Hans Stephani

Bio: Hans Stephani is an academic researcher from University of Jena. The author has contributed to research in topics: Einstein & General relativity. The author has an hindex of 12, co-authored 37 publications receiving 5071 citations.

Exact Solutions of Einstein's Field Equations

Abstract: A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

Differential Equations: Their Solution Using Symmetries

Abstract: Preface 1 Introduction Part I Ordinary Differential Equations: 2 Point transformations and their generators 3 Lie point symmetries of ordinary differential equations: the basic definitions and properties 4 How to find the Lie point symmetries of an ordinary differential equation 5 How to use Lie point symmetries: differential equations with one symmetry 6 Some basic properties of Lie algebras 7 How to use Lie point symmetries: second order differential equations admitting a G2 8 Second order differential equations admitting a G3IX 9 Higher order differential equations admitting more than one Lie point symmetry 10 Systems of second order differential equations 11 Symmetries more general than Lie point symmetries 12 Dynamical symmetries: the basic definitions and properties 13 How to find and use dynamical symmetries for systems possessing a Lagrangian 14 Systems of first order differential equations with a fundamental system of solutions Part II Partial Differential Equations: 15 Lie point transformations and symmetries 16 How to determine the point symmetries of partial differential equations 17 How to use Lie point symmetries of partial differential equations I: generating solutions by symmetry 18 How to use Lie point symmetries of partial differential equations II: similarity variables and reduction of the number of variables 19 How to use Lie point symmetries of partial differential equations III: multiple reduction of variables and differential invariants 20 Symmetries and the separability of partial differential classification 21 Contact transformations and contact symmetries of partial differential equations, and how to use them 22 Differential equations and symmetries in the language of forms 23 Lie-Backlund transformations 24 Lie-Backlund symmetries and how to find them 25 How to use Lie-Backlund symmetries Appendices Index

Relativity : an introduction to special and general relativity

Abstract: Thoroughly revised and updated, this textbook provides a pedagogical introduction to relativity. It is self-contained, but the reader is expected to have a basic knowledge of theoretical mechanics and electrodynamics. It covers the most important features of both special and general relativity, as well as touching on more difficult topics, such as the field of charged pole-dipole particles, the Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools (tensor calculus, Riemannian geometry) are provided, most of the derivations are given in full, and exercises are included where appropriate. Written as a textbook for undergraduate and introductory graduate courses, it will also be of use to researchers working in the field. The bibliography gives the original papers and directs the reader to useful monographs and review papers.

General Relativity: An Introduction to the Theory of the Gravitational Field

Abstract: This book is an introduction to the theory of gravitation. It deals in an elementary way with those parts of the theory that are essential to the beginning student of general relativity, giving all the mathematics necessary to an understanding of the theory. Starting from the foundations of Riemannian geometry and the tensor calculus, the author formulates and works out the essential laws of physics in a Riemannian space. Next, the Einstein field equations are derived. All important applications of the theory are dealt with, including issues of current importance, in particular the Schwarzchild metric, gravitational waves, gravitational collapse, black holes and cosmological models. All the associated basic physical problems are fully discussed, but many results that draw heavily on mathematics are given without derivation. In the rather more demanding chapters on selected vector fields, groups of motion and the Petrov classification, methods are discussed which have proved to be especially fruitful in modern research.

A covariant holographic entanglement entropy proposal

Abstract: With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

Black Holes in Higher Dimensions

Abstract: We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

Surface terms as counterterms in the AdS-CFT correspondence

Abstract: We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti--de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions $dl~7.$ As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.

f(T) teleparallel gravity and cosmology

Abstract: Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.