Is general relativity ‘essentially understood’?

  title={Is general relativity ‘essentially understood’?},
  author={Helmut Friedrich},
  journal={Annalen der Physik},
  • H. Friedrich
  • Published 3 August 2005
  • Physics
  • Annalen der Physik
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the domain of highly dynamical, strong field configurations is, however, still quite limited. The… 

New viewpoint of General Relativity that explains Mass and Gravity and some Enigmas of Modern Physics

Using different viewpoints on mass, volume, and spacetime, we may associate well-known theories (Le Sage, Higgs, and General Relativity) to solve some enigmas of modern science such as: What is the

New version of General Relativity that unifies Mass and Gravitation in a common 4D Theory

Eintein’s General Relativity does not explain recent enigmas of astrophysics such as dark energy or accelerating universe. A thorough examination of the Einstein Field Equations (EFE) highlights four

Unification of Mass and Gravitation in a Common 4D Higgs Compatible Theory

Since the 1920s, the formulas of mass and gravitation have worked perfectly with high accuracy. However, the basic principle of these two phenomena remains unknown. What is the origin of mass? How

Geometric asymptotics and beyond

The analysis of Einstein's field equations in the context of Penrose's notion of asymptotic simplicity, which was originally intro- duced to provide a geometric setting for the investigation of

Group analysis of equations arising in embedding theory.

Embedding theories are concerned with the embedding of a lower dimensional manifold (dim = n, say) into a higher dimensional one (usually dim = n+1, but not necessarily so). We are concerned with the

Strong coupling expansion for general relativity

Strong coupling expansion is computed for the Einstein equations in vacuum in the Arnowitt–Deser–Misner (ADM) formalism. The series is given by the duality principle in perturbation theory as

New Version of General Relativity that Unifies Mass and Gravity n a Common 4D Higgs Compatible Theory

Recent enigmas of astrophysics such as dark energy or accelerating universe need to update General Relativity. A thorough examination of the original Einstein Field Equations (EFE) hghlights three

Mathematical issues in a fully constrained formulation of the Einstein equations

Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D 70, 104007 (2004)] proposed a new formulation for $3+1$ numerical relativity. Einstein equations result, according to that formalism,

Non-gravitational Effects of the Metric Field over Complex Manifolds

Objective of this work is to study whether some of the known non-gravitational phenomena can be explained as motion on a straight line as gravity is treated within General Relativity. To do that,

Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S 3 and symmetry group U(1)

We apply a single patch pseudo-spectral scheme based on integer spin-weighted spherical harmonics presented in [1, 2] to Einstein’s equations. The particular hyperbolic reduction of Einstein’s



Investigations in relativistic cosmology

Abstract (by translator) A detailed report is given here of the general investigations carried out by the authors in the field of relativistic cosmology during the past years. The paper consists of

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.

Theorems on Existence and Global Dynamics for the Einstein Equations

  • A. Rendall
  • Mathematics
    Living reviews in relativity
  • 2005
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations and some miscellaneous topics connected with the main theme are collected in a separate section.

The initial value problem and the dynamical formulation of general relativity

In this chapter we discuss some of the interrelationships between the initial value problem, the canonical formalism, linearization stability and the space of gravitational degrees of freedom. In the

A proof of Price’s law for the collapse of a self-gravitating scalar field

A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates

The singularities of gravitational collapse and cosmology

  • S. HawkingR. Penrose
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected if

Gravitational collapse and spacetime singularities

accompanied by a violent release of energy, possible in the form of gravitational radiation. The detailed mathematical discussion of such situations is difficult since the full complexity of general

On the numerical integration of Einstein's field equations

Many numerical codes now under development to solve Einstein's equations of general relativity in $(3+1)$-dimensional spacetimes employ the standard ADM form of the field equations. This form

Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system

This paper is divided into four parts. In part A, some general considerations about gravitational radiation are followed by a treatment of the scalar wave equation in the manner later to be applied

Einstein’s equations with asymptotically stable constraint propagation

We introduce a proposal to modify Einstein’s equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first