Next Article in Journal / Special Issue
Collapsing Wormholes Sustained by Dustlike Matter
Previous Article in Journal / Special Issue
Gravitational Interaction of Cosmic String with Spinless Particle
Open AccessArticle

On the Discrete Version of the Schwarzschild Problem

Budker Institute of Nuclear Physics of Siberian Branch Russian Academy of Sciences, Novosibirsk 630090, Russia
Universe 2020, 6(10), 185; https://doi.org/10.3390/universe6100185
Received: 23 August 2020 / Revised: 5 October 2020 / Accepted: 15 October 2020 / Published: 17 October 2020
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge lengths. This elementary length scale is defined by the Planck scale and some free parameter of such a quantum extension of the theory. Besides, Regge action was reduced to an expansion over metric variations between the tetrahedra and, in the main approximation, is a finite-difference form of the Hilbert–Einstein action. Using for the Schwarzschild problem a priori general non-spherically symmetrical ansatz, we get finite-difference equations for its discrete version. This defines a solution which at large distances is close to the continuum Schwarzschild geometry, and the metric and effective curvature at the center are cut off at the elementary length scale. Slow rotation can also be taken into account (Lense–Thirring-like metric). Thus, we get a general approach to the classical background in the quantum framework in zero order: it is an optimal starting point for the perturbative expansion of the theory, finite-difference equations are classical, and the elementary length scale has quantum origin. Singularities, if any, are resolved. View Full-Text
Keywords: Einstein theory of gravity; minisuperspace theory; piecewise flat space-time; Regge calculus; Schwarzschild black hole Einstein theory of gravity; minisuperspace theory; piecewise flat space-time; Regge calculus; Schwarzschild black hole
Show Figures

Figure 1

MDPI and ACS Style

Khatsymovsky, V. On the Discrete Version of the Schwarzschild Problem. Universe 2020, 6, 185.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop