Exact solutions of Einstein’s equations for space‐time with local rotational symmetry in which the Dirac equation separates

1991 ◽  
Vol 32 (5) ◽  
pp. 1334-1336 ◽  
Author(s):  
Jiliang Jing
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Rotational Symmetry ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations

Exact solutions of Dirac equation on a static curved space–time

2019 ◽  
Vol 401 ◽  
pp. 21-39 ◽  
Author(s):  
M.D. de Oliveira ◽  
Alexandre G.M. Schmidt
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Space Time ◽  
Curved Space

Physics as an Art Form

2018 ◽  
pp. 1-4
Author(s):  
Alvaro De Rújula
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Ockham’S Razor ◽  
Art Form ◽  
Ockham's Razor ◽  
The Universe ◽  
The Way

Beauty and simplicity, a scientist’s view. A first encounter with Einstein’s equations of General Relativity, space-time, and Gravity. Ockham’s Razor. Why the Universe is the way it is: The origin of the laws of Nature.

scholarly journals Einstein's equations and a cosmology with finite matter

2015 ◽  
Vol 30 (13) ◽  
pp. 1550068
Author(s):  
L. Clavelli ◽  
Gary R. Goldstein
Keyword(s):  
Infinite Number ◽  
Total Mass ◽  
Delta Function ◽  
Big Bang ◽  
Space Time ◽  
Matter Density ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
The Big Bang

We discuss various space–time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.1 In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

scholarly journals Some axially symmetric zero mass meson solutions of Einstein's equations

1975 ◽  
Vol 19 (2) ◽  
pp. 140-145 ◽  
Author(s):  
L. K. Patel ◽  
V. M. Trivedi
Keyword(s):  
Exact Solutions ◽  
Electromagnetic Fields ◽  
Axially Symmetric ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Zero Mass ◽  
Oblate Spheroidal

AbstractAn axially symmetric metric in oblate spheroidal co-ordinates is considered. Two exact solutions of the field equations corresponding to zero mass meson fields are obtained. The details of the solutions are also discussed. These solutions are also generalized to include electromagnetic fields.

scholarly journals Solution-generating methods of Einstein’s equations by Hamiltonian reduction

2018 ◽  
Vol 33 (18) ◽  
pp. 1850101
Author(s):  
Seung Hun Oh ◽  
Kyoungtae Kimm ◽  
Yongmin Cho ◽  
Jong Hyuk Yoon
Keyword(s):  
Exact Solutions ◽  
Degrees Of Freedom ◽  
Hamiltonian Reduction ◽  
Einstein’S Equations ◽  
Schwarzschild Solution ◽  
Einstein's Equations ◽  
Constraint Equations ◽  
Dimensional Spacetime ◽  
Free Data ◽  
Privileged Coordinates

The purpose of this paper is to demonstrate a new method of generating exact solutions to Einstein’s equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged spacetime coordinates in which physical degrees of freedom manifestly reside in the conformal two-metric, and all the other metric components are determined by the conformal two-metric. In the privileged coordinates, Einstein’s constraint equations become trivial; the Hamiltonian and momentum constraints are simply the defining equations of a nonvanishing gravitational Hamiltonian and momentum densities in terms of conformal two-metric and its conjugate momentum, respectively. Thus, given any conformal two-metric, which is a constraint-free data, one can construct the whole four-dimensional spacetime by integrating the first-order superpotential equations. As the first examples of using Hamiltonian reduction in solving Einstein’s equations, we found two exact solutions to Einstein’s equations in the privileged coordinates. Suitable coordinate transformations from the privileged to the standard coordinates show that they are just the Einstein–Rosen wave and the Schwarzschild solution. The local gravitational Hamiltonian and momentum densities of these spacetimes are also presented in the privileged coordinates.

scholarly journals Exact solutions of Einstein's equations

Scholarpedia ◽  
2013 ◽  
Vol 8 (12) ◽  
pp. 8584 ◽  
Author(s):  
Malcolm MacCallum
Keyword(s):  
Exact Solutions ◽  
Einstein’S Equations ◽  
Einstein's Equations
Sign in / Sign up

Export Citation Format

Share Document