Quantum Gravity in Curved Space-Time of General Relativity

Abstract

The main contents of this thesis may be briefly summarized as follows: Chapter 1 contains a brief account of the Plebonski space­time . We specify there the various spacial class of spacetimes covered by the Plebanski spncetime • .Among the various special cases of the Plebanski spncetime a new spacetime discovered there· is the NUT - Kerr - Newman - Kasuya - de Sitter spacetime • This chapter also includes a discussion on the modification of the Plebanski space time and presents the modified fonn of the Plebanski spacetime • Chapter 2 deals with the separation of the variables of the Dirac equation in an arbitrary curved background spacetime • We dis­cuss there some of the special cases of the separated Dirac equationu The pertinent equation of the separated Dirac equation will be used to derive the radial decoupled Dirac equations for the concerned background spacetimes which will be useful in smdying the problems of.Hawking radiation . Since our efforts are con can tra tad on quan mm field theory in some interesting spacetimes of general rolativity which are not the black hole spacetimes but include the black hole spncetimes as special cases , we review in Chapter J , Hawking's quanmm effects near the event horizon of NUT- Kerr- Newman spo.cetime containing flat black hole spacetimes as special cases.Chapter 4 also reviews and extends the result obtained in Chapter 3. The Hawking radiation of Dirac particles is aw.died in NUT-Kerr-Newman de Sitter spacetime containing black hole space­times which are asymptotically flat as well as asymptotically de Sitter 6S special cases. Chapter 5 includes the investigation of Dirac particles in Kasner-type spacetime • Chapter 6 presents Hawking's thermal radiation by black hole near the horizons of the Plebanski spacctime containing a large number of spacetimes of which some are important from the physical point of view. The result obtained in this chapter not only encom­passes the lmown results but also includes some new results • This chapter ends with a concluding remarks •