On the Principle of Holographic Scaling: From College Physics to Black Hole Thermodynamics

Description

Holographic dualities are at the forefront of contemporary physics research, peering into the fundamental nature of our universe and providing best attempt answers to humankind's bold questions about basic physical phenomena. Yet, the concepts, ideas and mathematical rigors associated with these dualities have long been reserved for the specific field researchers and experts. This book shatters this long held paradigm by bringing several aspects of holography research into the class room, starting at the college physics level and moving up from there. PRELIMS.pdf Preface Acknowledgements Author biographies Leo Rodriguez Shanshan Rodriguez CH001.pdf Chapter 1 Introduction 1.1 The four forces and the geometric Universe 1.2 QFT + GR 1.3 Cosmological evolution 1.4 Black holes and holographic scaling References CH002.pdf Chapter 2 ADM mass and holographic scaling in general physics 2.1 Vector notation and coordinates 2.2 Vectorized area 2.3 Gaussian surfaces 2.4 Mass in college physics 2.5 The gravielectric duality 2.6 Mass in university physics 2.7 On black holes in college/university physics 2.8 Schwarzschild black hole 2.9 Rotating/Kerr black hole 2.10 Effective Newtonian black hole potentials and ADM mass References CH003.pdf Chapter 3 Nöther’s theorem: E&M and gravity 3.1 Nöther’s theorem: E&M 3.2 Nöther’s theorem: Newtonian gravity 3.3 Nöther’s theorem and gravity: the metric tensor References CH004.pdf Chapter 4 Tensor calculus on manifolds 4.1 Index notation 4.2 Some point set topology and manifolds 4.3 Vectors, tensors and fields 4.4 The Lie derivative 4.5 Exterior algebra 4.6 Exterior derivative 4.7 Orientation 4.8 Stokes’ theorem 4.9 Riemannian mainfolds 4.10 Covariant differentiation 4.11 Geodesic equation 4.12 Curvature References CH005.pdf Chapter 5 Lagrangian field theory 5.1 E&M 5.2 Energy momentum tensor 5.3 General relativity References CH006.pdf Chapter 6 Black hole thermodynamics and holographic scaling 6.1 Black holes 6.2 Killing vectors and horizons 6.3 Surface element for null generators 6.4 The laws of black hole mechanics 6.5 Black hole thermodynamics 6.6 2D holographic representations of 4D black holes 6.7 On ADM mass in general relativity 6.8 4D ADM mass and holographic Γ 6.9 Holographic black hole thermodynamics 6.10 Concluding remarks References APP1.pdf Chapter APP2.pdf Chapter B.1 Homomorphisms and isomorphisms B.2 Automorphisms and normal subgroups B.3 Normal subgroups B.4 Group action