curvature invariants
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2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Alfredo Herrera-Aguilar ◽  
Jhony A. Herrera-Mendoza ◽  
Daniel F. Higuita-Borja

AbstractWe present a spinning black hole solution in d dimensions with a maximal number of rotation parameters in the context of the Einstein–Maxwell-Dilaton theory. An interesting feature of such a solution is that it accommodates Lifshitz black holes when the rotation parameters are set to zero. We verify the rotating nature of the black hole solution by performing the quasi-local analysis of conserved charges and defining the corresponding angular momenta. In addition, we perform the thermodynamical analysis of the black hole configuration, show that the first law of thermodynamics is completely consistent, and obtain a Smarr-like formula. We further study the thermodynamic stability of the constructed solution from a local viewpoint, by computing the associated specific heats, and from a global perspective, by using the so-called new thermodynamic geometry. We finally make some comments related to a pathology found in the causal structure of the obtained rotating black hole spacetime and compute some of its curvature invariants.


2021 ◽  
Vol 65 (10) ◽  
pp. 947-951
Author(s):  
D. Gregoris

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Aykut Akgün ◽  
Mehmet Gülbahar

PurposeBi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.Design/methodology/approachSome properties of Di-geodesic and Di-umbilical bi-slant submanifolds are examined.FindingsThe Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants.Originality/valueThe topic is original, and the manuscript has not been submitted to any other journal.


2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Daniele Gregoris ◽  
Yen Chin Ong ◽  
Bin Wang

AbstractDifferent theories of gravity can admit the same black hole solution, but the parameters usually have different physical interpretations. In this work we study in depth the linear term $$\beta r$$ β r in the redshift function of black holes, which arises in conformal gravity, de Rham–Gabadadze–Tolley (dRGT) massive gravity, f(R) gravity (as approximate solution) and general relativity. Geometrically we quantify the parameter $$\beta $$ β in terms of the curvature invariants. Astrophysically we found that $$\beta $$ β can be expressed in terms of the cosmological constant, the photon orbit radius and the innermost stable circular orbit (ISCO) radius. The metric degeneracy can be broken once black hole thermodynamics is taken into account. Notably, we show that under Hawking evaporation, different physical theories with the same black hole solution (at the level of the metric) can lead to black hole remnants with different values of their physical masses with direct consequences on their viability as dark matter candidates. In particular, the mass of the graviton in massive gravity can be expressed in terms of the cosmological constant and of the formation epoch of the remnant. Furthermore the upper bound of remnant mass can be estimated to be around $$0.5 \times 10^{27}$$ 0.5 × 10 27 kg.


2021 ◽  
pp. 2140008
Author(s):  
Mark Green ◽  
Phillip Griffiths

Differential geometry, especially the use of curvature, plays a central role in modern Hodge theory. The vector bundles that occur in the theory (Hodge bundles) have metrics given by the polarizations of the Hodge structures, and the sign and singularity properties of the resulting curvatures have far reaching implications in the geometry of families of algebraic varieties. A special property of the curvatures is that they are [Formula: see text] order invariants expressed in terms of the norms of algebro-geometric bundle mappings. This partly expository paper will explain some of the positivity and singularity properties of the curvature invariants that arise in the Hodge theory with special emphasis on the norm property.


Author(s):  
S. I. Kruglov

A modified Hayward metric of magnetically charged black hole space–time based on rational nonlinear electrodynamics with the Lagrangian [Formula: see text] is considered. We introduce the fundamental length, characterizing quantum gravity effects. If the fundamental length vanishes the general relativity coupling to rational nonlinear electrodynamics is recovered. We obtain corrections to the Reissner–Nordström solution as the radius approaches infinity. The metric possesses a de Sitter core without singularities as [Formula: see text]. The Hawking temperature and the heat capacity are calculated. It was shown that phase transitions occur and black holes are thermodynamically stable at some event horizon radii. We demonstrate that curvature invariants are bounded and the limiting curvature conjecture takes place.


Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 241
Author(s):  
Pei-Ming Ho ◽  
Yuki Yokokura

For an effective field theory in the background of an evaporating black hole with spherical symmetry, we consider non-renormalizable interactions and their relevance to physical effects. The background geometry is determined by the semi-classical Einstein equation for an uneventful horizon where the vacuum energy–momentum tensor is small for freely falling observers. Surprisingly, after Hawking radiation appears, the transition amplitude from the Unruh vacuum to certain multi-particle states grows exponentially with time for a class of higher-derivative operators after the collapsing matter enters the near-horizon region, despite the absence of large curvature invariants. Within the scrambling time, the uneventful horizon transitions towards a firewall, and eventually the effective field theory breaks down.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hai-Shan Liu ◽  
H. Lü

Abstract We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. We consider two explicit examples in four and five dimensions and compute the central charges of the asymptotic symmetry algebras of the near horizon geometries, using the improved version of the BBC formalism that encompasses the information of the Lagrangian. We find that the resulting Cardy entropy differs from the Wald entropy, caused by the Riemann-squared RμνρσRμνρσ term.


Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Brandon Mattingly ◽  
Abinash Kar ◽  
Matthew Gorban ◽  
William Julius ◽  
Cooper K. Watson ◽  
...  

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.


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