Some Studies in k essence Hawking Temperature Black hole Thermodynamics and Geodesic Structure of Spacetime

Abstract

In this thesis, we investigated the effect of various cosmological scenarios in the newlinepresence of dark energy using the k-essence theory. Mainly, the thesis comprises newlinethe study of Hawking temperature, black hole thermodynamics, and the geodesic newlinestructure of spacetime. It demonstrates that the k-essence emergent Reissner- newlineNordstrom-de Sitter (RNdS) type metric with cosmological constant and#923; is exactly newlinemapped to the Robinson-Trautman (RT) type metric with positive cosmological newlineconstant and#923; when the dark energy is involved. In addition to this, we have newlinedemonstrated that the k-essence emergent Kerr Newman (KN) type and Kerr newline Newman Anti de Sitter (KNAdS) type metrics are mapped to the new KN and newlineKNAdS type metrics along and#952; = 0 when dark energy is present. It is worth noting newlinethat the k-essence emergent gravity metric for the Schwarzchild background is newlineexactly mapped to a Barriola-Vilenkin (BV) type metric by swapping the global newlinemonopole charge for a constant kinetic energy, as was established by Gangopadhyay newlineet al. in an issue of EPL in 2012. The three emergent metrics are distinct newlinefrom conventional gravitational metrics when the the kinetic energy of k-essence newlinescalar field and#981; (i.e., the dark energy density in a unit of critical density) is present. newlineWe have determined the various thermodynamical quantities for the emergent newlinek-essence RNdS metric, and we have shown that the Hawking Temperatures are newlinemodified for the emergent KN and KNAdS background metrics along and#952; = 0, since newlinethe hawking temperature is independent of and#952; and and#934;. For the k-essence emergent newlineRNdS black hole, we have set a limit on the value of the dark energy density (K), newlinespecifying that it must equal unity. In addition, we find that the k-essence emergent newlineRNdS black holes are thermodynamically unstable in the presence of dark newlineenergy when the charge Q and#824;= 0, and it will not radiate when the charge Q = 0, newlinedespite the fact that studying the gravitational effect in the presence of dark newlinevi newlineenergy is crucial. For the k-essence emerging KN, KNAdS black holes, the permissible