1999 (IPP)
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Item Derivation of the Maxwell equations and the relation between electric and magnetic charge(2015-03-01) Singh, Parampreet; Dadhich, NareshItem New classes of black hole spacetime in 2+1 gravity(2015-03-01) Bose, Sukanta; Dadhich, Naresh; Kar, SyanNew multi-parameter families of black holes in three-dimensional (3D) gravity are obtained. We apply the electrogravity transformation (which implies an exchange of the Ricci and Einstein tensors) to the 3D field equations to obtain these solutions. Several properties of these geometries, including the nature of the matter that threads them, are discussed. Some of these properties are found to be strikingly different from known black holes in (2+1) dimensions.Item Domain walls in kaluza-klein spacetime(2015-03-01) Patel, L.K.; Dadhich, Naresh; Tikekar, R.Three families of exact solutions of Einstein field equations are found. Each family contains three parameters. Two of these families represent thick domain walls in a five dimensional Kaluza-Klein spacetime.The dynamical behaviour of our models is briefly discussed. The spacetime in all the cases is found to be reflection symmetric with respect to the wall.Item Higher dimensional analogue of McVittie solution(2015-03-01) Patel, L.K.; Tikekar, R.; Dadhich, NareshItem Exact solutions for null fluid collapse in higher dimensions(2015-03-01) Patel, L.K.; Dadhich, NareshA large family of inhomogeneous non-static spherically symmetric solutions of the Einstein equation for null fluid in higher dimensions has been obtained. It encompasses higher dimensional versions of many previously known solutions such as Vaidya, charged Vaidya and Husain solutions and also some new solutions representing global monopole or string dust. It turns out that physical properties of the solutions carry over to higher dimensions.Item Electromagnetic duality in general relativity(2015-03-01) Dadhich, NareshBy resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.Item Gravoelectric-dual of the kerr solution(2015-03-01) Dadhich, Naresh; Patel, L.K.By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality-invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way that it still admits the Kerr solution but is not duality invariant. The dual equation is then solved to obtain the dual-Kerr solution which can be interpreted as the Kerr black hole sitting in a string dust universe.Item Global monopole as dual-vacuum solution in kaluza-klein spacetime(2015-03-01) Dadhich, Naresh; Patel, L.K.; Tikekar, R.By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in 4-dimensional Euclidean space and would have massless limit analogus to the 4-dimensional dual-flat solution.Item On the electrogravity-dual solution to stringy charged black holes(2015-03-01) Bose, Sukanta; Dadhich, NareshBy resolving the Riemann curvature tensor relative to a timelike unit vector into electric and magnetic parts, electrogravity-duality transformation is defined. Such a transformation interchanges the "active" and "passive" electric parts of this tensor and can be used to obtain spacetime metrics dual to known solutions of any geometric theory of gravity, such as Einstein gravity. The vacuum field equations of general relativity are invariant under such a transformation. It is possible to break this symmetry by introducing matter terms in such a way that the characteristic vacuum solution is still obtained as a special case of that matter distribution. Such a possibility exists for all stationary black hole solutions. Interestingly, solutions exist even for the dual equations with the matter terms. Here, we extend this formalism to study the static, charged black hole solutions of a four-dimensional low-energy effective action of heterotic string theory. We show that analogous to general relativity, the dual solution is itself a similar black hole spacetime, endowed with a global monopole charge.Item A simple shear-free-non-singular spherical model with heat flux(2015-03-01) Dadhich, Naresh; Patel, L.K.We obtain an exact simple solution of the Einstein equation describing a spherically symmetric cosmological model without the bigbang or any other kind of singularity. The matter content of the model is shear free isotropic fluid with radial heat flux and it satisfies the weak and strong energy conditions. It is pressure gradient combined with heat flux that prevents occurrence of singularity. So far all known non-singular models have non-zero shear. This is the first shear free non-singular model, which is also spherically symmetric.