Self-consistent solutions of the semiclassical Einstein-Dirac equations with cosmological constant

1995 ◽  
Vol 12 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Marcelo G Alé ◽  
Luis P Chimento
Keyword(s):  
Cosmological Constant ◽  
Dirac Equations ◽  
Self Consistent

scholarly journals Analysis of models for quantum transport of electrons in graphene layers

2014 ◽  
Vol 24 (11) ◽  
pp. 2287-2310 ◽  
Author(s):  
Raymond El Hajj ◽  
Florian Méhats
Keyword(s):  
Quantum Transport ◽  
Energy Band Diagram ◽  
Dirichlet Boundary Conditions ◽  
Laplacian Operator ◽  
Dirichlet Laplacian ◽  
Graphene Layers ◽  
Dirac Equations ◽  
Self Consistent ◽  
Time Existence ◽  
Uniqueness Of A Solution

We present and analyze two mathematical models for the self-consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane ℝ2, the model takes the form of a system of massless Dirac equations coupled together by a self-consistent potential, which is the trace in the plane of the graphene of the 3D Poisson potential associated to surface densities. In this case, we prove local in time existence and uniqueness of a solution in Hs(ℝ2), for [Formula: see text] which includes in particular the energy space H1/2(ℝ2). The main tools that enable to reach [Formula: see text] are the dispersive Strichartz estimates that we generalized here for mixed quantum states. Second, we consider a situation where the particles are constrained in a regular bounded domain Ω. In order to take into account Dirichlet boundary conditions which are not compatible with the Dirac Hamiltonian H0, we propose a different model built on a modified Hamiltonian displaying the same energy band diagram as H0 near the Dirac points. The well-posedness of the system in this case is proved in [Formula: see text], the domain of the fractional order Dirichlet Laplacian operator, for [Formula: see text].

scholarly journals THE VALUE OF THE COSMOLOGICAL CONSTANT

2011 ◽  
Vol 20 (14) ◽  
pp. 2875-2880 ◽  
Author(s):  
JOHN D. BARROW ◽  
DOUGLAS J. SHAW
Keyword(s):  
Wave Function ◽  
Cosmological Constant ◽  
Classical Limit ◽  
Constraint Equation ◽  
Einstein Equations ◽  
Spatial Curvature ◽  
Self Consistent ◽  
Curvature Parameter ◽  
The Universe ◽  
Planck Satellite

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, tU, be [Formula: see text], as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is [Formula: see text], which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.

scholarly journals NONSINGULAR BLACK HOLES FROM GRAVITY–MATTER-BRANE LAGRANGIANS

2010 ◽  
Vol 25 (08) ◽  
pp. 1571-1596 ◽  
Author(s):  
EDUARDO GUENDELMAN ◽  
ALEXANDER KAGANOVICH ◽  
EMIL NISSIMOV ◽  
SVETLANA PACHEVA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Radial Coordinate ◽  
De Sitter ◽  
Wormhole Solution ◽  
Interior Region ◽  
Exterior Region ◽  
Inner Horizon ◽  
Self Consistent

We consider self-consistent coupling of bulk Einstein–Maxwell–Kalb–Ramond system to codimension-one charged lightlikep-brane with dynamical (variable) tension (LL-brane). The latter is described by a manifestly reparametrization-invariant worldvolume action significantly different from the ordinary Nambu–Goto one. We show that the LL-brane is the appropriate gravitational and charge source in the Einstein–Maxwell–Kalb–Ramond equations of motion needed to generate a self-consistent solution describing nonsingular black hole. The latter consists of de Sitter interior region and exterior Reissner–Nordström region glued together along their common horizon (it is the inner horizon from the Reissner–Nordström side). The matching horizon is automatically occupied by the LL-brane as a result of its worldvolume Lagrangian dynamics, which dynamically generates the cosmological constant in the interior region and uniquely determines the mass and charge parameters of the exterior region. Using similar techniques we construct a self-consistent wormhole solution of Einstein–Maxwell system coupled to electrically neutral LL-brane, which describes two identical copies of a nonsingular black hole region being the exterior Reissner–Nordström region above the inner horizon, glued together along their common horizon (the inner Reissner–Nordström one) occupied by the LL-brane. The corresponding mass and charge parameters of the two black hole "universes" are explicitly determined by the dynamical LL-brane tension. This also provides an explicit example of Misner–Wheeler "charge without charge" phenomenon. Finally, this wormhole solution connecting two nonsingular black holes can be transformed into a special case of Kantowski–Sachs bouncing cosmology solution if instead of Reissner–Nordström we glue together two copies of the exterior Reissner–Nordström–de Sitter region with big enough bare cosmological constant, such that the radial coordinate becomes a timelike variable everywhere in the two "universes," except at the matching hypersurface occupied by the LL-brane.

scholarly journals The effect of the cosmological constant on a quadrupole signal in the linearized approximation

2018 ◽  
Vol 27 (02) ◽  
pp. 1850004 ◽  
Author(s):  
László Ábel Somlai ◽  
Mátyás Vasúth
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Equations Of Motion ◽  
Luminosity Distance ◽  
Background Term ◽  
Self Consistent ◽  
Linearized Theory

In this study the effects of a nonzero cosmological constant [Formula: see text] on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of [Formula: see text] GWs and [Formula: see text] background term, originated from [Formula: see text]. The [Formula: see text] term was also included in this study. To derive physically relevant consequences of [Formula: see text] comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

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