Introduction On the cosmic scale,gravitation dominates the universe.Nuclear and electromagnetic forces account for the detailed processes that allow stars to shine and astronomers to see them.But it is gravitation that shapes the universe, determining the geometry of space and time and thus the large-scale distribution of galaxies.Providing insight into gravitation-its effects,its nature and its causes -is therefore rightly seen as one of the most important goals of physics and astronomy Through more than a thousand years of human history the common explanation of gravitation was based on the Aristotelian belief that objects had a natural place in an Earth-centred universe that they would seek out if free to do so.For about two and a half centuries the Newtonian idea of gravity as a force held sway.Then,in the twentieth century,came Einstein's conception of gravity as a manifestation of spacetime curvature.It is this latter view that is the main concern of this book. The story of Einsteinian gravitation begins with a failure.Einstein's theory of special relativity,published in 1905 while he was working as a clerk in the Swiss Figure I Albert Einstein Patent Office in Bern,marked an enormous step forward in theoretical physics (1879-1955)depicted during the and soon brought him academic recognition and personal fame.However,it also time that he worked at the Patent showed that the Newtonian idea of a gravitational force was inconsistent with the Office in Bern.While there,he relativistic approach and that a new theory of gravitation was required.Ten years published a series of papers later,Einstein's general theory of relativity met that need,highlighting the relating to special relativity, important role of geometry in accounting for gravitational phenomena and leading quantum physics and statistical on to concepts such as black holes and gravitational waves.Within a year and a mechanics.He was awarded the half of its completion,the new theory was providing the basis for a novel approach Nobel Prize for Physics in 1921, to cosmology-the science of the universe-that would soon have to take account mainly for his work on the of the astronomy of galaxies and the physics of cosmic expansion.The change in photoelectric effect. thinking demanded by relativity was radical and profound.Its mastery is one of the great challenges and greatest delights of any serious study of physical science. This book begins with two chapters devoted to special relativity.These are followed by a mainly mathematical chapter that provides the background in geometry that is needed to appreciate Einstein's subsequent development of the theory.Chapter 4 examines the basic principles and assumptions of general relativity-Einstein's theory of gravity-while Chapters 5 and 6 apply the theory to an isolated spherical body and then extend that analysis to non-rotating and rotating black holes.Chapter 7 concerns the testing of general relativity,including the use of astronomical observations and gravitational waves.Finally,Chapter 8 examines modern relativistic cosmology,setting the scene for further and ongoing studies of observational cosmology. The text before you is the result of a collaborative effort involving a team of authors and editors working as part of the broader effort to produce the Open University course S383 The Relativistic Universe.Details of the team's membership and responsibilities are listed elsewhere but it is appropriate to acknowledge here the particular contributions of Jim Hague regarding Chapters 1 and 2,Derek Capper concerning Chapters 3,4 and 7,and Aiden Droogan in relation to Chapters 5,6 and 8.Robert Lambourne was responsible for planning and producing the final unified text which benefited greatly from the input of the S383 Course Team Chair,Andrew Norton,and the attention of production editorIntroduction On the cosmic scale, gravitation dominates the universe. Nuclear and electromagnetic forces account for the detailed processes that allow stars to shine and astronomers to see them. But it is gravitation that shapes the universe, determining the geometry of space and time and thus the large-scale distribution of galaxies. Providing insight into gravitation – its effects, its nature and its causes – is therefore rightly seen as one of the most important goals of physics and astronomy. Through more than a thousand years of human history the common explanation of gravitation was based on the Aristotelian belief that objects had a natural place in an Earth-centred universe that they would seek out if free to do so. For about two and a half centuries the Newtonian idea of gravity as a force held sway. Then, in the twentieth century, came Einstein’s conception of gravity as a manifestation of spacetime curvature. It is this latter view that is the main concern of this book. Figure 1 Albert Einstein (1879–1955) depicted during the time that he worked at the Patent Office in Bern. While there, he published a series of papers relating to special relativity, quantum physics and statistical mechanics. He was awarded the Nobel Prize for Physics in 1921, mainly for his work on the photoelectric effect. The story of Einsteinian gravitation begins with a failure. Einstein’s theory of special relativity, published in 1905 while he was working as a clerk in the Swiss Patent Office in Bern, marked an enormous step forward in theoretical physics and soon brought him academic recognition and personal fame. However, it also showed that the Newtonian idea of a gravitational force was inconsistent with the relativistic approach and that a new theory of gravitation was required. Ten years later, Einstein’s general theory of relativity met that need, highlighting the important role of geometry in accounting for gravitational phenomena and leading on to concepts such as black holes and gravitational waves. Within a year and a half of its completion, the new theory was providing the basis for a novel approach to cosmology – the science of the universe – that would soon have to take account of the astronomy of galaxies and the physics of cosmic expansion. The change in thinking demanded by relativity was radical and profound. Its mastery is one of the great challenges and greatest delights of any serious study of physical science. This book begins with two chapters devoted to special relativity. These are followed by a mainly mathematical chapter that provides the background in geometry that is needed to appreciate Einstein’s subsequent development of the theory. Chapter 4 examines the basic principles and assumptions of general relativity – Einstein’s theory of gravity – while Chapters 5 and 6 apply the theory to an isolated spherical body and then extend that analysis to non-rotating and rotating black holes. Chapter 7 concerns the testing of general relativity, including the use of astronomical observations and gravitational waves. Finally, Chapter 8 examines modern relativistic cosmology, setting the scene for further and ongoing studies of observational cosmology. The text before you is the result of a collaborative effort involving a team of authors and editors working as part of the broader effort to produce the Open University course S383 The Relativistic Universe. Details of the team’s membership and responsibilities are listed elsewhere but it is appropriate to acknowledge here the particular contributions of Jim Hague regarding Chapters 1 and 2, Derek Capper concerning Chapters 3, 4 and 7, and Aiden Droogan in relation to Chapters 5,6and 8. Robert Lambourne was responsible for planning and producing the final unified text which benefited greatly from the input of the S383 Course Team Chair, Andrew Norton, and the attention of production editor 9