On the definition of mass-energy of a static spherically-symmetric mass in the post-newtonian approximation of general relativity

1993 ◽  
Vol 207 (1) ◽  
pp. 145-150 ◽  
Author(s):  
R. Roy ◽  
N. C. Rana
Keyword(s):  
General Relativity ◽  
Spherically Symmetric ◽  
Mass Energy ◽  
Newtonian Approximation ◽  
Definition Of

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

On the definition of post-newtonian approximations

1992 ◽  
Vol 438 (1903) ◽  
pp. 341-360 ◽  
Keyword(s):  
General Relativity ◽  
Newtonian Limit ◽  
Minimal Set ◽  
Asymptotically Flat ◽  
Precise Formulation ◽  
The Third ◽  
Newtonian Approximation ◽  
Definition Of

A definition of post-newtonian approximations is presented where the whole formalism is derived from a minimal set of axioms. This establishes a link between the existing precise formulation of the newtonian limit of general relativity and the post-newtonian equations which are used in practical calculations. The breakdown of higher post-newtonian approximations is examined within this framework. It is shown that the choice of harmonic gauge leads to equations which do not admit asymptotically flat solutions at the second post-newtonian level if one starts with a generic newtonian solution. The most simple choice of gauge gives equations which are solvable at the 2PN level but which in general have no solutions in the case of the third post-newtonian approximation.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

Static spherically symmetric stiff matter in general relativity

1994 ◽  
Vol 11 (4) ◽  
pp. L69-L72 ◽  
Author(s):  
Salah Haggag ◽  
Joseph Hajj-Boutros
Keyword(s):  
General Relativity ◽  
Spherically Symmetric ◽  
Stiff Matter

scholarly journals Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

2014 ◽  
Vol 23 (08) ◽  
pp. 1450068 ◽  
Author(s):  
O. Goldoni ◽  
M. F. A. da Silva ◽  
G. Pinheiro ◽  
R. Chan
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Radiation Field ◽  
Relativity Theory ◽  
Covariant Theory ◽  
Spherically Symmetric ◽  
Theory U ◽  
General Relativity Theory ◽  
Infrared Limit ◽  
Symmetric Spacetime

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

scholarly journals Solving the Darwin problem in the first post-Newtonian approximation of general relativity

1997 ◽  
Vol 56 (2) ◽  
pp. 798-810 ◽  
Author(s):  
Keisuke Taniguchi ◽  
Masaru Shibata
Keyword(s):  
General Relativity ◽  
Newtonian Approximation

scholarly journals Spherically symmetric static solutions in a nonlocal infrared modification of General Relativity

2014 ◽  
Vol 2014 (8) ◽  
Author(s):  
Alex Kehagias ◽  
Michele Maggiore
Keyword(s):  
General Relativity ◽  
Spherically Symmetric ◽  
Static Solutions

scholarly journals Irrotational and Incompressible Ellipsoids in the First Post-Newtonian Approximation of General Relativity

1998 ◽  
Vol 100 (4) ◽  
pp. 703-735 ◽  
Author(s):  
K. Taniguchi ◽  
H. Asada ◽  
M. Shibata
Keyword(s):  
General Relativity ◽  
Newtonian Approximation

scholarly journals The Total Energy and Momentum Stored in a Particle

2017 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Eyal Brodet
Keyword(s):  
Total Energy ◽  
Special Relativity ◽  
Decay Time ◽  
Rest Mass ◽  
Minimum Time ◽  
Mass Energy ◽  
Light Velocity ◽  
Extra Energy ◽  
Definition Of ◽  
Energy And Momentum

In this paper we reconsider the conventional expressions given by special relativity to the energy and momentum of a particle. In the current framework, the particle's energy and momentum are computed using the particle's rest mass, M and rest mass time, t_m=h/M c^2  where t_m has the same time unit as conventionally used for the light velocity c. Therefore it is currently assumed that this definition of time describes the total kinetic and mass energy of a particle as given by special relativity. In this paper we will reexamine the above assumption and suggest describing the particle's energy as a function of its own particular decay time and not with respect to its rest mass time unit. Moreover we will argue that this rest mass time unit currently used is in fact the minimum time unit defined for a particle and that the particle may have more energy stored with in it. Experimental ways to search for this extra energy stored in particles such as electrons and photons are presented.

Sign in / Sign up

Export Citation Format

Share Document