GRAVITATIONAL SOLITONS

By N. GIRAL

CONTENTS INVERSE SCATTERING TECHNIQUE IN GRAVITY OUTLINE OF THE ISM 111 THE METHOD 112 GENERALIZATION AND EXAMPLES THE INTEGRABLE ANSATZ IN GENERAL RELATIVITY THE INTEGRATION SCHEME CONSTRUCTION OF THE N-SOLITON SOLUTION 141 THE PHYSICAL METRIC COMPONENTS GAB 142 THE PHYSICAL METRIC COMPONENT F MULTIDIMENSIONAL SPACETIME GENERAL PROPERTIES OF GRAVITATIONAL SOLITONS THE SIMPLE AND DOUBLE SOLITONS 211 POLE FUSION DIAGONAL BACKGROUND METRICS TOPOLOGICAL PROPERTIES 231 GRAVISOLITONS AND ANTIGRAVISOLITONS 232 THE GRAVIBREATHER SOLUTION EINSTEIN–MAXWELL ?ELDS THE EINSTEIN–MAXWELL ?ELD EQUATIONS THE SPECTRAL PROBLEM FOR EINSTEIN–MAXWELL ?ELDS THE COMPONENTS GAB AND THE POTENTIALS AA 331 THE N-SOLITON SOLUTION OF THE SPECTRAL PROBLEM 332 THE MATRIX X 333 VERI?CATION OF THE CONSTRAINTS 334 SUMMARY OF PRESCRIPTIONS THE METRIC COMPONENT F EINSTEIN–MAXWELL BREATHERS COSMOLOGY: DIAGONAL METRICS FROM KASNER ANISOTROPIC AND INHOMOGENEOUS COSMOLOGIES KASNER BACKGROUND GEOMETRICAL CHARACTERIZATION OF DIAGONAL METRICS 431 RIEMANN TENSOR AND PETROV CLASSI?CATION 432 OPTICAL SCALARS 433 SUPERENERGY TENSOR SOLITON SOLUTIONS IN CANONICAL COORDINATES 441 GENERALIZED SOLITON SOLUTIONS SOLUTIONS WITH REAL POLES 451 GENERATION OF BIANCHI MODELS FROM KASNER 452 PULSE WAVES 453 COSOLITONS SOLUTIONS WITH COMPLEX POLES 461 COMPOSITE UNIVERSES 462 COSOLITONS 463 SOLITON COLLISION COSMOLOGY: NONDIAGONAL METRICS AND PERTURBED FLRW NONDIAGONAL METRICS 511 SOLUTIONS WITH REAL POLES 512 SOLUTIONS WITH COMPLEX POLES BIANCHI II BACKGROUNDS COLLISION OF PULSE WAVES AND SOLITON WAVES SOLITONS ON FLRW BACKGROUNDS 541 SOLITONS ON VACUUM FLRW BACKGROUNDS 542 SOLITONS WITH A STIFF PERFECT ?UID ON FLRW 543 THE KALUZA–KLEIN ANSATZ AND THEORIES WITH SCALAR ?ELDS 544 SOLITONS ON RADIATIVE, AND OTHER, FLRW BACKGROUNDS CYLINDRICAL SYMMETRY CYLINDRICALLY SYMMETRIC SPACETIMES EINSTEIN–ROSEN SOLITON METRICS 621 SOLUTIONS WITH ONE POLE 622 COSOLITONS WITH ONE POLE 623 SOLITONS WITH TWO OPPOSITE POLES 624 COSOLITONS WITH TWO OPPOSITE POLES TWO POLARIZATION WAVES AND FARADAY ROTATION 631 ONE REAL POLE 632 TWO COMPLEX POLES 633 TWO DOUBLE COMPLEX POLES PLANE WAVES AND COLLIDING PLANE WAVES OVERVIEW PLANE WAVES 721 THE PLANE-WAVE SPACETIME 722 FOCUSING OF GEODESICS 723 PLANE-WAVE SOLITON SOLUTIONS COLLIDING PLANE WAVES 731 THE MATCHING CONDITIONS 732 COLLINEAR POLARIZATION WAVES: GENERALIZED SOLITON SOLUTIONS 733 GEOMETRY OF THE COLLIDING WAVES SPACETIME 734 NONCOLLINEAR POLARIZATION WAVES: NONDIAGONAL METRICS AXIAL SYMMETRY GENERAL N-SOLITON SOLUTION THE KERR AND SCHWARZSCHILD METRICS ASYMPTOTIC ?ATNESS OF THE SOLUTION GENERALIZED SOLITON SOLUTIONS OF THE WEYL CLASS 851 GENERALIZED ONE-SOLITON SOLUTIONS 852 GENERALIZED TWO-SOLITON SOLUTIONS TOMIMATSU–SATO SOLUTION