scholarly journals Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 696 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Event Horizon ◽  
Analytical Calculation ◽  
Tunneling Effect ◽  
Covariant Theory ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Stochastic Effects

The stochastic character of the cosmological constant arising from the non-linear quantum-vacuum Bohm interaction in the framework of the manifestly-covariant theory of quantum gravity (CQG theory) is pointed out. This feature is shown to be consistent with the axiomatic formulation of quantum gravity based on the hydrodynamic representation of the same CQG theory developed recently. The conclusion follows by investigating the indeterminacy properties of the probability density function and its representation associated with the quantum gravity state, which corresponds to a hydrodynamic continuity equation that satisfies the unitarity principle. As a result, the corresponding form of stochastic quantum-modified Einstein field equations is obtained and shown to admit a stochastic cosmological de Sitter solution for the space-time metric tensor. The analytical calculation of the stochastic averages of relevant physical observables is obtained. These include in particular the radius of the de Sitter sphere fixing the location of the event horizon and the expression of the Hawking temperature associated with the related particle tunneling effect. Theoretical implications for cosmology and field theories are pointed out.

scholarly journals Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 531 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Space Time ◽  
Energy Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Screening Effect ◽  
Periodic Perturbations ◽  
Desitter Space

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

A static generalization of the Einstein universe

1958 ◽  
Vol 245 (1241) ◽  
pp. 202-212
Keyword(s):  
General Problem ◽  
Constant Density ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Einstein Universe

Solutions of the Einstein field equations are found for the problem of a sphere of constant density surrounded by matter of different constant density. The solutions are discussed and particular attention paid to the topology of the surrounding matter. The Schwarzschild, de Sitter, and Einstein solutions emerge as particular cases of the general problem.

scholarly journals ON THE HAMILTONIAN FORMULATION OF THE EINSTEIN–HILBERT ACTION IN TWO DIMENSIONS

2006 ◽  
Vol 21 (11) ◽  
pp. 899-905 ◽  
Author(s):  
N. KIRIUSHCHEVA ◽  
S. V. KUZMIN
Keyword(s):  
Hamiltonian Formulation ◽  
Two Dimensions ◽  
General Covariance ◽  
Sufficient Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Transformations ◽  
Total Divergence ◽  
Hilbert Action

It is shown that if general covariance is to be preserved (i.e. a coordinate system is not fixed) the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein–Hilbert action to be a total divergence. Consequently, a Hamiltonian formulation is possible without any modification of the two-dimensional Einstein–Hilbert action. We find the resulting constraints and the corresponding gauge transformations of the metric tensor.

Vector-tensor field theories and the Einstein-Maxwell field equations

1974 ◽  
Vol 341 (1626) ◽  
pp. 285-297 ◽  
Keyword(s):  
Dimensional Space ◽  
Field Theories ◽  
Maxwell Field ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lagrange Equations ◽  
Third Order ◽  
Metric Tensor ◽  
First Order ◽  
First Derivative

The Euler-Lagrange equations corresponding to a Lagrange density which is a function of the metric tensor g ij and its first two derivatives together with the first derivative of a vector field ψ i are investigated. In general, the Euler-Lagrange equations obtained by variation of g ij are of fourth order in g ij and third order in ψ i . It is shown that in a four dimensional space the only Euler-Lagrange equations which are of second order in g ij and first order in ψ i are the Einstein field equations (with an energy-momentum term). Various conditions are obtained under which the Einstein-Maxwell field equations are then an inevitable consequence.

scholarly journals SCHWARZSCHILD SOLUTION OF THE MODIFIED EINSTEIN FIELD EQUATIONS

2017 ◽  
Vol 13 (4) ◽  
pp. 4895-4900
Author(s):  
D.S. Wamalwa ◽  
Carringtone Kinyanjui
Keyword(s):  
Event Horizon ◽  
Interior Solution ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Exterior Solution ◽  
Finsler Spacetime ◽  
Energy Approximation ◽  
Three Stages

A reformulation of the Schwarzschild solution of the linearized Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further application of Kruskal-Szekeres coordinates reveals that the interior solution contains maximally extensible geodesics.

scholarly journals Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 511
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Field Equations ◽  
Central Mass ◽  
Event Horizons ◽  
Covariant Quantum ◽  
Gravitational Fields ◽  
New Type

A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.

scholarly journals GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

Anisotropic universe and generalized ghost dark energy in Brans–Dicke theory

2016 ◽  
Vol 94 (2) ◽  
pp. 201-208 ◽  
Author(s):  
V. Fayaz ◽  
H. Hossienkhani ◽  
A. Pasqua ◽  
Z. Zarei ◽  
M. Ganji
Keyword(s):  
Dark Energy ◽  
State Parameter ◽  
Anisotropic Universe ◽  
Type I ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ghost Dark Energy ◽  
The Stability ◽  
Generalized Ghost Dark Energy

In this paper, we consider the generalized ghost dark energy in a Bianchi type-I metric (which is a spatially homogeneous and anisotropic) in the framework of Brans–Dicke theory. For this purpose, we use the squared sound speed [Formula: see text] the sign of which determines the stability of the model. At first, we obtain the equation of state parameter, ωΛ = pΛ/ρΛ, the deceleration parameter q and the evolution equation of the generalized ghost dark energy. We find that, in this case, ωΛ cannot cross the phantom line (ωΛ > –1) and eventually the universe approaches a de-Sitter phase of expansion (ωΛ → –1). Then, we extend our study to the case of generalized ghost dark energy in a non-isotropic and Brans–Dicke framework and find out that the transition of ωΛ to the phantom regime can be more easily accounted for than when it is restored into the Einstein field equations. In conclusion, we find evidence that the generalized ghost dark energy in BD theory can lead to a stable universe favored by observations at the present time.

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