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4.4.33 Hayward-Kim-Lee wormhole type 1 4.4. EXACT SOLUTIONS OF THE EINSTEIN FIELD EQUATION Angular parts have been assumed as identical to the spherically symmetric line element. λ is a parameter. Charge and current density contain diverging terms for large r. Coordinates x = Metric ⎛ ⎜ ⎝ gµν = t r ϑ ϕ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 m r Contravariant Metric − 1 0 0 0 0 1 4 (1− 2 m r ) r 2 λ 2 0 0 0 0 r 2 0 0 0 0 r 2 sin 2 ϑ g µν ⎛ − ⎜ = ⎜ ⎝ r r−2 m 0 0 0 0 4 r (r − 2 m) λ2 0 0 1 0 0 0 Christoffel Connection Γ 0 01 = Γ 0 10 = Γ 0 01 Γ 1 00 = Γ 1 11 = − r 2 ⎞ ⎟ ⎠ 0 0 0 1 r 2 sin 2 ϑ m r (r − 2 m) 4 m (r − 2 m) λ2 r r − m r (r − 2 m) Γ 1 22 = −4 r 2 (r − 2 m) λ 2 Γ 1 33 = −4 r 2 (r − 2 m) sin 2 ϑ λ 2 ⎞ ⎟ ⎠ 326
CHAPTER 4. VIOLATION OF THE DUAL BIANCHI IDENTITY . . . Γ 2 12 = 1 r Γ 2 21 = Γ 2 12 Γ 2 33 = − cos ϑ sin ϑ Γ 3 13 = 1 r Γ 3 23 = cos ϑ sin ϑ Γ 3 31 = Γ 3 13 Γ 3 32 = Γ 3 23 Metric Compatibility ———— o.k. Riemann Tensor R 0 101 = m r 2 (r − 2 m) R 0 110 = −R 0 101 R 0 202 = −4 m r λ 2 R 0 220 = −R 0 202 R 0 303 = −4 m r sin 2 ϑ λ 2 R 0 330 = −R 0 303 327
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CRITICISMS OF THE EINSTEIN FIELD EQ
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Preface This monograph evolved out
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PREFACE in which the structure of t
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Contents 1 Introduction 5 2 A Revie
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CONTENTS 4.4.38 Perfect spherical f
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Chapter 1 Introduction by Myron W.
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CHAPTER 1. INTRODUCTION dynamics, d
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Chapter 2 A Review of Einstein Cart
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CHAPTER 2. A REVIEW OF EINSTEIN CAR
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where: CHAPTER 2. A REVIEW OF EINST
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Bibliography [1] M. W. Evans, “Ge
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Chapter 3 Fundamental Errors in the
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CHAPTER 3. FUNDAMENTAL ERRORS IN TH
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Hawking [80] says, CHAPTER 3. FUNDA
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where CHAPTER 3. FUNDAMENTAL ERRORS
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Bibliography [1] Schwarzschild, K.
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BIBLIOGRAPHY [28] Hughes, S. A. Tru
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BIBLIOGRAPHY [59] Lorentz, H. A. Ve
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Chapter 4 Violation of the Dual Bia
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CHAPTER 4. VIOLATION OF THE DUAL BI
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Charge Density ρ CHAPTER 4. VIOLAT
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Current Density J 1 CHAPTER 4. VIOL
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Current Density J 2 , J 3 CHAPTER 4
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Current Density J 3 Charge Density
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Current Density J 1 Current Density
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Charge Density ρ Current Density J
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Metric CHAPTER 4. VIOLATION OF THE
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Charge Density ρ Current Density J
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R 3 001 = CHAPTER 4. VIOLATION OF T
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G 12 = G 13 = CHAPTER 4. VIOLATION
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Bibliography [1] M. W. Evans, "Gene
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Chapter 5 Einstein’s Great Contri
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CHAPTER 5. EINSTEIN’S GREAT CONTR
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