New large family of vacuum solutions of the equations of general relativity

1980 ◽  
Vol 21 (6) ◽  
pp. 1695-1697 ◽  
Author(s):  
B. Kent Harrison
Keyword(s):  
General Relativity ◽  
Large Family ◽  
Vacuum Solutions

scholarly journals Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 398 ◽  
Author(s):  
Rand Dannenberg
Keyword(s):  
General Relativity ◽  
Gravitational Constant ◽  
Excluded Volume ◽  
Newtonian Gravity ◽  
Least Action Principle ◽  
Rotation Curves ◽  
Least Action ◽  
A Charge ◽  
Vacuum Solutions ◽  
Galaxy Rotation Curves

Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

New Exact Vacuum Solutions in Brans–Dicke Theory

1997 ◽  
Vol 12 (25) ◽  
pp. 1865-1870 ◽  
Author(s):  
Luis O. Pimentel
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Initial Data ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Spherical Symmetry ◽  
Physical System ◽  
Special Value ◽  
Isotropic Cosmological Model ◽  
Vacuum Solutions

A family of exact solutions to vacuum Brans–Dicke theory with spherical symmetry is found. In the limit of large ω this family reduces to the solutions obtained in general relativity with a scalar field. The solutions show curvature singularities for all times, therefore they do not represent the gravitational collapse of a physical system with regular initial data in the theory. One would like to interpret it as an inhomogeneous dynamical cosmology, but the lack of a regular spacelike slice forbids it. For a special value of an integration constant we have an isotropic cosmological model without the problems mentioned above.

scholarly journals New physical parameterizations of monopole solutions in five-dimensional general relativity and the role of negative scalar field energy in vacuum solutions

2021 ◽  
Author(s):  
Y. Balytskyi ◽  
D. Hoyer ◽  
A. O. Pinchuk ◽  
L. L. Williams
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Energy Density ◽  
Electric Field ◽  
Electric Charge ◽  
Field Energy ◽  
Scalar Charge ◽  
Field Energy Density ◽  
Vacuum Solutions

Abstract Novel parameterizations are presented for monopole solutions to the static, spherically-symmetric vacuum field equations of five-dimensional general relativity. First proposed by Kaluza, 5D general relativity unites gravity and classical electromagnetism with a scalar field. These monopoles correspond to bodies carrying mass, electric charge, and scalar charge. The new parameterizations provide physical insight into the nature of electric charge and scalar field energy. The Reissner-Nordstr\"om limit is compared with alternate physical interpretations of the solution parameters. The new parameterizations explore the role of scalar field energy and the relation of electric charge to scalar charge. The Kaluza vacuum equations imply the scalar field energy density is the negative of the electric field energy density for all known solutions, so the total electric and scalar field energy of the monopole is zero. The vanishing of the total electric and scalar field energy density for vacuum solutions seems to imply the scalar field can be understood as a negative-energy foundation on which the electric field is built.

scholarly journals Palatini formulation of non-local gravity

2017 ◽  
Vol 14 (02) ◽  
pp. 1750019 ◽  
Author(s):  
F. Briscese ◽  
M. L. Pucheu
Keyword(s):  
General Relativity ◽  
Gravity Model ◽  
Local Model ◽  
Dynamical Equations ◽  
Palatini Formalism ◽  
Local Gravity ◽  
Non Local ◽  
Vacuum Solutions

We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have show that, in some specific case, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein’s gravity are not removed.

scholarly journals Dust content solutions for the Alcubierre warp drive spacetime

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Osvaldo L. Santos-Pereira ◽  
Everton M. C. Abreu ◽  
Marcelo B. Ribeiro
Keyword(s):  
General Relativity ◽  
Shock Waves ◽  
Burgers Equation ◽  
Plane Waves ◽  
Massive Particle ◽  
Einstein Equations ◽  
Inviscid Fluid ◽  
Matter Distribution ◽  
Spacetime Geometry ◽  
Vacuum Solutions

Abstract The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This is a consequence of general relativity, which allows for global superluminal velocities but restricts local speeds to subluminal ones as required by special relativity. In this work we solved the Einstein equations for the Alcubierre warp drive spacetime geometry considering the dust matter distribution as source, since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as a spacetime geometry proposed without a source gravity field. We found that all Einstein equations solutions of this geometry containing pressureless dust lead to vacuum solutions. We also concluded that these solutions connect the Alcubierre metric to the Burgers equation, which describes shock waves moving through an inviscid fluid. Our results also indicated that these shock waves behave as plane waves.

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