A fourth-order indirect integration method for black hole perturbations: even modes

We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. Form2l2>1/2withm2being the mass parameter of fourth-order terms andl2AdS3curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. Form2l2<1/2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.

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LUKEWARM BLACK HOLES IN QUADRATIC GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732311035560 ◽

2011 ◽

Vol 26 (14) ◽

pp. 999-1007 ◽

Cited By ~ 6

Author(s):

JERZY MATYJASEK ◽

KATARZYNA ZWIERZCHOWSKA

Keyword(s):

Black Holes ◽

Black Hole ◽

Event Horizon ◽

Fourth Order ◽

Spherically Symmetric ◽

Cosmological Horizon ◽

De Sitter ◽

Quadratic Gravity ◽

De Sitter Universe ◽

Electrically Charged

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.

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MIDAS III...a compiler version of MIDAS

SIMULATION ◽

10.1177/003754976600600307 ◽

1966 ◽

Vol 6 (3) ◽

pp. 160-168 ◽

Cited By ~ 1

Author(s):

George H. Burgin

Keyword(s):

Boundary Value Problem ◽

Fourth Order ◽

Execution Time ◽

Integration Method ◽

Fortran Program ◽

Machine Language ◽

Point Boundary ◽

Language Program ◽

Engineering Problems ◽

Efficient Machine

The original MIDAS program (MIDAS I, Wright Patterson AFB1) and the enlarged version of MIDAS (MIDAS II, North American Aviation2) proved to be effective tools for the digital solution of comple,, engineering problems. For large problems, however, running times for these programs were excessive and means were sought to improve the run-time efficiency. This is achieved in MIDAS III, which is no longer an interpretive type program as are MIDAS I and II, but rather a pre-compiler generating a FORTRAN program which is then compiled and assembled into an efficient machine language program. The execution times for this program are on the average between four and ten times shorter than in the earlier versions of MIDAS. This ap proach not only reduces computer execution time, it also gives the program more flexibility and expansion capa bility. A fourth order Runge-Kutta Merson integration method with automatic stepsize adjustment is used for the solution of the differential equations. As an application of MIDAS III, a two point boundary value problem is solved.

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Black hole shadows in fourth-order conformal Weyl gravity

Canadian Journal of Physics ◽

10.1139/cjp-2017-0241 ◽

2017 ◽

Vol 95 (12) ◽

pp. 1299-1306 ◽

Cited By ~ 19

Author(s):

Jonas R. Mureika ◽

Gabriele U. Varieschi

Keyword(s):

Black Hole ◽

Event Horizon ◽

Fourth Order ◽

Conformal Gravity ◽

Weyl Gravity ◽

General Relativistic

We calculate the characteristics of the “black hole shadow” for a rotating, neutral black hole in fourth-order conformal Weyl gravity. It is shown that the morphology is not significantly affected by the underlying framework, except for very large masses. Conformal gravity black hole shadows would also significantly differ from their general relativistic counterparts if the values of the main conformal gravity parameters, γ and κ, were increased by several orders of magnitude. Such increased values for γ and κ are currently ruled out by gravitational phenomenology. Therefore, it is unlikely that these differences in black hole shadows will be detected in future observations, carried out by the Event Horizon Telescope or other such experiments.

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Black hole initial data by numerical integration of the parabolic–hyperbolic form of the constraints

International Journal of Modern Physics D ◽

10.1142/s021827182150111x ◽

2021 ◽

Author(s):

Anna Nakonieczna ◽

Łukasz Nakonieczny ◽

István Rácz

Keyword(s):

Black Holes ◽

Black Hole ◽

Initial Data ◽

Fourth Order ◽

Main Part ◽

Strong Field ◽

Method Of Lines ◽

Time Integration ◽

The Method Of Lines ◽

Hyperbolic Form

The parabolic–hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is fourth-order accurate (in the spatial directions) while “time”-integration is made by using the method of lines with a fourth-order order accurate Runge–Kutta scheme. The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors is determined by comparing numerically and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations. The main part of our investigations is, however, centered on the construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content. Remarkably, the applied new method is unprecedented in that it allows to construct initial data for highly boosted and spinning black holes, essentially for the full physical allowed ranges of these parameters. In addition, the use of the evolutionary form of the constraints is free from applying any sort of boundary conditions in the strong field regime.

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Numerical integration of rotation with geometry propagators

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962316500173 ◽

2016 ◽

Vol 07 (03) ◽

pp. 1650017

Author(s):

Jianhua Tang ◽

Linfang Qian ◽

Qiang Yin

Keyword(s):

Numerical Integration ◽

Fourth Order ◽

Integration Method ◽

Dynamic Equations ◽

Reconstruction Method ◽

Order Accuracy ◽

Runge Kutta ◽

Multi Body ◽

Different Order ◽

Body Dynamic

Commutator free method is an effective method for solving rotating integration. Numerical examples show that the use of the proposed combining method can achieve the same order accuracy with less computation than other geometry integration method. However, it is difficult to be directly applied to mechanic dynamics solutions. In this paper, commutator free method which is often applied to rotation integration and classical Runge–Kutta (RK) method which is usually operated in Linear space are combined to solve the multi-body dynamic equations. The explicit Runge–Kutta coefficients are reconstructed to meet different order accuracy integration methods. The reconstruction method is discussed and coefficients are given. With this method, the dynamic equations can be solved accurately and economically without much modification on the classical numerical integration. Moreover, CG method and CF method can also be combined with adaptive RK method without many changes. Finally, the results of the examples show that with less computation, fourth-order combining method is as accurate as fourth-order Crouch–Grossman algorithm.

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NONLINEAR CHARGED BLACK HOLES IN AdS QUASI-TOPOLOGICAL GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271813500764 ◽

2013 ◽

Vol 22 (13) ◽

pp. 1350076 ◽

Cited By ~ 5

Author(s):

MOHAMMAD GHANAATIAN ◽

AFSANEH BAZRAFSHAN

Keyword(s):

Black Holes ◽

Black Hole ◽

Electromagnetic Field ◽

Fourth Order ◽

Naked Singularity ◽

Charged Black Holes ◽

Topological Parameters ◽

Mass Temperature ◽

Topological Gravity ◽

The Stability

In this paper, we present the static charged solutions of quartic quasi-topological gravity in the presence of a nonlinear electromagnetic field. Two branches of these solutions present black holes with one or two horizons or a naked singularity depending on the charge and mass of the black hole. The entropy of the charged black holes of fourth-order quasi-topological gravity through the use of Wald formula is computed and the mass, temperature and the charge of these black holes are found as well. We show that black holes with spherical, flat and hyperbolical horizon in quasi-topological gravity are stable for any allowed quasi-topological parameters. We also investigate the stability of nonlinear charged black holes.

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