Non-local equations for general relativity

1992 ◽  
Vol 8 (1-4) ◽  
pp. 195-209 ◽  
Author(s):  
Carlos N. Kozameh ◽  
Ezra T. Newman ◽  
Savitri V. Iyer
Keyword(s):  
General Relativity ◽  
Non Local ◽  
Non Local Equations

scholarly journals Replica wormholes for an evaporating 2D black hole

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kanato Goto ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Path Integral ◽  
Island Rule ◽  
Technical Challenge ◽  
Local Boundary ◽  
Lorentzian Signature ◽  
Special Cases ◽  
Non Local ◽  
Non Local Equations

Abstract Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking’s paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations for the Schwarzian mode are non-local, so it is unclear how to connect to the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local ‘boundary particle’ description in special cases.

scholarly journals Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

Development and Calculation of a Computer Model and Modern Distributed Algorithms for Dispersed Systems Aggregation

2020 ◽  
Vol 11 (2) ◽  
pp. 56-68
Author(s):  
Nurlybek Zhumatayev ◽  
Zhanat Umarova ◽  
Gani Besbayev ◽  
Almira Zholshiyeva
Keyword(s):  
Distributed Algorithms ◽  
Computer Model ◽  
Initial Conditions ◽  
Relaxation Times ◽  
Calculation Algorithm ◽  
Dispersed Systems ◽  
Perfect Model ◽  
Aggregation Processes ◽  
Non Local ◽  
Non Local Equations

In this work, an attempt has been made to eliminate the contradiction of the Smoluchowski equation, using modern distributed algorithms for creating calculation algorithm and implementation a program for building a more perfect model by changing the type of the kinetic equation of aggregation taking into account the relaxation times. On the basis of the applied Mathcad package, there is a developed computer model for calculating the aggregation of dispersed systems. The obtained system of differential equations of the second order is solved by the Runge-Kutt method. The authors are presetting the initial conditions of the calculation. A subsequent analysis was made of the obtained non-local equations and the study of the behavior of solutions of different orders. Also, this research can be aimed at the generalization of the proposed approach for the analysis of aggregation processes in heterogeneous dispersed systems, involving the creation of aggregation models, taking into account both time and space non-locality.

scholarly journals Approximating travelling waves by equilibria of non-local equations

2012 ◽  
Vol 78 (3) ◽  
pp. 145-186 ◽  
Author(s):  
Jose M. Arrieta ◽  
María López-Fernández ◽  
Enrique Zuazua
Keyword(s):  
Travelling Waves ◽  
Non Local ◽  
Non Local Equations

Stationary States of the Classically Radiating Electron in an Attractive Potential

1977 ◽  
Vol 32 (6) ◽  
pp. 659-660 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Equations Of Motion ◽  
Numerical Calculations ◽  
Attractive Potential ◽  
Stationary States ◽  
Non Local ◽  
Non Local Equations

Abstract It is shown by explicit numerical calculations, that the recently proposed non-local equations of motion, which can be supplied by a modified form of the well-known Caldirola equation, all admit the possibility of stationary radiationless motions in an attractive potential.

scholarly journals On the nature of Time and Entanglement

2021 ◽  
Author(s):  
Alessandro Capurso
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Imaginary Time ◽  
The Core ◽  
Time Order ◽  
Non Local ◽  
Nature Of Time ◽  
Free Will Theorem

The nature of Time is often at the root of the physical debate and possibly sits at the core of General Relativity and Quantum Mechanics frameworks incompatibility. In the context of the Free Will theorem and of a spacetime described through information, we identify in a thick present the only quantum information potential needed to describe evolution. The analysis of undefined causal orders (through a quantum Controlled-NOT gate and the evolution of the information along an imaginary time) allowed us to describe entanglement (both in space position and time order) as the potential related to an open choice and expressed in a CTC, which develops in a non-local imaginary space within the thick present considered.

Sign in / Sign up

Export Citation Format

Share Document