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1 Introduction2 Equation of State; 3 Relativistic Fluids: Outflows; 3.1 Time Dependent Relativistic Hydrodynamics; 3.2 Radiatively Driven Stationary Jets in Curved Space Time; 3.3 Relativistic MHD; 4 Accretion Flows; 4.1 Around Black Holes; 4.2 Accretion Around Compact Objects with Hard Surface; 5 Summary and Future Direction; References; Evolution of Imaging of Black Hole Accretion-Outflow System over Half a Century; 1 What to See?; 2 How to See?; 2.1 Semi Analytical Approach; 2.2 Ray Tracing; 3 Images of Accretion Disk-Outflow; 3.1 Observed Spectra of TCAF; 4 Sgr A*: The Prime Candidate

4.1 Spectral States5 Discussions and Conclusions; References; Gravitational Wave Emission from Binary Mergers: Ideal Versus Real Picture; 1 Introduction; 2 EMRI Dynamics; 2.1 GW Emission; 2.2 Hydrodynamic Drag; 3 Explorations So Far; 4 The Case of Transonic Accretion Flow; 4.1 Nature of Disk Flow; 4.2 Drag Effects on the Companion Black Hole; 4.3 Effects on GW Emission; 4.4 Issue of the Formation of Gap; 5 Discussion and Conclusion; References; Part II Solutions of Model Flows Around Compact Objects; My Experiences and Experiments with Transonic Flows Around Compact Objects; 1 Introduction

2 Global Accretion Solution2.1 Critical Point Analysis; 2.2 Accretion Solutions Containing Shocks; 2.3 Shocks in Two-Temperature Accretion Flow; 2.4 Accretion-Ejection Solutions; 3 Conclusion; References; Transonic Flow Solutions with Explicit Cooling and Viscosity; 1 Introduction; 1.1 Accretion onto Black Holes; 1.2 Two Component Advective Flow Model Description; 2 Transonic Solution in Dissipative Flows; 2.1 Effects of Compton Cooling in Transonic Flow; 2.2 Effects of Viscosity in Transonic Flows; 2.3 Spectral Signature of Presence of Jet; 3 Fitting of Satellites Data with TCAF

3.1 Presence of Double Horn Iron Line and Estimation of Spin3.2 Observational Signatures of Cooling and Viscosity; 4 Concluding Remarks; References; On the Nature of Outflows from Low Angular Momentum Inflows Around Black Holes; 1 Introduction; 2 Theoretical Predictions; 3 Observational Signatures; 4 Numerical Studies; 5 Outlook; References; Generalized Flows Around Neutron Stars; 1 Introduction; 2 Evolution of Theories: Timing Properties; 3 Evolution of Theories: Spectral Properties; 4 Two-Component Advective Flows Around Neutron Stars; 4.1 Prospect of TCAF as the Generalized Flow Around NS; 5 Spectral Modelling

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