Faculty of Applied Sciences
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Item Charged radiation collapse in Einstein-Gauss-Bonnet gravity(Springer Science and Business Media LLC, 2022-04-25) Brassel, Byron P.; Maharaj, Sunil D.; Goswami, RituparnoWe generalise the continual gravitational col lapse of a spherically symmetric radiation shell of matter in f ive dimensional Einstein–Gauss–Bonnet gravity to include theelectromagneticfield.Thepresenceofchargehasasignif icant effectinthecollapsedynamics.Wenotethatthereexists a maximal charge contribution for which the metric func tions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of col lapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singular ity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity sepa rating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions N ≥ 5, charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post col lapse for all N ≥ 6 and a weak conical singularity forms when N =5.Acomparison with charged radiation collapse in general relativity is also given.Item Isotropic perfect fluids in modified gravity(MDPI AG, 2023-01) Naicker, Shavani; Maharaj, Sunil D.; Brassel, Byron P.We generate the Einstein–Gauss–Bonnet field equations in higher dimensions for a spherically symmetric static spacetime. The matter distribution is a neutral fluid with isotropic pressure. The condition of isotropic pressure, an Abel differential equation of the second kind, is transformed to a first order nonlinear canonical differential equation. This provides a mechanism to generate exact solutions systematically in higher dimensions. Our solution generating algorithm is a different approach from those considered earlier. We show that a specific choice of one potential leads to a new solution for the second potential for all spacetime dimensions. Several other families of exact solutions to the condition of pressure isotropy are found for all spacetime dimensions. Earlier results are regained from our treatments. The difference with general relativity is highlighted in our study.Item The role of dimension and electric charge on a collapsing geometry in Einstein–Gauss–Bonnet gravity(Springer Science and Business Media LLC, 2024-03) Brassel, Byron P.The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximumelectric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnetgravityaswellasgeneralrelativity. The charged gravitational collapse process is also similar for all dimensions N ≥ 5 unlike in the neutral scenario where there is a marked difference between the N = 5 and N > 5 cases. In the case where N = 5uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, beforesuccumbingtoaneventhorizon.Thesimilarityofchargedcollapseforallhigher dimensionsisauniquefeatureinthetheory.Thesufficientconditionsfortheformation of anakedsingularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested andit is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible.Item Radiating composite stars with electromagnetic fields(Springer Science and Business Media LLC, 2021-09) Maharaj, Sunil D.; Brassel, Byron P.We derive the junction conditions for a general spherically symmetric radiating star with an electromagnetic field across a comoving surface. The interior consists of a charged composite field containing barotropic matter, a null dust and a null string fluid. The exterior atmosphere is described by the generalised Vaidya spacetime. We generate the boundary condition at the stellar surface showing that the pressure is determined by the interior heat flux, anisotropy, null density, charge distribution and the exterior null string density. A new physical feature that arises in our analysis is that the surface pressure depends on the internal charge distribution for generalised Vaidya spacetimes. It is only in the special case of charged Vaidya spacetimes that the matching interior charge distribution is equal to the exterior charge at the surface as measured by an external observer. Previous treatments, for neutral matter and charged matter, arise as special cases in our treatment of composite matter.Item Radiating stars with composite matter distributions(Springer Science and Business Media LLC, 2021-04) Maharaj, Sunil D.; Brassel, Byron P.In this paper we study the junction conditions for a generalised matter distribution in a radiating star. The internal matter distribution is a composite distribution consisting of barotropic matter, null dust and a null string fluid in a shear-free spherical spacetime. The external matter distribution is a combination of a radiation field and a null string fluid. We find the boundary condition for the composite matter distribution at the stellar surface which reduces to the familiar Santos result with barotropic matter. Our result is extended to higher dimensions. We also find the boundary condition for the general spherical geometry in the presence of shear and anisotropy for a generalised matter distribution.Item Generalised radiating fields in Einstein-Gauss-Bonnet gravity(Springer Science and Business Media LLC, 2020-10-20) Brassel, Byron P.; Maharaj, Sunil D.A five-dimensional spherically symmetric generalised radiating field is studied in Einstein–Gauss–Bonnet gravity. We assume the matter distribution is an extended Vaidya-like source and the resulting Einstein–Gauss–Bonnet field equations are solved for the matter variables and mass function. The evolution of the mass, energy density and pressure are then studied within the spacetime manifold. The effects of the higher order curvature corrections of Einstein–Gauss–Bonnet gravity are prevalent in the analysis of the mass function when compared to general relativity. The effects of diffusive transport are then considered and we derive the specific equation for which diffusive behaviour is possible. Gravitational collapse is then considered and we show that collapse ends with a weak and conical singularity for the generalised source, which is not the case in Einstein gravity.Item Diffusive and dynamical radiating stars with realistic equations of state(Springer Science and Business Media LLC, 2017-03) Brassel, Byron P.; Maharaj, Sunil D.; Goswami, RituparnoWe model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.Item The effect of a two-fluid atmosphere on relativistic stars(Springer Science and Business Media LLC, 2015-07-11) Govender, Gabriel; Brassel, Byron P.; Maharaj, Sunil D.We model the physical behaviour at the surface of a relativistic radiating star in the strong gravity limit. The spacetime in the interior is taken to be spherically symmetrical and shear-free. The heat conduction in the interior of the star is governed by the geodesic motion of fluid particles and a nonvanishing radially directed heat flux. The local atmosphere in the exterior region is a two-component system consisting of standard pressureless (null) radiation and an additional null fluid with nonzero pressure and constant energy density. We analyse the generalised junction condition for the matter and gravitational variables on the stellar surface and generate an exact solution. We investigate the effect of the exterior energy density on the temporal evolution of the radiating fluid pressure, luminosty, gravitational redshift and mass flow at the boundary of the star. The influence of the density on the rate of gravitational collapse is also probed and the strong, dominant and weak energy conditions are also tested. We show that the presence of the additional null fluid has a significant effect on the dynamical evolution of the star.Item Charged fluids in higher order gravity(Springer Science and Business Media LLC, 2023-04-28) Naicker, Shavani; Maharaj, Sunil D.; Brassel, Byron P.We generate the field equations for a charged gravitating perfect fluid in Einstein–Gauss–Bonnet gravity for all spacetime dimensions. The spacetime is static and spherically symmetric which gives rise to the charged condition of pressure isotropy that is an Abel differential equation of the second kind. We show that this equation can be reduced to a canonical differential equation that is first order and nonlinear in nature, in higher dimensions. The canonical form admits an exact solution generating algorithm, yielding implicit solutions in general, by choosing one of the potentials and the electromagnetic field. An exact solution to the canonical equation is found that reduces to the neutral model found earlier. In addition, three new classes of solutions arise without specifying the gravitational potentials and the electromagnetic field; instead constraints are placed on the canonical differential equation. This is due to the fact that the presence of the electromagnetic field allows for a greater degree of freedom, and there is no correspondence with neutral matter. Other classes of exact solutions are presented in terms of elementary and special functions (the Heun confluent functions) when the canonical form cannot be applied.Item Charged dust in Einstein–Gauss–Bonnet models(Springer Science and Business Media LLC, 2023-10) Naicker, Shavani; Maharaj, Sunil D.; Brassel, Byron P.We investigate the influence of the higher order curvature terms on the static configuration of a charged dust distribution in EGB gravity. The EGB field equations for such a fluid are generated in higher dimensions. The governing equation can be written as an Abel differential equation of the second kind, or a second order linear differential equation. Exact solutions are found to these equations in terms of special functions, series and polynomials. The Abel differential equation of the second kind is reducible to a canonical differential equation; three new families of solutions are found by constraining the coefficients of the canonical equation. The charged dust model is shown to be physically well behaved in a region at the centre, and dust spheres can be generated. The higher order curvature terms influence the dynamics of charged dust and the gravitational behaviour which is distinct from general relativity.