scholarly journals The Deng Algorithm in Higher Dimensions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Y. Nyonyi ◽  
S. D. Maharaj ◽  
K. S. Govinder
Keyword(s):  
Heat Flow ◽  
Cosmological Model ◽  
Higher Dimensions ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Four Dimensions ◽  
Symmetric Spacetimes ◽  
Special Cases ◽  
Spherically Symmetric Spacetimes

We extend an algorithm of Deng in spherically symmetric spacetimes to higher dimensions. We show that it is possible to integrate the generalised condition of pressure isotropy and generate exact solutions to the Einstein field equations for a shear-free cosmological model with heat flow in higher dimensions. Three new metrics are identified which contain results of four dimensions as special cases. We show graphically that the matter variables are well behaved and the speed of sound is causal.

scholarly journals Thermodynamic structure of field equations near apparent horizon for radiating black holes

2014 ◽  
Vol 29 (34) ◽  
pp. 1450188 ◽  
Author(s):  
Uma Papnoi ◽  
Megan Govender ◽  
Sushant G. Ghosh
Keyword(s):  
Black Holes ◽  
Apparent Horizon ◽  
Higher Dimensions ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Four Dimensions ◽  
Thermodynamic Structure ◽  
Kinematical Parameters

We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity T dS = dE+P dV.

scholarly journals GENERALIZED MODEL FOR Λ DARK ENERGY

2009 ◽  
Vol 18 (03) ◽  
pp. 389-396 ◽  
Author(s):  
UTPAL MUKHOPADHYAY ◽  
P. C. RAY ◽  
SAIBAL RAY ◽  
S. B. DUTTA CHOUDHURY
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Cosmological Model ◽  
A Priori ◽  
State Parameter ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Two Fluid

Einstein field equations under spherically symmetric space–times are considered here in connection with dark energy investigation. A set of solutions is obtained for a kinematic Λ model, viz. [Formula: see text], without assuming any a priori value for the curvature constant and the equation-of-state parameter ω. Some interesting results, such as the nature of cosmic density Ω and deceleration parameter q, have been obtained with the consideration of two-fluid structure instead of the usual unifluid cosmological model.

scholarly journals A Relativistic Algorithm with Isotropic Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Ngubelanga ◽  
S. D. Maharaj
Keyword(s):  
Spherically Symmetric ◽  
Conformally Flat ◽  
Einstein Field Equations ◽  
Elementary Functions ◽  
Field Equations ◽  
Isotropic Coordinates ◽  
New Exact Solutions ◽  
Symmetric Spacetimes ◽  
Particular Solution ◽  
Conformally Flat Metric

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contain isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.

scholarly journals NONEXTREME BLACK HOLES FROM INTERSECTING M-BRANES

1998 ◽  
Vol 13 (08) ◽  
pp. 1305-1328 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
TAKASHI SHIMIZU
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Higher Dimensions ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Deformation Parameters ◽  
Special Cases ◽  
Two Parameter ◽  
Black Hole Solutions

We investigate the possibility of extending nonextreme black hole solutions made of intersecting M-branes to those with two nonextreme deformation parameters, similar to Reissner–Nordstrøm solutions. General analysis of possible solutions is carried out to reduce the problem of solving field equations to a simple algebraic one for static spherically-symmetric case in D dimensions. The results are used to show that the extension to two-parameter solutions is possible for D= 4,5 dimensions but not for higher dimensions, and that the area of horizon always vanishes in the extreme limit for black hole solutions for D≥6 except for two very special cases which are identified. Various solutions are also summarized.

Final fate of charged anisotropic fluid collapse in f(R) gravity

2020 ◽  
Vol 35 (29) ◽  
pp. 2050238
Author(s):  
Suhail Khan ◽  
Muhammad Shoaib Khan ◽  
Amjad Ali
Keyword(s):  
Physical Significance ◽  
Anisotropic Fluid ◽  
Time Interval ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Closed Form Solutions ◽  
Symmetric Spacetimes ◽  
Apparent Horizons ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

In this paper, the spherically symmetric gravitational collapse of anisotropic fluid in the presence of charge in metric [Formula: see text] theory is analyzed. We consider the static and non static spherically symmetric spacetimes for outer and inner regions of collapsing object respectively. For the smooth matching of inner and outer regions, the Senovilla as well as Darmois matching conditions are utilized. The closed form solutions are obtained from field equations. Moreover, we examine the apparent horizons and their physical significance. The effect of cosmological constant and [Formula: see text] term is same and the collapsing rate speeds up as compared to that of anisotropic fluid case when the electromagnetic field is introduced. Electromagnetic charge also affects the time interval of singularities and cosmological horizons.

scholarly journals ENERGY–MOMENTUM DISTRIBUTION: A CRUCIAL PROBLEM IN GENERAL RELATIVITY

2005 ◽  
Vol 20 (18) ◽  
pp. 4309-4330 ◽  
Author(s):  
M. SHARIF ◽  
TASNIM FATIMA
Keyword(s):  
General Relativity ◽  
Cosmological Model ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Hamiltonian Approach ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Special Cases ◽  
Crucial Problem ◽  
Electromagnetic Generalization

This paper is aimed to elaborate the problem of energy–momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under consideration are the nonnull Einstein–Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel metric become special cases of the nonnull Einstein–Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these space–times. These inconsistent results verify the well-known proposal that the idea of localization does not follow the lines of pseudotensorial construction but instead follows from the energy–momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.

ROTATING STRING COSMOLOGIES WITH SCALAR FIELD AND HEAT FLUX

2001 ◽  
Vol 10 (06) ◽  
pp. 935-942 ◽  
Author(s):  
HÜSNÜ BAYSAL ◽  
İHSAN YILMAZ ◽  
İSMAIL TARHAN
Keyword(s):  
Heat Flux ◽  
Temperature Distribution ◽  
Scalar Field ◽  
Heat Flow ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Rotating String

We obtain some cosmological model that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Gödel-type cosmological model and the curvature source is a string cloud with scalar field and heat flow. The solutions have nonzero expansion, shear, and rotating. The properties of the solutions are studied and the temperature distribution is also given explicitly.

Global monopoles in f(R) gravity

2015 ◽  
Vol 30 (40) ◽  
pp. 1550217 ◽  
Author(s):  
Melis Ulu Dog̃ru ◽  
Dog̃ukan Taṣer
Keyword(s):  
Black Holes ◽  
Cold Dark Matter ◽  
Spherically Symmetric ◽  
Approximation Methods ◽  
Field Equations ◽  
Symmetric Spacetimes ◽  
Form Field ◽  
Spherically Symmetric Spacetimes ◽  
Global Monopoles ◽  
Static Spherically Symmetric Spacetimes

In this study, we investigate whether global monopoles cause black holes or wormholes to form. Field equations for static spherically symmetric spacetimes with global monopoles are obtained in [Formula: see text] gravity. We found exact solutions for the field equations without using any perturbation or approximation methods. It is shown that the obtained [Formula: see text] function is in accordance with the [Formula: see text]-cold dark matter ([Formula: see text]-CDM) model. Also, it is shown that the static spherically symmetric spacetimes associated with global monopoles form black holes or wormhole structures under some restrictions. Finally, geometrical and physical results of the solutions are discussed.

Classification of Static Spherically Symmetric Spacetimes by Noether Symmetries

2013 ◽  
Vol 52 (10) ◽  
pp. 3534-3542 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. G. Johnpillai ◽  
A. H. Kara ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes
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