Curvature invariants of static spherically symmetric geometries

We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell–Lagrangian, in modifications of the Einstein–Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

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Construction of thin shell wormholes from metric f(R) gravity

Modern Physics Letters A ◽

10.1142/s0217732317501115 ◽

2017 ◽

Vol 32 (20) ◽

pp. 1750111 ◽

Cited By ~ 6

Author(s):

M. Zaeem-ul-Haq Bhatti ◽

A. Anwar ◽

S. Ashraf

Keyword(s):

Black Hole ◽

Equation Of State ◽

Thin Shell ◽

Chaplygin Gas ◽

Spherically Symmetric ◽

Modified Chaplygin Gas ◽

Potential Approach ◽

Curvature Invariants ◽

Radial Perturbation ◽

Thin Shell Wormholes

In this paper, we have constructed spherically symmetric thin-shell wormholes (WHs) by surgically grafting two geometries of charged black hole in the framework of f(R) higher curvature invariants (threaded by exotic matter). We have investigated the stable/unstable regimes for couple of f(R) models using the potential approach formulated by Eiroa with radial perturbation. We have categorized our analysis for different values of charge as well as the parameters involved in the particular mode of f(R) gravity. We have found both stable and unstable regions using modified Chaplygin gas in this scenario and the results are shown through plots. We found that there exists a parametric space for equation of state and quadratic as well as cubic gravities in which one can accommodate more stable thin-shell WHs.

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Curvature Invariants for Lorentzian Traversable Wormholes

Universe ◽

10.3390/universe6010011 ◽

2020 ◽

Vol 6 (1) ◽

pp. 11 ◽

Cited By ~ 2

Author(s):

Brandon Mattingly ◽

Abinash Kar ◽

William Julius ◽

Matthew Gorban ◽

Cooper Watson ◽

...

Keyword(s):

Spherically Symmetric ◽

Curvature Invariant ◽

Invariant Functions ◽

Curvature Invariants ◽

Traversable Wormholes ◽

Nonzero Curvature ◽

Coordinate Mapping ◽

Line Elements ◽

Coordinate Basis ◽

Exponential Metric

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).

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Design of N-dimensional multiplierless spherically symmetric FIR digital filters by transformation

IEE Proceedings G (Electronic Circuits and Systems) ◽

10.1049/ip-g-1.1988.0030 ◽

1988 ◽

Vol 135 (5) ◽

pp. 203

Author(s):

C. Charalambous

Keyword(s):

Digital Filters ◽

Spherically Symmetric ◽

Fir Digital Filters

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Global existence of the spherically symmetric flow of a self-gravitating viscous gas

Nonlinear Dynamics in Partial Differential Equations ◽

10.2969/aspm/06410515 ◽

2019 ◽

Author(s):

Morimichi Umehara

Keyword(s):

Global Existence ◽

Spherically Symmetric ◽

Symmetric Flow ◽

Viscous Gas

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Study A Non-Spherically Symmetric Gravitational Lens

10.37376/1571-000-015-001 ◽

2016 ◽

pp. 1

Author(s):

Tarig S. El Mabrouk

Keyword(s):

Gravitational Lens ◽

Spherically Symmetric

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The two-body problem: an effective-one-body approach

10.1093/oso/9780198786399.003.0056 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Body Problem ◽

Equations Of Motion ◽

Reaction Force ◽

Kerr Black Hole ◽

Radiation Reaction ◽

Spherically Symmetric ◽

Geodesic Motion ◽

Two Body Problem ◽

Symmetric Spacetime ◽

Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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