scholarly journals Classical confinement of test particles in higher-dimensional models: Stability criteria and a new energy condition

2003 ◽  
Vol 68 (10) ◽  
Author(s):  
Sanjeev S. Seahra
Keyword(s):  
Energy Condition ◽  
Stability Criteria ◽  
Test Particles ◽  
Higher Dimensional ◽  
New Energy ◽  
Dimensional Models

scholarly journals Higher-dimensional evolving wormholes satisfying the null energy condition

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
Mahdi Kord Zangeneh ◽  
Francisco S. N. Lobo ◽  
Nematollah Riazi
Keyword(s):  
Energy Condition ◽  
Null Energy Condition ◽  
Higher Dimensional

Characteristics of earthquake sequences: comparison from 0D to 3D

2021 ◽  
Author(s):  
Meng Li ◽  
Casper Pranger ◽  
Ylona van Dinther
Keyword(s):  
Stress Drop ◽  
Dynamic Models ◽  
Numerical Models ◽  
Recurrence Interval ◽  
Staggered Grid ◽  
Earthquake Parameters ◽  
Higher Dimensional ◽  
Dimensional Models ◽  
As Stress ◽  
Earthquake Sequences

<p>Numerical models are well-suited to overcome limited spatial-temporal observations to understand earthquake sequences, which is fundamental to ultimately better assess seismic hazard. However, high-resolution numerical models in 3D are computationally time and memory consuming. This is not optimal if the aspects of lateral or depth variations within the results are not needed to answer a particular objective. In this study we quantify and summarize the limitations and advantages for simulating earthquake sequences in all spatial dimensions.</p><p> </p><p>We simulate earthquake sequences on a strike-slip fault with rate-and-state friction from 0D to 3D using both quasi-dynamic and fully dynamic approaches. This cross-dimensional comparison is facilitated by our newly developed, flexible code library <em>Garnet</em>, which adopts a finite difference method with a fully staggered grid. We have validated our models using problems BP1-QD & FD and BP4-QD & FD of the SEAS (Sequences of Earthquakes and Aseismic Slip) benchmarks from the Southern California Earthquake Center.</p><p> </p><p>Our results demonstrate that lower-dimensional/quasi-dynamic models are qualitatively similar in terms of earthquake cycle characteristics to their higher-dimensional/fully-dynamic counterparts, while they could be hundreds to millions times faster at the same time. Quantitatively, we observe that certain earthquake parameters, such as stress drop and fracture energy release, can be accurately reproduced in each of these simpler models as well. However, higher dimensional models generally produce lower maximum slip velocities and hence longer coseismic durations. This is mainly due to lower rupture speeds, which result from increased energy consumption along added rupture front directions. In the long term, higher dimensional models produce shorter recurrence interval and hence smaller total slip, which is mainly caused by the higher interseismic stress loading rate inside the nucleation zone. The same trend is also observed when comparing quasi-dynamic models to fully dynamic ones. We extend a theoretical calculation that to first order approximates the aforementioned physical observables in 3D to all other dimensions. These theoretical considerations confirm the same trend as what is observed for stress drop, recurrence interval and total slip across dimensions. These findings on similarities and differences of different dimensional models and a corresponding quantification of computational efficiency can guide model design and facilitate result interpretation in future studies.</p>

scholarly journals New gedanken experiment on higher-dimensional asymptotically AdS Reissner–Nordström black hole

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Ming Zhang ◽  
Jie Jiang
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Order Approximation ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Matter Field ◽  
Second Order ◽  
Field Perturbation ◽  
Higher Dimensional ◽  
Dynamical Quantity

AbstractViewing the negative cosmological constant as a dynamical quantity derived from the matter field, we study the weak cosmic censorship conjecture for the higher-dimensional asymptotically AdS Reissner–Nordström black hole. To this end, using the stability assumption of the matter field perturbation and the null energy condition of the matter field, we first derive the first-order and second-order perturbation inequalities containing the variable cosmological constant and its conjugate quantity for the black hole. We prove that the higher-dimensional RN-AdS black hole cannot be destroyed under a second-order approximation of the matter field perturbation process.

scholarly journals SCALAR DEFORMATIONS OF SCHWARZSCHILD HOLES AND THEIR STABILITY

1998 ◽  
Vol 13 (05) ◽  
pp. 741-764 ◽  
Author(s):  
HELGE DENNHARDT ◽  
OLAF LECHTENFELD
Keyword(s):  
Scalar Field ◽  
Energy Condition ◽  
Linear Perturbation ◽  
Dominant Energy Condition ◽  
Stability Criteria ◽  
Field Equations ◽  
Effective Potentials ◽  
Scalar Hair ◽  
Linear Perturbation Theory ◽  
Scalar Field Equations

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schrödinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.

scholarly journals Higher-dimensional models in gravitational theories of quartic Lagrangians

1997 ◽  
Vol 38 (6) ◽  
pp. 3166-3188 ◽  
Author(s):  
K. Kleidis ◽  
A. Kuiroukidis ◽  
D. B. Papadopoulos ◽  
H. Varvoglis
Keyword(s):  
Gravitational Theories ◽  
Higher Dimensional ◽  
Dimensional Models

scholarly journals GENERATING STATIC, SPHERICALLY SYMMETRIC BLACK HOLES IN LOVELOCK GRAVITY

2009 ◽  
Vol 18 (13) ◽  
pp. 2061-2082 ◽  
Author(s):  
S. HABIB MAZHARIMOUSAVI ◽  
O. GURTUG ◽  
M. HALILSOY
Keyword(s):  
Black Holes ◽  
Higher Dimensions ◽  
Matter Field ◽  
Spherically Symmetric ◽  
Lovelock Gravity ◽  
Third Order ◽  
Naked Singularities ◽  
Test Particles ◽  
Higher Dimensional ◽  
Symmetric Black Hole

We present the generalization of a known theorem to generate static, spherically symmetric black hole solutions in higher-dimensional Lovelock gravity. Particular limits such as Gauss–Bonnet (GB) and Einstein–Hilbert (EH) in any dimension N yield all the solutions known to date with an energy–momentum. In our generalization, with special emphasis on third order Lovelock gravity, we have found two different class of solutions characterized by the matter field parameter. Several particular cases are studied and properties related to asymptotic behaviors are discussed. Our general solution, which covers topological black holes as well, splits naturally into distinct classes such as Chern–Simon (CS) and Born–Infeld (BI) in higher-dimensions. The occurence of naked singularities is studied and it is found that the space–time behaves nonsingularly in the quantum-mechanical sense when it is probed with quantum test particles. The theorem is extended to cover Bertotti–Robinson (BR) type solutions in the presence of the GB parameter alone. Finally, we prove also that extension of the theorem for a scalar–tensor source of higher dimensions (N > 4) fails to work.

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