Mass and Angular Momentum in General Relativity

@inproceedings{Jaramillo2010MassAA,
  title={Mass and Angular Momentum in General Relativity},
  author={J L Jaramillo and E. Gourgoulhon},
  year={2010}
}
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy–momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy–momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy–momentum density for the gravitational field. This leads to the understanding… 

Energy of cosmological spacetimes and perturbations: a quasilocal approach

Quasilocal definitions of stress–energy–momentum—that is, in the form of boundary densities (rather than local volume densities)—have proven generally very useful in formulating and applying

Motion of localized sources in general relativity: Gravitational self-force from quasilocal conservation laws

An idealized “test” object in general relativity moves along a geodesic. However, if the object has a finite mass, this will create additional curvature in the spacetime, causing it to deviate from

Noether's Theorems and Energy in General Relativity

This paper has three main aims: first, to give a pedagogical introduction to Noether’s two theorems and their implications for energy conservation in general relativity, which was a central point of

Study of the relativistic dynamics of extreme-mass-ratio inspirals

The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime - that is, where one mass is significantly smaller than the other - in the full context of

Einstein and Beyond: A Critical Perspective on General Relativity

An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological

Canonical Gravity and Relativistic Metrology: from Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

Clock synchronization leads to the definition of instantaneous 3-spaces (to be used as Cauchy surfaces) in non-inertial frames, the only ones allowed by the equivalence principle. ADM canonical

Dirac-Bergmann Constraints in Relativistic Physics: Non-Inertial Frames, Point Particles, Fields and Gravity

There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of

Covariant Noether charges for type IIB and 11-dimensional supergravities

The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism

Energy and entropy in the Geometrical Trinity of gravity

All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have

The Physics of Eccentric Binary Black Hole Mergers. A Numerical Relativity Perspective

This work presents a catalog of 89 numerical relativity waveforms that describe binary systems of non-spinning black holes with mass-ratios, and quantifies the loss of energy and angular momentum through gravitational radiation, and the astrophysical properties of the black hole remnant, including its final mass and spin, and recoil velocity.
...

References

SHOWING 1-10 OF 106 REFERENCES

On conserved quantities in general relativity

Recently, definitions of total 4‐momentum and angular momentum of isolated gravitating systems have been introduced in terms of the asymptotic behavior of the Weyl curvature (of the underlying

Angular momentum conservation for dynamical black holes

Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the

Angular momentum and an invariant quasilocal energy in general relativity

A key feature of the Brown and York definition of quasilocal energy is that under local boosts of the fleet of observers measuring the energy, the quasilocal energy surface density transforms as one

Binary black holes in circular orbits. I. A global spacetime approach

We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are

A Relativist's Toolkit

This textbook fills a gap in the existing literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The

Thermodynamics of binary black holes and neutron stars

We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^\alpha, heuristically, the generator of time-translations in a

General definition of “conserved quantities” in general relativity and other theories of gravity

In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with

Linkages in general relativity

For an asymptotically flat space–time in general relativity there exist certain integrals, called linkages, over cross sections of null infinity, which represent the energy, momentum, or angular

The Large Scale Structure of Space-Time

The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article

The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed. First the general ideas, concepts, and strategies, as well as the
...