In this thesis we study some aspects of cosmology and black holes using field theoretic techniques. In second chapter, we present Lagrangian formulation for the non-relativistic as well as relativistic generalized Chaplygin gas (GCG). In rest of the thesis we discuss alternative approaches to compute the fluxes of Hawking radiation. These methods are based on covariant gauge/gravitational anomalies and chiral effective action. We also discuss a criterion to differentiate various black hole vacua within the framework of covariant anomaly approach.
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