The First Solutions and the Challenge of Their Interpretation

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Exact Solutions ◽  
De Sitter ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Nonlinear Character ◽  
Georges Lemaître

This chapter discusses the first wave of the exploration of exact solutions to Einstein's gravitational field equations. When Einstein published the final form of the field equations in 1915, only an approximate solution was known. Given the complicated nonlinear character of the field equations, he did not expect that exact solutions could easily be found. He was all the more surprised when the astronomer Karl Schwarzschild presented him with just such an exact solution. Thus, this chapter presents a series of these solutions, beginning with the work of Karl Schwarzschild, Johannes Droste, Willem de Sitter, Alexander Friedmann, Hans Reissner, Gunnar Nordström, and finally, Georges Lemaître.

scholarly journals Exact Solutions in Poincaré Gauge Gravity Theory

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 127 ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Gravitational Field ◽  
Gravity Models ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Yang Mills ◽  
Gravitational Field Equations ◽  
Poincaré Symmetry ◽  
Gauge Gravity ◽  
Vacuum Solutions

In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

scholarly journals PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY

2007 ◽  
Vol 04 (08) ◽  
pp. 1285-1334 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Killing Vector ◽  
Field Equations ◽  
Finsler Spaces ◽  
Gravitational Field Equations ◽  
Pp Wave ◽  
Physical Consequences

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.

scholarly journals TACHYON MONOPOLE

2005 ◽  
Vol 20 (23) ◽  
pp. 5491-5499 ◽  
Author(s):  
XIN-ZHOU LI ◽  
DAO-JUN LIU
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Tachyon Field ◽  
Field Equations ◽  
Monopole Solution ◽  
Static Space

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.

scholarly journals Exact causal bulk viscous stiff cosmologies.

2000 ◽  
Vol 53 (2) ◽  
pp. 241 ◽  
Author(s):  
M. K. Mak ◽  
T. Harko
Keyword(s):  
Exact Solution ◽  
Gravitational Field ◽  
Viscosity Coefficient ◽  
Field Equations ◽  
Bulk Viscous Fluid ◽  
Gravitational Field Equations ◽  
Bulk Viscous ◽  
Fourth Root ◽  
Bulk Viscosity Coefficient ◽  
Friedmann Robertson Walker

An exact solution of the gravitational field equations is presented for a homogeneous flat Friedmann-Robertson-Walker universe filled with a causal bulk viscous fluid obeying the Zeldovich stiff equation of state and having bulk viscosity coefficient proportional to the fourth root of the energy density.

Sign in / Sign up

Export Citation Format

Share Document