scholarly journals Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 957
Author(s):  
Lawrence Paul Horwitz ◽  
Vishnu S Namboothiri ◽  
Gautham Varma K ◽  
Asher Yahalom ◽  
Yosef Strauss ◽  
...  
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Harmonic Oscillator ◽  
Chaos Theory ◽  
Space Time ◽  
Raychaudhuri Equation ◽  
Geometric Flow ◽  
Geodesic Deviation

The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.

The Direct Detection of Gravitational Waves

2018 ◽  
pp. 106-109
Author(s):  
Alvaro De Rújula
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Waves ◽  
Direct Detection ◽  
Space Time ◽  
New Era ◽  
The Third ◽  
Perfect Storm

Gravitational waves emitted by black hole mergers. The first LIGO event: GW150917, the coalescence of two black holes of twenty nine and thirty six solar masses into one of “only” sixty two. The remaining three solar masses were emitted as energy in gravitational waves, a gigantic and perfect storm in the fabric of space-time. This is the dawn of a new era: The opening of the third “window” through which to look at the sky. Yet another triumph of general relativity. How much progress astrophysics has made since my time as a student.

AN ANSWER TO THE MAIN BLACK HOLE PATHOLOGY: FORMING NONSINGULAR BLACK HOLES FROM DUST COLLAPSE

2009 ◽  
Vol 18 (14) ◽  
pp. 2221-2229 ◽  
Author(s):  
R. MAIER ◽  
I. DAMIÃO SOARES
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Event Horizon ◽  
Nonlinear Resonance ◽  
Space Time ◽  
Low Energy ◽  
Spherically Symmetric ◽  
Energy Limit ◽  
Exterior Space

The dynamics of gravitational collapse is examined in the realm of string-based formalism of D-branes which encompasses general relativity as a low energy limit. A complete analytical solution is given to the spherically symmetric collapse of a pure dust star, including its matching with a corrected Schwarzschild exterior space–time. The collapse forms a black hole (an exterior event horizon) enclosing not a singularity but perpetually bouncing matter in the infinite chain of space–time maximal analytical extensions inside the outer event horizon. This chain of analytical extensions has a structure analogous to that of the Reissner–Nordstrom solution. The interior trapped bouncing matter has the possibility of being expelled by disruptive nonlinear resonance mechanisms.

scholarly journals EFFECT OF SPIN–TORSION INTERACTION ON RAYCHAUDHURI EQUATION

2009 ◽  
Vol 24 (27) ◽  
pp. 5025-5032 ◽  
Author(s):  
M. I. WANAS ◽  
M. A. BAKRY
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Space Time ◽  
Quantum Spin ◽  
Raychaudhuri Equation ◽  
Absolute Parallelism ◽  
Singularity Theorems ◽  
Moving Particle

Raychaudhuri equation is generalized in the parametrized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between the quantum spin of the moving particle and the torsion of the background gravitational field. The generalized Raychaudhuri equation obtained contains some extra terms, depending on the torsion of space–time, that would have some effects on the singularity theorems of general relativity. Under a certain condition, this equation could be reduced to the original Raychaudhuri equation without any need for a vanishing torsion.

scholarly journals Numerical Relativity: Solving Geodesics equation for Massive Particle Around Black Holes Horizon

2016 ◽  
Vol 35 ◽  
pp. 79-85
Author(s):  
Shohel Ahmed ◽  
Md Showkat Ali
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Physical Theory ◽  
Equations Of Motion ◽  
Massive Particle ◽  
Space Time ◽  
Special Focus ◽  
The World ◽  
Macroscopic Objects ◽  
The Universe

General relativity is the most beautiful physical theory ever invented. It describes one of the most pervasive features of the world we experience - gravitation. The gravitational field acts on nearby matter defines by the curvature of space-time. The black holes of nature are the most perfect macroscopic objects there are in the universe that constructed our concept of space-time. In this paper we use Einstein’s general relativity to model the motions of massive particles around the two black holes: static and rotating. These equations of motion around black holes will be studied with special focus towards the variation of symmetry by the change of gravitational effect.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 79-85

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

scholarly journals Driven black holes: from Kolmogorov scaling to turbulent wakes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Tomas Andrade ◽  
Christiana Pantelidou ◽  
Julian Sonner ◽  
Benjamin Withers
Keyword(s):  
Nonlinear Dynamics ◽  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Strong Field ◽  
De Sitter ◽  
Event Horizons ◽  
Binary Mergers ◽  
Tidal Deformations ◽  
Proof Of Principle

Abstract General relativity governs the nonlinear dynamics of spacetime, including black holes and their event horizons. We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov’s theory of 1941. As a proof of principle we focus on black holes in asymptotically anti-de Sitter spacetimes in a large number of dimensions, where greater analytic control is gained. We focus on cases where the effective horizon dynamics is restricted to 2+1 dimensions. We also demonstrate that tidal deformations of the horizon induce turbulent dynamics. When set in motion relative to the horizon a deformation develops a turbulent spacetime wake, indicating that turbulent spacetime dynamics may play a role in binary mergers and other strong-field phenomena.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

scholarly journals Generalisation for regular black holes on general relativity to f(R) gravity

2016 ◽  
Vol 76 (5) ◽  
Author(s):  
Manuel E. Rodrigues ◽  
Júlio C. Fabris ◽  
Ednaldo L. B. Junior ◽  
Glauber T. Marques
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Regular Black Holes
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