scholarly journals Four Spacetime Dimensions from Multifractal Geometry

2021 ◽  
Author(s):  
Ervin Goldfain
Keyword(s):  
General Relativity ◽  
Complex Behavior ◽  
Generalized Dimension ◽  
Self Similar ◽  
Underlying Geometry

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1678-1685 ◽  
Author(s):  
REZA TAVAKOL
Keyword(s):  
General Relativity ◽  
String Theory ◽  
Riemannian Geometry ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Spacetime Geometry ◽  
Test Particles ◽  
Light Rays ◽  
Recent Developments ◽  
Underlying Geometry

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more recent developments such as those in String theory, whereby Lorentz invariance is partially broken.

scholarly journals HOLLOWGRAPHY DRIVEN HOLOGRAPHY: BLACK HOLE WITH VANISHING VOLUME INTERIOR

2010 ◽  
Vol 19 (14) ◽  
pp. 2345-2351 ◽  
Author(s):  
AHARON DAVIDSON ◽  
ILYA GURWICH
Keyword(s):  
Phase Transition ◽  
General Relativity ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Schwarzschild Solution ◽  
Entropy Formula ◽  
Gravitational Theories ◽  
Hollow Interior ◽  
Spatial Volume ◽  
Self Similar

Hawking–Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one-parameter family degenerates) which takes place precisely at the would-have-been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel "hollow" interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called "hollowgraphy" driven holography.

scholarly journals Universal interferometric signatures of a black hole’s photon ring

2020 ◽  
Vol 6 (12) ◽  
pp. eaaz1310 ◽  
Author(s):  
Michael D. Johnson ◽  
Alexandru Lupsasca ◽  
Andrew Strominger ◽  
George N. Wong ◽  
Shahar Hadar ◽  
...  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Event Horizon ◽  
Infinite Sequence ◽  
High Order ◽  
Black Hole Mass ◽  
Tests Of General Relativity ◽  
Supermassive Black Hole ◽  
The Galaxy ◽  
Self Similar

The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin “photon ring,” which is composed of an infinite sequence of self-similar subrings that are indexed by the number of photon orbits around the black hole. The subrings approach the edge of the black hole “shadow,” becoming exponentially narrower but weaker with increasing orbit number, with seemingly negligible contributions from high-order subrings. Here, we show that these subrings produce strong and universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array.

Disappearance of Black Hole Criticality in Semiclassical General Relativity

1997 ◽  
Vol 12 (10) ◽  
pp. 709-718 ◽  
Author(s):  
Takeshi Chiba ◽  
Masaru Siino
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Scalar Field ◽  
Critical Phenomena ◽  
Equations Of Motion ◽  
Quantum Effects ◽  
Hole Formation ◽  
Trace Anomaly ◽  
Self Similar ◽  
Similar Solutions

We investigate the quantum effects on the so-called critical phenomena in black hole formation. Quantum effects of a scalar field are treated semiclassically via a trace anomaly method. It is found that the demand of regularity at the origin implies the disappearance of the echo. It is also found that semiclassical equations of motion do not admit continuously self-similar solutions. The quantum effects would change the critical solution from a discretely self-similar one to a solution without critical phenomena.

Self-similar symmetry in general relativity

1993 ◽  
Vol 25 (9) ◽  
pp. 865-880 ◽  
Author(s):  
J. Ponce de Leon
Keyword(s):  
General Relativity ◽  
Self Similar
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