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 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.