Lecture Notes in Physics

Stationary black holes in General Relativity.- Introduction.- Stationary black holes of General Relativity.- Schwarzschild spacetime.- Reissner-Nordstrom metric.- Kerr spacetime.- Kerr-Newman metric.- Energy conditions.- Conclusions.- Problems.- Horizons.- Introduction.- Null geodesic congruences and trapped surfaces.- Rindler horizons for accelerated observers in Minkowski spacetime.- Event horizons.- Killing horizons.- Apparent horizons.- Trapping horizons.- Isolated and dynamical horizons.- Kodama vector and surface gravity.- Surface gravities.- Spherical symmetry.- Rindler horizons revisited.- Conclusions.- Problems.- Cosmological horizons.- Introduction.- . 3.2 Hyperspherical coordinates for FLRW space.- Kruskal-Szekeres coordinates for de Sitter space.- Painlev'e-Gullstrand and Schwarzschild-like coordinates for k = 0 FLRW space.- Schwarzschild-like coordinates for general FLRW spaces.- Painleve-Gullstrand coordinates for general FLRW spaces.- Congruences of radial null geodesics in FLRW space.- Horizons in FLRW space.- Dynamics of cosmological horizons.- Another notation.- de Sitter space.- Thermodynamics of cosmological horizons in General Relativity.- Thermodynamics of de Sitter space.- Thermodynamics of apparent/trapping horizons in FLRW space.- Conclusions.- Problems.- Inhomogeneities in cosmological "backgrounds" in Einstein theory.- Introduction.- Schwarzschild-de Sitter-Kottler spacetime.- McVittie solution.- Charged McVittie spacetime.- An application to the quantization of black hole areas.- Generalized McVittie spacetimes.- Sultana-Dyer spacetime.- Husain-Martinez-Nunez spacetime.- Fonarev solutions.- Other analytic cosmological black hole solutions of the Einstein Equations.- Conclusions.- Cosmological inhomogeneities in alternative gravity.- Introduction.- Brans-Dicke cosmological black holes.- f (R) cosmological black holes.- Conclusions.- A Appendix.- A.1 Painleve-Gullstrand coordinates for general spherically symmetric metrics.- A.2 Kodama vector in FLRW space.- A2.1 Pseudo-Painlev'e-Gullstrand coordinates.- A.2.2 Comoving coordinates.- References.- Index.