98.80 Hw

**[Introduction]{}**
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There have been various attempts towards a resolution of the problem of time in quantum general relativity [@hal:prd; @kie:cqg1; @kie:prd1; @kie:prd2; @kie:gr-qc; @wad:np; @singh:ann; @pad:prd; @pad:pram]. The classical Hamiltonian constraint, in quantum theory of gravity, leads in an appropriate operator version to the Wheeler-DeWitt equation $$\hat{H} \Psi =0,$$ where $\Psi$ is the wavefunction of the universe. The equation (1) when compared to a Schroedinger equation does not show the presence of time variable. In short, this is the problem of time in quantum gravity. Secondly, the interpretation of conservation of probability remain obscure without external time. Towards a solution of the problem of time in quantum gravity, a time variable $t$ is obtained [@kie:ttn; @kuch:grra] by performing an appropriate canonical transformation in which conjugate momentum $p_t$ occurs linearly such that $$H=H_r+p_t=0$$ in which $H_r$ is the reduced Hamiltonian with conjugate momentum occurring quadratically. Upon quantization this becomes $$\hat{H}\Psi=o\Leftrightarrow (\hat{H_r}+{\hbar\over i}
{\partial\over {\partial t}})\Psi=0\,.$$ Though this approach has been successful in cylindrical gravitational waves or eternal blackholes, its general viability remains unclear. In the second approach one starts with the Wheeler-DeWitt equations and looks at a sensible concept of time. In this approach the normalization of the 