GRAVITATIONAL RADIATION, LUMINOUS BLACK HOLES AND GAMMA-RAY BURST SUPERNOVAE

By L. GILAT

CONTENTS LORENTZ TRANSFORMATIONS KINEMATIC EFFECTS QUASAR REDSHIFTS DOPPLER SHIFT RELATIVISTIC EQUATIONS OF MOTION CURVED SPACETIME AND SGRA? THE ACCELERATED LETTER “L” THE LENGTH OF TIMELIKE TRAJECTORIES GRAVITATIONAL REDSHIFT SPACETIME AROUND A STAR MERCURY’S PERIHELION PRECESSION A SUPERMASSIVE BLACK HOLE IN SGRA? PARALLEL TRANSPORT AND ISOMETRY OF TANGENT BUNDLES COVARIANT AND CONTRAVARIANT TENSORS THE METRIC GAB THE VOLUME ELEMENT GEODESIC TRAJECTORIES THE EQUATION OF PARALLEL TRANSPORT PARALLEL TRANSPORT ON THE SPHERE FERMI–WALKER TRANSPORT NONGEODESIC OBSERVERS THE LIE DERIVATIVE MAXWELL’S EQUATIONS P-FORMS AND DUALITY GEOMETRICAL INTERPRETATION OF FAB TWO REPRESENTATIONS OF FAB EXTERIOR DERIVATIVES STOKES’ THEOREM SOME SPECIFIC EXPRESSIONS THE LIMIT OF IDEAL MHD RIEMANNIAN CURVATURE DERIVATIONS OF THE RIEMANN TENSOR SYMMETRIES OF THE RIEMANN TENSOR FOLIATION IN SPACELIKE HYPERSURFACES CURVATURE COUPLING TO SPIN THE RIEMANN TENSOR IN CONNECTION FORM THE WEYL TENSOR THE HILBERT ACTION GRAVITATIONAL RADIATION NONLINEAR WAVE EQUATIONS LINEAR GRAVITATIONAL WAVES IN HIJ QUADRUPOLE EMISSIONS SUMMARY OF EQUATIONS COSMOLOGICAL EVENT RATES THE COSMOLOGICAL PRINCIPLE OUR FLAT AND OPEN UNIVERSE THE COSMOLOGICAL STAR-FORMATION RATE BACKGROUND RADIATION FROM TRANSIENTS OBSERVED VERSUS TRUE EVENT RATES COMPRESSIBLE FLUID DYNAMICS SHOCKS IN 1D CONSERVATION LAWS COMPRESSIBLE GAS DYNAMICS SHOCK JUMP CONDITIONS ENTROPY CREATION IN A SHOCK RELATIONS FOR STRONG SHOCKS THE MACH NUMBER OF A SHOCK POLYTROPIC EQUATION OF STATE RELATIVISTIC PERFECT FLUIDS WAVES IN RELATIVISTIC MAGNETOHYDRODYNAMICS IDEAL MAGNETOHYDRODYNAMICS A COVARIANT HYPERBOLIC FORMULATION CHARACTERISTIC DETERMINANT SMALL AMPLITUDE WAVES RIGHT NULLVECTORS WELL-POSEDNESS SHOCK CAPTURING IN RELATIVISTIC MHD MORPHOLOGY OF A RELATIVISTIC MAGNETIZED JET NONAXISYMMETRIC WAVES IN A TORUS THE KELVIN–HELMHOLTZ INSTABILITY MULTIPOLE MASS-MOMENTS IN A TORUS RAYLEIGH’S STABILITY CRITERION DERIVATION OF LINEARIZED EQUATIONS FREE BOUNDARY CONDITIONS STABILITY DIAGRAM NUMERICAL RESULTS GRAVITATIONAL RADIATION-REACTION FORCE PHENOMENOLOGY OF GRB SUPERNOVAE TRUE GRB ENERGIES A REDSHIFT SAMPLE OF 33 GRBS TRUE GRB SUPERNOVA EVENT RATE SUPERNOVAE: THE ENDPOINT OF MASSIVE STARS SUPERNOVA EVENT RATES REMNANTS OF GRB SUPERNOVAE X-RAY FLASHES CANDIDATE INNER ENGINES OF GRB/XRF SUPERNOVAE KERR BLACK HOLES KERR METRIC MACH’S PRINCIPLE ROTATIONAL ENERGY GRAVITATIONAL SPIN–ORBIT ENERGY E = J ORBITS AROUND KERR BLACK HOLES EVENT HORIZONS HAVE NO HAIR PENROSE PROCESS IN THE ERGOSPHERE LUMINOUS BLACK HOLES BLACK HOLES SURROUNDED BY A TORUS HORIZON FLUX OF A KERR BLACK HOLE ACTIVE BLACK HOLES A LUMINOUS TORUS IN GRAVITATIONAL RADIATION SUSPENDED ACCRETION MAGNETIC STABILITY OF THE TORUS LIFETIME AND LUMINOSITY OF BLACK HOLES RADIATION CHANNELS BY THE TORUS EQUATIONS OF SUSPENDED ACCRETION ENERGIES EMITTED BY THE TORUS A COMPACTNESS MEASURE GRB SUPERNOVAE FROM ROTATING BLACK HOLES CENTERED NUCLEATION AT LOW KICK VELOCITIES BRANCHING RATIO BY KICK VELOCITIES SINGLE AND DOUBLE BURSTERS RADIATIVELY DRIVEN SUPERNOVAE SN1998BW AND SN2002DH TRUE GRB AFTERGLOW ENERGIES OBSERVATIONAL OPPORTUNITIES FOR LIGO AND VIRGO SIGNAL-TO-NOISE RATIOS DIMENSIONLESS STRAIN AMPLITUDES BACKGROUND RADIATION FROM GRB-SNE LIGO AND VIRGO DETECTORS SIGNAL-TO-NOISE RATIOS FOR GRB-SNE A TIME-FREQUENCY DETECTION ALGORITHM CONCLUSIONS EPILOGUE: GRB/XRF SINGLETS, DOUBLETS? TRIPLETS!