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The Cauchy Problem in General Relativity
 
Hans Ringström KTH Royal Institute of Technology, Stockholm, Sweden
A publication of European Mathematical Society
The Cauchy Problem in General Relativity
Softcover ISBN:  978-3-03719-053-1
Product Code:  EMSESILEC/6
List Price: $58.00
AMS Member Price: $46.40
Please note AMS points can not be used for this product
The Cauchy Problem in General Relativity
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The Cauchy Problem in General Relativity
Hans Ringström KTH Royal Institute of Technology, Stockholm, Sweden
A publication of European Mathematical Society
Softcover ISBN:  978-3-03719-053-1
Product Code:  EMSESILEC/6
List Price: $58.00
AMS Member Price: $46.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS ESI Lectures in Mathematics and Physics
    Volume: 62009; 307 pp
    MSC: Primary 83;

    The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann–Lemaître–Robertson–Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions.

    This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship.

    The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

    Readership

    Graduate students and research mathematicians interested in mathematical physics.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 62009; 307 pp
MSC: Primary 83;

The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann–Lemaître–Robertson–Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions.

This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship.

The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.