Black holes are becoming increasingly important in contemporary research in astrophysics, cosmology, theoretical physics, and mathematics. Indeed, they provoke some of the most fascinating questions in fundamental physics, which may lead to revolutions in scientific thought. Written by distinguished scientists, Classical and Quantum Black Holes provides a comprehensive panorama of black hole physics and mathematics from a modern point of view. The book begins with a general introduction, followed by five parts that cover several modern aspects of the subject, ranging from the observational and the experimental to the more theoretical and mathematical issues. The material is written at a level suitable for postgraduate students entering the field.

Black holes are becoming increasingly important in contemporary research in astrophysics, cosmology, theoretical physics, and mathematics. Indeed, they provoke some of the most fascinating questions in fundamental physics, which may lead to revolutions in scientific thought. Written by distinguished scientists, Classical and Quantum Black Holes provides a comprehensive panorama of black hole physics and mathematics from a modern point of view. The book begins with a general introduction, followed by five parts that cover several modern aspects of the subject, ranging from the observational and the experimental to the more theoretical and mathematical issues. The material is written at a level suitable for postgraduate students entering the field.

Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.
With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.

Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected. With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.

Black holes are among the most mysterious objects that the human mind has been capable of imagining. As pure mathematical constructions, they are tools for exploiting the fundamental laws of physics. As astronomical sources, they are part of our cosmic landscape, warping space-time, coupled to the large-scale properties and life cycle of their host galaxy, and perhaps even linked to galaxy formation. This volume, which grew from a recent doctoral school sponsored by the Italian Society of Relativity and Gravitation, brings together contributions from leading authorities to provide a review of recent developments in the study of the astrophysical black holes that inhabit nearby galaxies and distant quasars. These lectures reveal the deep symbiotic relationship between black holes and their cosmic environment and show that black holes are key sources for exploring not only our local universe, but also our cosmic dawn. Topics range from the observational evidence for supermassive black holes and the joint evolution of black holes and galaxies to the cold dark matter paradigm of hierarchical galaxy formation and from the cosmic history of the diffuse intergalactic medium to the ecology of black holes in star clusters.

Black holes are among the most mysterious objects that the human mind has been capable of imagining. As pure mathematical constructions, they are tools for exploiting the fundamental laws of physics. As astronomical sources, they are part of our cosmic landscape, warping space-time, coupled to the large-scale properties and life cycle of their host galaxy, and perhaps even linked to galaxy formation. This volume, which grew from a recent doctoral school sponsored by the Italian Society of Relativity and Gravitation, brings together contributions from leading authorities to provide a review of recent developments in the study of the astrophysical black holes that inhabit nearby galaxies and distant quasars. These lectures reveal the deep symbiotic relationship between black holes and their cosmic environment and show that black holes are key sources for exploring not only our local universe, but also our cosmic dawn. Topics range from the observational evidence for supermassive black holes and the joint evolution of black holes and galaxies to the cold dark matter paradigm of hierarchical galaxy formation and from the cosmic history of the diffuse intergalactic medium to the ecology of black holes in star clusters.

Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theories, such as homological mirror symmetry and quantum cohomology.
Geometry and Physics of Branes provides an introduction to current research in some of these different areas, both in physics and mathematics. The book opens with a lucid introduction to the basic aspects of branes in string theory. Topics covered in subsequent chapters include tachyon condensation, the geometry surrounding the Gopakumar-Vafa conjecture (a duality between the SU(N) Chern-Simons theory on S3 and a IIA string theory compactified on a Calabi-Yau 3-fold), two-dimensional conformal field theory on open and unoriented surfaces, and the development of a homology theory naturally attached to the deformations of vector bundles that should be relevant to the study of homological mirror symmetry.