our model is physically acceptable.

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Generalized geodesic radiating models

Cited by 8 publications

References 26 publications

New Riccati equations for radiating matter

New Riccati equations for radiating matter

Embedding with Vaidya geometry

Stability and gravitational collapse of neutron stars with realistic equations of state

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