scholarly journals Curvature Invariants for Charged and Rotating Black Holes

Universe ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 22 ◽  
Author(s):  
James Overduin ◽  
Max Coplan ◽  
Kielan Wilcomb ◽  
Richard Conn Henry
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Riemann Curvature ◽  
Geometrical Properties ◽  
Curvature Invariants ◽  
Dimensional Spacetime ◽  
Rotating Black Holes ◽  
General Kind ◽  
Degenerate Cases ◽  
Explicit Expressions

Riemann curvature invariants are important in general relativity because they encode the geometrical properties of spacetime in a manifestly coordinate-invariant way. Fourteen such invariants are required to characterize four-dimensional spacetime in general, and Zakhary and McIntosh showed that as many as seventeen can be required in certain degenerate cases. We calculate explicit expressions for all seventeen of these Zakhary–McIntosh curvature invariants for the Kerr–Newman metric that describes spacetime around black holes of the most general kind (those with mass, charge, and spin), and confirm that they are related by eight algebraic conditions (dubbed syzygies by Zakhary and McIntosh), which serve as a useful check on our results. Plots of these invariants show richer structure than is suggested by traditional (coordinate-dependent) textbook depictions, and may repay further investigation.

General Relativity

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Kerr Metric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Rotating Black Holes

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.

scholarly journals Aspects of Semiclassical Black Holes: Development and Open Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Alexander Y. Yosifov
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Information Loss ◽  
Quantum Corrections ◽  
Open Problems ◽  
Naked Singularities ◽  
Geometrical Properties ◽  
Energy Quantum ◽  
Information Loss Problem ◽  
Black Hole Solutions

The current work is a review, dedicated to the study of semiclassical aspects of black holes. We begin by briefly looking at the main statements of general relativity. We then consider the Schwarzschild, Kerr, and Reissner-Nordstrom black hole solutions and discuss their geometrical properties. Later, the thermodynamic nature of black holes is established. In light of this, we formulate the information loss problem and present the most promising approaches for addressing it with emphasis on introducing low-energy quantum corrections to the classical general relativity picture. Finally, in the context of multimessenger astronomy, we look at naked singularities as possible gravitational collapse endstates and their role in the unitarity of quantum mechanics and discuss their observational prospects.

scholarly journals The geometry of warped product singularities

2017 ◽  
Vol 14 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Ovidiu Cristinel Stoica
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Big Bang ◽  
Warping Function ◽  
Warped Products ◽  
Riemann Curvature ◽  
The Big Bang

In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

scholarly journals Twisted light, a new tool for general relativity and beyond — Revealing the properties of rotating black holes with the vorticity of light —

2021 ◽  
Author(s):  
F. Tamburini ◽  
F. Feleppa ◽  
B. Thidé
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Gravitational Lensing ◽  
Compact Object ◽  
Additional Tool ◽  
Physical Observable ◽  
Rotating Black Holes

We describe and present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum. The novel use of this physical observable as an additional tool for the previously known techniques of gravitational lensing allows us to directly measure, for the first time, the spin parameter of a black hole. With the additional information encoded in the orbital angular momentum, not only can we reveal the actual rotation of the compact object, but we can also use rotating black holes as probes to test general relativity.

scholarly journals Dynamics of particles in slowly rotating black holes with dipolar halos

2007 ◽  
Vol 3 (S248) ◽  
pp. 498-499
Author(s):  
W. B. Han
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Field Structure ◽  
Resonant Orbits ◽  
Test Particles ◽  
Rotating Black Holes ◽  
Fast Lyapunov Indicator ◽  
Dynamical Parameters ◽  
Dynamics Of Particles

AbstractIn general, the model of galaxy assumes a central huge black hole surrounded by a massive halo, disk or ring. In this paper, we investigate the gravitational field structure of a slowly rotating black hole with a dipolar halo, and the dynamics and chaos of test particles moving in it. Using Poincaré sections and fast Lyapunov indicator (FLI) in general relativity, we investigate chaos under different dynamical parameters, and find that the FLI is suitable for detecting chaos and even resonant orbits.

scholarly journals CHARGED ROTATING BLACK HOLES ON DGP BRANE

2009 ◽  
Vol 24 (23) ◽  
pp. 4389-4401 ◽  
Author(s):  
DAEHO LEE ◽  
CHANG-YOUNG EE ◽  
MYUNGSEOK YOON
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
De Sitter ◽  
Type Solution ◽  
Rotating Black Holes ◽  
Particular Solution

We consider charged rotating black holes localized on a three-brane in the DGP model. Assuming a Z2-symmetry across the brane and with a stationary and axisymmetric metric ansatz on the brane, a particular solution is obtained in the Kerr–Schild form. This solution belongs to the accelerated branch of the DGP model and has the characteristic of the Kerr–Newman–de Sitter-type solution in general relativity. Using a modified version of Boyer–Lindquist coordinates we examine the structures of the horizon and ergosphere.

MODIFIED NEWTONIAN POTENTIALS FOR OPTICALLY THIN ACCRETION DISKS AROUND BLACK HOLES

1998 ◽  
Vol 07 (03) ◽  
pp. 471-488 ◽  
Author(s):  
T. LØVÅS
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Field ◽  
Accretion Disks ◽  
Rotating Black Holes ◽  
Relativistic Result ◽  
Do So

The use of modified Newtonian potentials to describe the gravitational field around black holes has proven successful. I will present here an investigation of the accuracy of several modified Newtonian potentials proposed in the literature, by comparing the result with the exact relativistic solution. I will do so for optically thin accretion disks that are more sensitive to the form of the potential than optically thick standard disks. I find that simple modified Newtonian potentials capture the essential features of general relativity, and the results from using the modified Newtonian potentials deviate from the relativistic result only by 20% at most for nonrotating black holes. For rotating black holes the accuracy depends on the rotation of the black hole.

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