The solutions so far have all be “in vacuum,” away from sources. In this chapter, we study gravity “in material.” For comparison, we review the continuum form of Newton’s second law and think about Newtonian gravitational predictions for, for example, hydrostatic equilibrium. Then we develop the relativistic version of those equations directly from Einstein’s equation with various source assumptions (spherical symmetry, perfect fluid) and obtain the interior Schwarzschild solution. Cosmology is another example of working “in material,” and we briefly review the Robertson–Walker starting point and solutions both with and without a cosmological constant. At the end of the chapter, spacetimes requiring exotic sources, including the Ellis wormhole and Alcubierre warp drive, are described.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

With the form of the target theory built up over the previous two chapters, we move to a geometric description of gravitational motion. By recasting the relative dynamics of a pair of falling objects as the deviation of nearby geodesic trajectories in a spacetime with a metric, Einstein’s equation is motivated. To describe geodesic deviation quantitatively, the Riemann tensor is introduced, and its role in characterizing spacetime structure is developed. With the full field equation of general relativity in place, the linearized limit is carefully developed and compared with the gravito-electro-magnetic theory from the first chapter.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.

Gravitational plane waves and their detection start the chapter off in parallel with electromagnetic plane waves and their detection. Geodesic deviation is reviewed and allows for a brief introduction to LIGO. The stress tensor source of radiation (and therefore, at least local, plane waves) and its conservation of energy and momentum are tied to the radiation solution of the linearized form of Einstein’s equation. A highlight is the role of gauge freedom in making gravitational plane waves physically relevant (by gauge fixing to reveal the underlying plus and cross polarizations). Power loss to gravitational radiation is discussed in the linearized limit by comparison with electric quadrupole radiation.