This book is devoted to researchers who would like to investigate interactions among gravitational waves and matter fields beyond linear order, including the phenomena of memory effects, gravitational Faraday rotation, soft theorems, and formations of spacetime singularities due to the mutual focus of gravitational waves. Readers only require a basic understanding of general relativity to understand the materials.The book starts with an overview on the fundamentals of the Newman-Penrose formalism and a brief introduction to distribution theory, with which the author systematically develops a mathematical description of spacetimes of colliding plane waves. Then, the author presents a frame-independent definition of polarization of a plane gravitational wave in a curved spacetime, studies in detail the gravitational Faraday rotation of two plane gravitational waves, and shows that each of them can serve as a medium to the other precisely due to their nonlinear interactions. Exact solutions are also presented, which represent a variety of models including the collisions of two plane gravitational waves and the collisions of a plane gravitational wave with a dust shell, a massless scalar wave, an electromagnetic wave, or a neutrino wave. The formation of spacetime singularities due to nonlinear interactions and the effects of gravitational wave polarization on the nature of singularities are also explored.

This book is devoted to researchers who would like to investigate interactions among gravitational waves and matter fields beyond linear order, including the phenomena of memory effects, gravitational Faraday rotation, soft theorems, and formations of spacetime singularities due to the mutual focus of gravitational waves. Readers only require a basic understanding of general relativity to understand the materials. The book starts with an overview on the fundamentals of the Newman-Penrose formalism and a brief introduction to distribution theory, with which the author systematically develops a mathematical description of spacetimes of colliding plane waves. Then, the author presents a frame-independent definition of polarization of a plane gravitational wave in a curved spacetime, studies in detail the gravitational Faraday rotation of two plane gravitational waves, and shows that each of them can serve as a medium to the other precisely due to their nonlinear interactions. Exact solutions are also presented, which represent a variety of models including the collisions of two plane gravitational waves and the collisions of a plane gravitational wave with a dust shell, a massless scalar wave, an electromagnetic wave, or a neutrino wave. The formation of spacetime singularities due to nonlinear interactions and the effects of gravitational wave polarization on the nature of singularities are also explored.

This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.

This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Many of the calculations are done in detail, without difficult mathematics, to help the students. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations.In the second edition, the famous twin paradox with acceleration is solved in full from the accelerated observer's frame. The findings of the Event Horizon Telescope (EHT) collaboration, who captured the first ever image of a black hole, are discussed in detail. The geodetic and frame drag precessions of gyroscopes in orbit about a rotating Earth are worked out and the Gravity Probe B (GPB) experiment is discussed. Also in the second edition are some new exercise problems.Resources are provided to instructors who adopt this textbook for their courses. Adopting instructors can print and copy portions of these resources solely for their teaching needs. All instructional resources are furnished for informational use only, and are subject to change without notice.

This volume presents the experimental and theoretical methods of studying soft interaction physics in high energy collisions. The topics include: dynamical and Bose-Einstein correlations, multiplicity fluctuation, soft photons, disoriented chiral condensate, self-similarity and self-affine behaviors, wavelet analysis, intermittency, chaos, and phase transition.

A theory that's combined with a collection of other theories about the workings of the universe in relation to a natural mathematical distribution of momentum or force. This is a book of personally typed up writings and handmade drawings about the universe. This is unprofessionally made to inspire the poor to pursue education or a career in science even if they think that they can’t afford resources or are too poor to figure things out that relate to science. Kinetic force is the natural mathematical distribution of momentum. It is the way force or energy naturally distributes itself in matter and spacetime to create everything in the universe from the smallest particles to the largest astronomical objects. This book is a theory like mainstream theoretical physics theories about how the universe formed and how everything in it works. This is kinetic force theory

Providing students with an in-depth account of the astrophysics of high energy phenomena in the Universe, the third edition of this well-established textbook is ideal for advanced undergraduate and beginning graduate courses in high energy astrophysics. Building on the concepts and techniques taught in standard undergraduate courses, this textbook provides the astronomical and astrophysical background for students to explore more advanced topics. Special emphasis is given to the underlying physical principles of high energy astrophysics, helping students understand the essential physics. The third edition has been completely rewritten, consolidating the previous editions into one volume. It covers the most recent discoveries in areas such as gamma-ray bursts, ultra-high energy cosmic rays and ultra-high energy gamma rays. The topics have been rearranged and streamlined to make them more applicable to a wide range of different astrophysical problems.

Our Universe is made of a dozen fundamental building blocks. Among these, neutrinos are the most mysterious - but they are the second most abundant particles in the Universe. This book provides detailed discussions of how to describe neutrinos, their basic properties, and the roles they play in nature.

The Marcel Grossmann Meetings have been conceived with the aim of reviewing recent advances in gravitation and general relativity, with particular emphasis on mathematical foundations and physical predictions. The overall programme includes the broad categories of mathematical techniques, cosmology, quantum gravity, astrophysics, gravitational radiation and experimental developments.The proceedings contain invited and contributed papers.