GENERAL RELATIVITY
CONTENTS THE PRINCIPLE OF SOLIDARITY: GEOMETRICAL DESCRIPTIONS OF INTERACTIONS THE FINZI PRINCIPLE OF SOLIDARITY AN AXIOMATIC VIEW TO SPECIAL RELATIVITY ENERGY AND THE FINZI PRINCIPLE DESCRIPTION OF INTERACTIONS BY ENERGY-DEPENDENT METRICS DEFORMED MINKOWSKI SPACE–TIME ENERGY AS DYNAMIC VARIABLE DEFORMED SPECIAL RELATIVITY POSTULATES OF DEFORMED SPECIAL RELATIVITY MAXIMAL CAUSAL SPEED BOOSTS IN DSR DEFORMED LORENTZ TRANSFORMATIONS ALONG A COORDINATE AXIS BOOST IN A GENERIC DIRECTION SYMMETRIZATION OF DEFORMED BOOSTS CHOOSING THE BOOST DIRECTION IN DSR RECOVERING LORENTZ INVARIANCE IN DSR VELOCITY COMPOSITION LAW IN M AND THE INVARIANT MAXIMAL SPEED DSR AND LORENTZIAN RELATIVITY KINEMATICS AND WAVE PROPAGATION IN A DEFORMED MINKOWSKI SPACE DYNAMIC DE?NITION OF PROPER TIME DEFORMED RELATIVISTIC KINEMATICS WAVE PROPAGATION IN A DEFORMED SPACE–TIME FIELD DEFORMATION METRIC DESCRIPTION OF INTERACTIONS REVIEW OF PHENOMENOLOGICAL METRICS ELECTROMAGNETIC INTERACTION WEAK INTERACTION STRONG INTERACTION GRAVITATION THRESHOLD ENERGIES AND RECURSIVE METRICS ASYMPTOTIC METRICS DSR AS METRIC GAUGE THEORY II MATHEMATICS OF DEFORMED SPACE–TIME GENERALIZED MINKOWSKI SPACES AND KILLING SYMMETRIES GENERALIZED MINKOWSKI SPACES MAXIMAL KILLING GROUP OF A N-DIMENSIONAL GENERALIZED MINKOWSKI SPACE LIE GROUPS, PBW THEOREM AND THE TRANSFORMATION REPRESENTATION KILLING EQUATIONS IN A N-DIMENSIONAL GENERALIZED MINKOWSKI SPACE MAXIMAL KILLING GROUP OF MN SOLUTION OF KILLING EQUATIONS IN A 4D GENERALIZED MINKOWSKI SPACE IN?NITESIMAL STRUCTURE OF GENERALIZED SPACE–TIME ROTATION GROUPS FINITE-DIMENSIONAL REPRESENTATION OF IN?NITESIMAL GENERATORS AND GENERALIZED LORENTZ ALGEBRA GENERALIZED LORENTZ ALGEBRA DEPENDENCE OF THE TRANSFORMATION COMMUTATIVITY ON THE PARAMETRIC LEVEL THE CASE OF A 4D GENERALIZED MINKOWSKI SPACE SELF-REPRESENTATION OF THE IN?NITESIMAL GENERATORS DECOMPOSITION OF THE PARAMETRIC 4-TENSOR ??µ?(G) SPACE–TIME ROTATIONS IN A 4D DEFORMED MINKOWSKI SPACE DEFORMED LORENTZ GROUP AND SELF-REPRESENTATION BASIS OF IN?NITESIMAL GENERATORS DECOMPOSITION OF THE PARAMETRIC 4-TENSOR IN DSR IN?NITESIMAL TRANSFORMATIONS OF THE 4D DEFORMED LORENTZ GROUP 4D DEFORMED LORENTZ ALGEBRA FINITE STRUCTURE OF DEFORMED CHRONOTOPICAL GROUPS SPACE–TIME ROTATIONS IN A 4D GENERALIZED MINKOWSKI SPACE GENERAL CASE DEFORMED LORENTZ GROUP OF DSR FINITE SPACE–TIME ROTATIONS IN M IN?NITESIMAL GENERATORS FINITE DEFORMED BOOST ALONG A COORDINATE AXIS FINITE DEFORMED ROTATION ABOUT A COORDINATE AXIS ANTISYMMETRIC TENSOR OF DEFORMED ROTATION PARAMETERS PARAMETER RANGE AND GROUP COMPACTNESS DEFORMED BOOSTS AS PSEUDOROTATIONS DEFORMED TRUE ROTATION ABOUT A GENERIC AXIS PARAMETRIC DECOMPOSITION EXPONENTIATING THE DEFORMED IN?NITESIMAL ROTATION FINITE 3D DEFORMED BOOSTS IN A GENERIC DIRECTION DEFORMED GENERIC BOOST FROM VELOCITY DECOMPOSITION PARAMETRIC CHANGE OF BASIS FOR A DEFORMED BOOST IN A GENERIC DIRECTION DEFORMED SPACE–TIME TRANSLATIONS IN FOUR DIMENSIONS TRANSLATIONS IN 4D GENERALIZED MINKOWSKI SPACES THE GROUP OF 4D DEFORMED TRANSLATIONS 5D REPRESENTATION OF THE IN?NITESIMAL CONTRAVARIANT GENERATORS “MIXED” DEFORMED POINCAR´E ALGEBRA IN?NITESIMAL AND FINITE DEFORMED TRANSLATIONS IN DSR DEFORMED MINKOWSKI SPACE AS GENERALIZED LAGRANGE SPACE GENERALIZED LAGRANGE SPACES GENERALIZED LAGRANGIAN STRUCTURE OF M CANONICAL METRIC CONNECTION OF M INTRINSIC PHYSICAL STRUCTURE OF A DEFORMED MINKOWSKI SPACE: GAUGE FIELDS III EXPERIMENTS ON DEFORMED SPACE–TIME 10 LORENTZ AND CPT SYMMETRIES IN DSR 11 LORENTZ INVARIANCE BREAKDOWN: A BRIEF SURVEY 111 THEORETICAL DEVELOPMENTS 112 EXPERIMENTAL TESTS 12 SUPERLUMINAL PROPAGATION OF ELECTROMAGNETIC WAVES 13 THE SHADOW OF LIGHT: LORENTZIAN VIOLATION OF ELECTRODYNAMICS IN PHOTON SYSTEMS 131 DOUBLE-SLIT-LIKE EXPERIMENTS 132 CROSSING PHOTON BEAM EXPERIMENTS 133 THE SHADOW OF LIGHT: HOLLOW WAVE, LLI BREAKDOWN AND VIOLATION OF ELECTRODYNAMICS 14 THE COIL EXPERIMENT 141 EXPERIMENTAL SETUP AND RESULTS 142 LLI BREAKDOWN PARAMETER 143 INTERPRETATION IN TERMS OF DSR 15 THE SPEED OF GRAVITY 151 HOW FAST IS GRAVITY? 152 CAVENDISH-LIKE EXPERIMENT 1521 EXPERIMENTAL SETUP 1522 MEASUREMENT ANALYSIS AND RESULTS 153 INTERPRETATION IN TERMS OF DSR 16 PIEZONUCLEAR REACTIONS IN CAVITATED WATER 161 CAN PRESSURE WAVES TRIGGER NUCLEAR REACTIONS? 162 CAVITATING WATER EXPERIMENTS 1621 FIRST EXPERIMENT 1622 SECOND EXPERIMENT 1623 THIRD EXPERIMENT 163 PHENOMENOLOGICAL MODEL OF PIEZONUCLEAR REACTIONS 1631 CLASSICAL CAVITATION MODEL 1632 APPLICATION TO EUROPIUM 1633 LIMITS OF THE CLASSICAL MODEL 1634 DEFORMED SPACE–TIME OF STRONG INTERACTION 1635 THRESHOLD ENERGY FOR PIEZONUCLEAR REACTIONS 17 PIEZONUCLEAR REACTIONS IN CAVITATED SOLUTIONS 171 THE THORIUM EXPERIMENT 1711 EXPERIMENTAL SETUP AND RESULTS 1712 HADRO-LEPTONIC THORIUM DECAY IN DSR 172 EVIDENCE FOR NEUTRON EMISSION IN NON-MINKOWSKIAN CONDITIONS 1721 FIRST INVESTIGATION 1722 SECOND INVESTIGATION IV DEFORMED SPACE–TIME IN FIVE DIMENSIONS: GEOMETRY 18 MULTIDIMENSIONAL SPACE–TIME 19 EMBEDDING DEFORMED MINKOWSKI SPACE IN A 5D RIEMANN SPACE 191 FROM LLI BREAKDOWN TO ENERGY AS FIFTH DIMENSION 192 THE 5D SPACE–TIME–ENERGY MANIFOLD ?5 193 PHENOMENOLOGICAL 5D METRICS OF FUNDAMENTAL INTERACTIONS 20 EINSTEIN’S FIELD EQUATIONS IN ?5 AND THEIR SOLUTIONS 201 RIEMANNIAN STRUCTURE OF ?5 202 VACUUM EINSTEIN’S EQUATIONS 2021 CASE (I): SPACE ISOTROPY 2022 CASE (II): POWER ANSATZ 2023 PHENOMENOLOGICAL METRICS IN THE POWER ANSATZ 203 SOLVING EINSTEIN’S EQUATIONS 204 DISCUSSION OF SOLUTIONS 205 DR5 AND WARPED GEOMETRY 211 GENERAL CASE 212 THE HYPOTHESIS ? OF FUNCTIONAL INDEPENDENCE 213 SOLVING KILLING EQUATIONS IN ?5 IN THE ?-HYPOTHESIS 214 POWER ANSATZ AND REDUCTIVITY OF THE HYPOTHESIS ? 22 KILLING SYMMETRIES FOR THE 5D METRICS OF FUNDAMENTAL INTERACTIONS 221 ELECTROMAGNETIC AND WEAK INTERACTIONS 2211 VALIDITY OF THE ?-HYPOTHESIS 2212 KILLING ISOMETRIES FOR ELECTROMAGNETIC AND WEAK METRICS 2213 SOLUTION OF KILLING EQUATIONS BELOW THRESHOLD WITH VIOLATED ?-HYPOTHESIS 222 STRONG INTERACTION 2221 VALIDITY OF THE ?-HYPOTHESIS 2222 KILLING ISOMETRIES FOR STRONG METRIC 2223 SOLUTION OF STRONG KILLING EQUATIONS ABOVE THRESHOLD WITH VIOLATED ?-HYPOTHESIS 223 GRAVITATIONAL INTERACTION 2231 VALIDITY OF THE ?-HYPOTHESIS 2232 THE 5D ?-VIOLATING METRICS OF GRAVITATION 224 IN?NITESIMAL-ALGEBRAIC STRUCTURE OF KILLING SYMMETRIES IN ?5 2241 METRIC WITH CONSTANT SPACE–TIME COE?CIENTS 2242 STRONG METRIC FOR VIOLATED ?-HYPOTHESIS 2243 POWER ANSATZ METRICS WITH VIOLATED ?-HYPOTHESIS 225 FEATURES OF KILLING ISOMETRIES IN ?5 V DEFORMED SPACE–TIME IN FIVE DIMENSIONS: DYNAMICS 231 PROPER TIME IN DR5 232 GEODESICS EQUATIONS IN ?5 24 SOLUTION OF THE GEODESIC EQUATIONS IN THE POWER ANSATZ 241 GENERAL SOLUTION 242 GEODESIC MOTIONS FOR THE 5D METRICS OF FUNDAMENTAL INTERACTIONS 2421 GENERATING FUNCTION FOR ELECTROMAGNETIC AND WEAK METRICS 2422 GENERATING FUNCTION FOR STRONG AND GRAVITATIONAL METRICS 2423 GEODESICS FOR ELECTROMAGNETIC AND WEAK INTERACTIONS 2424 GEODESICS FOR STRONG AND GRAVITATIONAL INTERACTIONS 243 GRAVITATIONAL METRIC OF THE EINSTEIN TYPE 244 CLASS VIII AND THE HEISENBERG TIME–ENERGY UNCERTAINTY 25 COMPLETE SOLUTIONS OF GEODESIC EQUATIONS 251 MINKOWSKIAN BEHAVIOR 252 NON-MINKOWSKIAN BEHAVIOR 2521 ELECTROMAGNETIC AND WEAK INTERACTIONS UNDER THRESHOLD 2522 STRONG INTERACTION ABOVE THRESHOLD 2523 GRAVITATIONAL INTERACTION ABOVE THRESHOLD 253 SLICING AND DYNAMICS