THE LOCALISATION OF GRAVITATIONAL ENERGY, MOMENTUM, AND SPIN
CONTENTS INTRODUCTION HISTORICAL BACKGROUND OVERVIEW ABSTRACTS PHYSICAL SIGNI?CANCE OF THE BABAK-GRISHCHUK ENERGY-MOMENTUM TENSOR FLAT-SPACE GRAVITATION PHYSICAL CONTENT OF TAB GAUGE TRANSFORMATIONS TRANSFORMATION PROPERTIES OF TAB CONCLUSION 1 A APPENDIX: IN?NITESIMAL TRANSFORMATIONS BOOTSTRAPPING GRAVITY GRAVITON ACTION THE FIERZ-PAULI ACTION FIELD EQUATIONS ENERGY-MOMENTUM TENSOR PERTURBATIVE GRAVITY CONSERVATION LAW CONSTRUCTING THE GRAVITON ACTION MATTER MATTER PERTURBATIONS NON-VACUUM BACKGROUND 2 A APPENDIX: PADMANABHAN’S ANALYSIS 2 B APPENDIX: EXPANSION OF GAB LOCALISING THE ENERGY AND MOMENTUM OF LINEAR GRAVITY MOTIVATION AND DERIVATION PRELIMINARIES ENERGY-MOMENTUM CURRENTS DETERMINING THE ENERGY-MOMENTUM TENSOR PROPERTIES GAUGE INVARIANCE OF PLANE-WAVES POSITIVITY INTERACTIONS PULSES AND POINT-SOURCES GAUGE INVARIANCE AND MICROAVERAGING ARBITRARY GRAVITATIONAL FIELDS ENERGY-MOMENTUM AND TRANSVERSE-TRACELESS GAUGE TIME-INDEPENDENT FIELDS APPLICATIONS PLANE-WAVES LINEARISED SCHWARZSCHILD SPACETIME GRAVITATIONAL FIELD OF A COMPACT SOURCE 3 A APPENDIX: SOURCES THE COMPACT SOURCE THE POINT-SOURCE 3 B APPENDIX: PERSISTENT TRANSVERSE-TRACELESS GAUGE LOCALISING THE ANGULAR MOMENTUM OF LINEAR GRAVITY LOCAL ANGULAR MOMENTUM EXCHANGE GRAVITATIONAL INTRINSIC SPIN TENSOR THE PLANE-WAVE CONDITION THE TRACELESS CONDITION ANGULAR MOMENTUM MICROAVERAGE MOMENT OF ENERGY DE?NITIONS AND INTERPRETATION MOMENT OF ENERGY EXCHANGE GRAVITATIONAL PLANE-WAVES 4 A APPENDIX: MOMENT OF ENERGY EXCHANGE FROM FIRST PRINCIPLES LOCALISED ENERGETICS OF LINEAR GRAVITY: THEORETICAL DEVELOPMENT LAGRANGIAN FORMULATION THE FIERZ-PAULI LAGRANGIAN ENERGY-MOMENTUM TENSOR AND SPIN TENSOR BACKGROUND COUPLING AND SUPERPOTENTIALS BASIC PROPERTIES AND BELINFANTE TENSOR SELF-INTERACTION IN THE GRAVITATIONAL FIELD EQUATIONS THE EINSTEIN EQUATIONS THE EINSTEIN-CARTAN EQUATIONS FIELD REDE?NITION THE “CENTRAL” EXPANSION EXPANSION OF THE EINSTEIN HILBERT LAGRANGIAN FIELD REDE?NITIONS AND SUPERPOTENTIALS BEYOND SECOND ORDER NEW FIELDS FOR EINSTEIN-CARTAN 5 A APPENDIX: EINSTEIN-CARTAN THEORY KINEMATICS CURVATURE AND TORSION DYNAMICS PERTURBATIONS 5 B APPENDIX: AN IDENTITY 5 C APPENDIX: ADM ENERGY-MOMENTUM CLOSING REMARKS REFERENCES