Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This doctoral thesis by Samuele Silvervalle focuses on isolated objects within the framework of quadratic gravity, particularly examining static and spherically symmetric solutions. The work is situated within Stelle's theory, incorporating quadratic curvature terms as corrections to General Relativity. Through analytical and numerical methods, the thesis explores black holes, naked singularities, and non-vacuum solutions, assessing their geometrical properties and stability. It also analyzes the evaporation process of black holes and the implications of generalizing Stelle's theory with a scale-invariant approach. The research aims to provide insights into the behavior of compact objects under quadratic gravity, contributing to the broader understanding of gravitational theories beyond General Relativity. The intended audience includes physicists and researchers interested in advanced gravitational theories.

Mathematical physics --- Geophysics --- zwaartekracht --- wiskunde --- fysica --- General relativity (Physics) --- Quantum gravity. --- Quantum gravity

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified? The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones. The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective.

Mathematical physics. --- Gravitation. --- Astrophysics. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravity. --- Black holes (Astronomy)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this book the author derives, under the classical non-relativistic consideration of the space-time, general forms of the most common physical laws invariant under the changes of inertial or non-inertial coordinate systems, both in the Classical and the Quantum regime. Some important examples of such invariant Physical Laws are the Maxwell Equations, the Newtonian gravity as well as several more complicated models of gravity and many other Physical Laws including many Laws of Quantum Mechanics, Thermodynamics and Statistical Physics, Continuum Mechanics, Optics et. al. Moreover, several basic Laws of Relativistic Physics, both in the classical and Quantum levels can be still formulated invariant under the non-relativistic consideration of the space-time, like the Classical Relativistic Second Law of Newton and Quantum Dirac and Klein--Gordon equations for relativistic particles, including their interaction with the outer gravitational field. In particular, we introduce the Hamiltonian formulation of the Dirac equation, and moreover, we were able to formulate the Dirac equation for multiple particles, similarly to what was done for the Schroedinger equation of the Non-relativistic Quantum Mechanics. One of the goals of this work is the general self-contained and simple mathematical formulation of the most general Physical Laws in a manner understandable to the reader familiar only with basic calculus, Classical Mechanics and some basic elements of non-relativistic Quantum Mechanics.

Gravitation. --- Electrodynamics. --- General relativity (Physics). --- Classical and Quantum Gravity. --- Classical Electrodynamics. --- General Relativity. --- Electromagnetism.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook offers you a profound understanding of the core concepts in electrostatics and magnetostatics. Emphasis is placed on establishing strong mathematical fundamentals while also equipping you with problem-solving skills crucial for mastering these disciplines. It covers basic equations of electrostatics and solution of the Poisson equation as well as Magnetostatics. Reiner M. Dreizler, Professor emeritus of Theoretical Physics at Goethe University, Frankfurt/Main, works on many-body systems in quantum mechanics. Cora S. Lüdde, Diplom-physicist, research associate at Goethe University, Frankfurt/Main, Germany, working on application-oriented programming, researches computer arithmetic.

Electrodynamics. --- Gravitation. --- Mathematical physics. --- Classical Electrodynamics. --- Classical and Quantum Gravity. --- Theoretical, Mathematical and Computational Physics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book aims to present the topic of nonlinear and chaotic dynamics in a manner that is useful and beneficial to students and young researchers from various domains such as physics, mathematics, biology, or even medicine. A very important aspect of that topic is that the constraints of determinism do not imply a regular behavior or do not rely on predictability in describing the dynamics of natural systems. Exploring the evolution of natural systems has a great impact nowadays on a wide range of scientific domains. The dynamics of populations, cardiac fibrillation, communication systems, fluid flow, and atmospheric systems are just a few topics in which nonlinearity and chaos are a regular manifestation. This leads to the idea that it is necessary to find universal laws that govern these dynamics. The aforementioned variety in scientific topics is also sustained by an exponential interest in recent decades from readers in the scientific community and the non-scientific one as well. The book is devoted to the nonlinear and chaotic dynamics topic, a domain that is both trans- and multi-disciplinary and has been the focus of the scientific community in past decades.

System theory. --- Astrophysics. --- Mathematical physics. --- Gravitation. --- Complex Systems. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravity. --- Multifractals. --- Motion --- Mathematics.