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This volume is based on the lectures given at the First Inter
University Graduate School on Gravitation and Cosmology organized
by IUCAA, Pune, in 1989. This series of Schools have been carefully
planned to provide a sound background and preparation for students
embarking on research in these and related topics. Consequently,
the contents of these lectures have been meticulously selected and
arranged. The topics in the present volume offer a firm
mathematical foundation for a number of subjects to be de veloped
later. These include Geometrical Methods for Physics, Quantum Field
Theory Methods and Relativistic Cosmology. The style of the book is
pedagogical and should appeal to students and research workers
attempt ing to learn the modern techniques involved. A number of
specially selected problems with hints and solutions have been
included to assist the reader in achieving mastery of the topics.
We decided to bring out this volume containing the lecture notes
since we felt that they would be useful to a wider community of
research workers, many of whom could not participate in the school.
We thank all the lecturers for their meticulous lectures, the
enthusiasm they brought to the discussions and for kindly writing
up their lecture notes. It is a pleasure to thank G. Manjunatha for
his meticulous assistence over a long period, in preparing this
volume for publication."
This book evolved out of some one hundred lectures given by twenty
experts at a special instructional conference sponsored by the
University Grants Commis sion, India. It is pedagogical in style
and self-contained in several interrelated areas of physics which
have become extremely important in present-day theoretical
research. The articles begin with an introduction to general
relativity and cosmology as well as particle physics and quantum
field theory. This is followed by reviews of the standard gauge
models of high-energy physics, renormalization group and grand
unified theories. The concluding parts of the book comprise
discussions in current research topics such as problems of the
early universe, quantum cosmology and the new directions towards a
unification of gravitation with other forces. In addition, special
concise treatments of mathematical topics of direct relevance are
also included. The content of the book was carefully worked out for
the mutual education of students and research workers in general
relativity and particle physics. This ambitious programe
consequently necessitated the involvement of a number of different
authors. However, care has been taken to ensure that the material
meshes into a unified, cogent and readable book. We hope that the
book will serve to initiate and guide a student in these different
areas of investigation starting from first principles and leading
to the exciting current research problems of an interdisciplinary
nature in the context of the origin and structure of the universe."
Our esteemed colleague C. V. Vishveshwara, popularly known as
Vishu, turned sixty on 6th March 1998. His colleagues and well
wishers felt that it would be appropriate to celebrate the occasion
by bringing out a volume in his honour. Those of us who have had
the good fortune to know Vishu, know that he is unique, in a class
by himself. Having been given the privilege to be the volume's
editors, we felt that we should attempt something different in this
endeavour. Vishu is one of the well known relativists from India
whose pioneer ing contributions to the studies of black holes is
universally recognised. He was a student of Charles Misner. His Ph.
D. thesis on the stability of the Schwarzschild black hole,
coordinate invariant characterisation of the sta tionary limit and
event horizon for Kerr black holes and subsequent seminal work on
quasi-normal modes of black holes have passed on to become the
starting points for detailed mathematical investigations on the
nature of black holes. He later worked on other aspects related to
black holes and compact objects. Many of these topics have matured
over the last thirty years. New facets have also developed and
become current areas of vigorous research interest. No longer are
black holes, ultracompact objects or event horizons mere
idealisations of mathematical physicists but concrete entities that
astrophysicists detect, measure and look for. Astrophysical
evidence is mounting up steadily for black holes."
Our esteemed colleague C. V. Vishveshwara, popularly known as
Vishu, turned sixty on 6th March 1998. His colleagues and well
wishers felt that it would be appropriate to celebrate the occasion
by bringing out a volume in his honour. Those of us who have had
the good fortune to know Vishu, know that he is unique, in a class
by himself. Having been given the privilege to be the volume's
editors, we felt that we should attempt something different in this
endeavour. Vishu is one of the well known relativists from India
whose pioneer ing contributions to the studies of black holes is
universally recognised. He was a student of Charles Misner. His Ph.
D. thesis on the stability of the Schwarzschild black hole,
coordinate invariant characterisation of the sta tionary limit and
event horizon for Kerr black holes and subsequent seminal work on
quasi-normal modes of black holes have passed on to become the
starting points for detailed mathematical investigations on the
nature of black holes. He later worked on other aspects related to
black holes and compact objects. Many of these topics have matured
over the last thirty years. New facets have also developed and
become current areas of vigorous research interest. No longer are
black holes, ultracompact objects or event horizons mere
idealisations of mathematical physicists but concrete entities that
astrophysicists detect, measure and look for. Astrophysical
evidence is mounting up steadily for black holes."
This volume is based on the lectures given at the First Inter
University Graduate School on Gravitation and Cosmology organized
by IUCAA, Pune, in 1989. This series of Schools have been carefully
planned to provide a sound background and preparation for students
embarking on research in these and related topics. Consequently,
the contents of these lectures have been meticulously selected and
arranged. The topics in the present volume offer a firm
mathematical foundation for a number of subjects to be de veloped
later. These include Geometrical Methods for Physics, Quantum Field
Theory Methods and Relativistic Cosmology. The style of the book is
pedagogical and should appeal to students and research workers
attempt ing to learn the modern techniques involved. A number of
specially selected problems with hints and solutions have been
included to assist the reader in achieving mastery of the topics.
We decided to bring out this volume containing the lecture notes
since we felt that they would be useful to a wider community of
research workers, many of whom could not participate in the school.
We thank all the lecturers for their meticulous lectures, the
enthusiasm they brought to the discussions and for kindly writing
up their lecture notes. It is a pleasure to thank G. Manjunatha for
his meticulous assistence over a long period, in preparing this
volume for publication."
This book evolved out of some one hundred lectures given by twenty
experts at a special instructional conference sponsored by the
University Grants Commis sion, India. It is pedagogical in style
and self-contained in several interrelated areas of physics which
have become extremely important in present-day theoretical
research. The articles begin with an introduction to general
relativity and cosmology as well as particle physics and quantum
field theory. This is followed by reviews of the standard gauge
models of high-energy physics, renormalization group and grand
unified theories. The concluding parts of the book comprise
discussions in current research topics such as problems of the
early universe, quantum cosmology and the new directions towards a
unification of gravitation with other forces. In addition, special
concise treatments of mathematical topics of direct relevance are
also included. The content of the book was carefully worked out for
the mutual education of students and research workers in general
relativity and particle physics. This ambitious programe
consequently necessitated the involvement of a number of different
authors. However, care has been taken to ensure that the material
meshes into a unified, cogent and readable book. We hope that the
book will serve to initiate and guide a student in these different
areas of investigation starting from first principles and leading
to the exciting current research problems of an interdisciplinary
nature in the context of the origin and structure of the universe."
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