# Asymptotic behavior of a matter filled universe with exotic topology

@article{Mondal2019AsymptoticBO, title={Asymptotic behavior of a matter filled universe with exotic topology}, author={Puskar Mondal}, journal={Classical and Quantum Gravity}, year={2019}, volume={37} }

The ADM formalism together with a constant mean curvature (CMC) temporal gauge is used to derive the monotonic decay of a weak Lyapunov function of the Einstein dynamical equations in an expanding universe with a positive cosmological constant and matter sources satisfying suitable energy conditions. While such a Lyapunov function does not, in general, represent a true Hamiltonian of the matter-coupled gravity dynamics (unlike in the vacuum case when it does), it can nevertheless be used to…

## 4 Citations

### The linear stability of the n + 1 dimensional FLRW spacetimes

- MathematicsClassical and Quantum Gravity
- 2021

Here we prove the linear stability of a family of ‘n + 1’-dimensional cosmological models of general relativity locally isometric to the Friedmann Lemaître Robertson Walker (FLRW) spacetimes…

### The linear stability of the Einstein-Euler field equations on negative Einstein spaces in CMCSH gauge

- Mathematics
- 2020

Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the…

### The linear stability of the Einstein-Euler system on negative Einstein spaces

- Mathematics
- 2020

Here we prove the linear stability of a family of ‘n + 1’-dimensional cosmological models of general relativity locally isometric to the Friedmann Lemâıtre Robertson Walker (FLRW) spacetimes…

### Attractors of the `n+1' dimensional Einstein-$\Lambda$ flow.

- Mathematics, Physics
- 2019

Here we prove a global existence theorem for sufficiently small however fully nonlinear perturbations of a family of background solutions of the $`n+1$' vacuum Einstein equations in the presence of a…

## References

SHOWING 1-10 OF 64 REFERENCES

### Hamiltonian formalism for relativistic perfect fluids

- Physics
- 1977

We apply Arnowitt, Deser, and Misner (ADM) reduction techniques to Taub's variational principle for self-gravitating, relativistic perfect fluids. We derive conditions upon the fluid configuration…

### Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle

- Mathematics, Materials Science
- 1970

The equations of hydrodynamics for a perfect fluid in general relativity are cast in Eulerian form, with the four-velocity being expressed in terms of six velocity potentials:…

### Convergence and stability issues in mathematical cosmology Gen. Relativ

- 2015

### Could the universe have an exotic topology?

- PhysicsPure and Applied Mathematics Quarterly
- 2019

A recent article uncovered a surprising dynamical mechanism at work within the (vacuum) Einstein `flow' that strongly suggests that many closed 3-manifolds that do not admit a locally homogeneous and…

### General Relativity and the Einstein Equations

- Mathematics
- 2009

FOREWORD ACKNOWLEDGEMENTS 1. Lorentzian Geometry 2. Special Relativity 3. General Relativity and the Einstein Equations 4. Schwarzschild Space-time and Black Holes 5. Cosmology 6. Local Cauchy…

### Hamiltonian reduction and perturbations of continuously self-similar (n + 1)-dimensional Einstein vacuum spacetimes

- Mathematics, Physics
- 2002

We investigate some of the properties of the vacuum Einstein equations on manifolds of the form V = I × M where M is a compact n-manifold, n ≥ 2, of negative Yamabe type, and where V admits a…

### Hamiltonian reduction of Einstein's equations of general relativity

- Physics, Mathematics
- 1997

### Convergence and Stability Issues in Mathematical Cosmology, Gen

- Rel. Grav
- 2015

### Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

- Physics, Mathematics
- 1999

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it…

### Hamiltonian reduction and perturbations of continuously self-similar (n + 1)-dimensional Einstein vacuum spacetimes

- Mathematics, Physics
- 2002

We investigate some of the properties of the vacuum Einstein equations on manifolds of the form V = I × M where M is a compact n-manifold, n ≥ 2, of negative Yamabe type, and where V admits a…