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Abstract:

General relativity has entered a new phase of its development as technical advances have led to the direct detection of gravitational radiation from the merging of single pairs of stellar-sized black holes. The exquisite sensitivity of pulsar signal timing measurements has also been exploited to reveal the presence of a background of gravitational waves, most likely arising from the mergers of supermassive black holes thought to be present at the center of most galaxies. This book demonstrates how general relativity is central to understanding these and other observations while explaining the role of relativity in modern cosmology. An Introduction to General Relativity and Cosmology is an essential entrée to the subject, combining full discussions of underlying principles with detailed derivations as well as an accessible treatment of the mathematical foundations of singularity theorems and more advanced topics. Combines rigor with a conversational, highly pedagogical approach Emphasizes connections with other areas of physics to sharpen intuition while emphasizing general relativity’s unique contributions to modern theoretical physics Presents a novel derivation of the energy flux of gravitational waves Provides detailed and explicit derivations of important results, including binary star evolution by gravitational radiation losses Features a detailed treatment of the Hellings-Downs formula, key to understanding pulsar timing array results for gravitational radiation Provides a reexamination of the equivalence principle for relativistic particles Presents new results on the mathematical solutions of the innermost orbits of the gaseous disks that surround black holes Includes a wealth of exercises Solutions manual (available only to instructors)

Abstract:

We present an extremely simple derivation of the general relativistic periastron advance for Schwarzschild geometry. The method lends itself to iteration, and so in principle may achieve an arbitrary level of accuracy with relative ease. Our technique involves no analysis of differential equations beyond that of a simple harmonic oscillator. The practical utility of the calculation is limited by its neglect of frame-dragging rotational effects.

Abstract:

A set of analytic solutions for the plunging region thermodynamics has been developed recently under the assumption that the fluid undergoes a gravity-dominated geodesic plunge into the black hole. We test this model against a dedicated 3D global general relativistic magnetohydrodynamics simulation of a thin accretion disc around a Schwarzschild black hole using the code athenak . Provided that we include the effects of non-adiabatic heating (plausibly from grid-scale magnetic dissipation), we find excellent agreement between the analytic model and the simulated quantities. These results are particularly important for existing and future electromagnetic black hole spin measurements, many of which do not include the plunging fluid in their emission modelling. This exclusion typically stems from the assumption of a zero-stress boundary condition at the innermost stable circular orbit (ISCO), forcing all thermodynamic quantities to vanish. Instead, we find a non-zero drop in the angular momentum over the plunging region, which is consistent with both prior simulations and observations. We demonstrate that this stress is small enough for the dynamics of the fluid in the plunging region to be well-described by geodesic trajectories, yet large enough to cause measurable dissipation near to the ISCO – keeping thermodynamic quantities from vanishing. In the plunging region, constant -disc models are a physically inappropriate framework.

Abstract:

We show by direct calculation that the common equivalence principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is, therefore, possible, at least as a matter of principle, to tell the difference between local acceleration and a true gravitational field by measuring the local deflection of light. We calculate as well the deflection of test particles of arbitrary energy and construct a leading-order coordinate transformation from Schwarzschild to local inertial coordinates, which shows explicitly how the effects of spatial curvature manifest locally for relativistic trajectories of both finite and vanishing rest mass particles.