To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Annals of physics

We describe new optically thin solutions for rotating accretion flows around black holes and neutron stars. These solutions are advection dominated, so that most of the viscously dissipated energy is advected radially with the flow. We model the accreting gas as a two temperature plasma and include cooling by bremsstrahlung, synchrotron, and Comptonization. We obtain electron temperatures $T_e\sim 10^{8.5}-10^{10}$K. The new solutions are present only for mass accretion rates $\dot M$ less than a critical rate $\dot M_{crit}$ which we calculate as a function of radius $R$ and viscosity parameter $\alpha$. For $\dot M<\dot M_{crit}$ we show that there are three equilibrium branches of solutions. One of the branches corresponds to a cool optically thick flow which is the well-known thin disk solution of Shakura \& Sunyaev (1973). Another branch corresponds to a hot optically thin flow, discovered originally by Shapiro, Lightman \& Eardley (1976, SLE). This solution is thermally unstable. The third branch corresponds to our new advection-dominated solution. This solution is hotter and more optically thin than the SLE solution, but is viscously and thermally stable. It is related to the ion torus model of Rees et al. (1982) and may potentially explain the hard X-ray and $\gamma$-ray emission from X-ray binaries and active galactic nuclei.

/pdf/advection-dominated-accretion-underfed-black-holes-and-cc41v8tdhl.pdf

Advection-Dominated Accretion: Underfed Black Holes and Neutron Stars

Mathematical Handbook for Scientists and Engineers

Advances in physics

We give a derivation of general relativity (GR) and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace (the space of Riemannian 3-geometries on a given bare manifold). It has two key properties. The first is symmetry under 3-diffeomorphisms. This is the only postulated symmetry, and it leads to a constraint linear in the canonical momenta. The second property is that the Lagrangian is constructed from a 'local' square root of an expression quadratic in the velocities. The square root is 'local' because it is taken before integration over 3-space. It gives rise to quadratic constraints that do not correspond to any symmetry and are not, in general, propagated by the Euler–Lagrange equations. Therefore these actions are internally inconsistent. However, one action of this form is well behaved: the Baierlein–Sharp–Wheeler (Baierlein R F, Sharp D and Wheeler J A 1962 Phys. Rev. 126 1864) reparametrization-invariant action for GR. From this viewpoint, spacetime symmetry is emergent. It appears as a 'hidden' symmetry in the (underdetermined) solutions of the Euler–Lagrange equations, without being manifestly coded into the action itself. In addition, propagation of the linear diffeomorphism constraint together with the quadratic square-root constraint acts as a striking selection mechanism beyond pure gravity. If a scalar field is included in the configuration space, it must have the same characteristic speed as gravity. Thus Einstein causality emerges. Finally, self-consistency requires that any 3-vector field must satisfy Einstein causality, the equivalence principle and, in addition, the Gauss constraint. Therefore we recover the standard (massless) Maxwell equations.

Relativity without relativity

The initial-value equations of Einstein's theory of general relativity are formulated as a system of four coupled quasilinear elliptic equations. These equations result from a covariant orthogonal decomposition of symmetric tensors and a generalized technique of conformal deformation of initial data. Mathematical properties and global integrability conditions of the equations are discussed. Physical interpretation of the independent and dependent data is given for both spatially closed and asymptotically flat initial-data sets. In the latter case, the four dependent functions constitute long-range scalar and vector potentials which determine the total mass and total linear and angular momenta of an isolated system. The definitions of linear and angular momenta suggest a unique extension to asymptotically flat three-spaces of the group of translations and rotations of flat three-space. In turn, the "almost symmetries" thus defined lead to Gaussian theorems expressing the equality of certain surface and volume integrals for total linear and angular momenta. An interpretation of the scalar and vector potentials for closed three-spaces is also given. In the Appendix we treat the special case of conformally flat initial data.

Initial-value problem of general relativity. I. General formulation and physical interpretation

When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving three-dimensional conformal Riemannian geometries obtained by imposing two general principles: (1) time is derived from change; (2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation, but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.

http://iopscience.iop.org/article/10.1088/0264-9381/22/9/020/pdf

The physical gravitational degrees of freedom

Significant advances in numerical simulations of black-hole binaries have recently been achieved using the puncture method. We examine how and why this method works by evolving a single black hole. The coordinate singularity and hence the geometry at the puncture are found to change during evolution, from representing an asymptotically flat end to being a cylinder. We construct an analytic solution for the stationary state of a black hole in spherical symmetry that matches the numerical result and demonstrates that the evolution is not dominated by artefacts at the puncture but indeed finds the analytical result.

Geometry and regularity of moving punctures.

We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary $1+\mathrm{log}﻿$ foliations of the Schwarzschild solution, and outline a transformation to isotropic coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent $1+\mathrm{log}﻿$ data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of $1+\mathrm{log}﻿$ slicing during a simulation.

Niall Ó Murchadha

Papers

Relativity without relativity

Initial-value problem of general relativity. I. General formulation and physical interpretation

The physical gravitational degrees of freedom

Geometry and regularity of moving punctures.

Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation