Spherically symmetric solutions in dimensionally reduced spacetimes with a higher-dimensional cosmological constant

1991 ◽  
Vol 44 (4) ◽  
pp. 1100-1114 ◽  
Author(s):  
David L. Wiltshire
Keyword(s):  
Cosmological Constant ◽  
Spherically Symmetric ◽  
Higher Dimensional ◽  
Spherically Symmetric Solutions

Further spherically symmetric solutions

2021 ◽  
pp. 249-259
Author(s):  
Andrew M. Steane
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Stellar Structure ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Schwarzschild Solution ◽  
Spherically Symmetric Solutions ◽  
Structure Equations

We obtain the interior Schwarzschild solution; the stellar structure equations (Tolman-Oppenheimer-Volkoff); the Reissner-Nordstrom metric (charged black hole) and the de Sitter-Schwarzschild metric. These both illustrate how the field equation is tackled in non-vacuum cases, and bring out some of the physics of stars, electromagnetic fields and the cosmological constant.

scholarly journals An instability of the standard model of cosmology creates the anomalous acceleration without dark energy

2017 ◽  
Vol 473 (2207) ◽  
pp. 20160887
Author(s):  
Joel Smoller ◽  
Blake Temple ◽  
Zeke Vogler
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Phase Portrait ◽  
Simple Wave ◽  
Space Time ◽  
Spherically Symmetric ◽  
Third Order ◽  
Rest Point ◽  
Spherically Symmetric Solutions ◽  
Anomalous Acceleration

We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein’s original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p =0. In this phase portrait, the critical k =0 Friedmann space–time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space–time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space–times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein’s original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

scholarly journals Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 372 ◽  
Author(s):  
Francesco Bajardi ◽  
Konstantinos F. Dialektopoulos ◽  
Salvatore Capozziello
Keyword(s):  
Topological Invariant ◽  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Curvature Scalar ◽  
Bonnet Gravity ◽  
Higher Dimensional ◽  
Point Transformations ◽  
Spherically Symmetric Solutions ◽  
Functional Forms ◽  
Symmetric Spacetime

We study a theory of gravity of the form f ( G ) where G is the Gauss–Bonnet topological invariant without considering the standard Einstein–Hilbert term as common in the literature, in arbitrary ( d + 1 ) dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure f ( G ) gravity can be considered a further generalization of General Relativity like f ( R ) gravity. Searching for Noether symmetries, we specify the functional forms invariant under point transformations in a static and spherically symmetric spacetime and, with the help of these symmetries, we find exact solutions showing that Gauss–Bonnet gravity is significant without assuming the Ricci scalar in the action.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

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