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 Field of a charged particle in the presence of scalar meson fields in general relativity

1983 ◽  
Vol 24 (4) ◽  
pp. 461-465 ◽  
Author(s):  
D. R. K. Reddy ◽  
V. U. M. Rao
Keyword(s):  
Charged Particle ◽  
Point Charge ◽  
Scalar Meson ◽  
Scalar Fields ◽  
Flat Space ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Field Equations ◽  
Conformally Flat Metric ◽  
Scalar Meson Field

AbstractField equations for coupled gravitational and zero mass scalar fields in the presence of a point charge are obtained with the aid of a static spherically symmetric conformally flat metric. A closed from exact solution of the field equations is presented which may be considered as describing the field of a charged particle at the origin surrounded by the scalar meson field in a flat space-time.

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 Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Haroldo C. D. Lima Junior ◽  
Luís C. B. Crispino ◽  
Pedro V. P. Cunha ◽  
Carlos A. R. Herdeiro
Keyword(s):  
Black Holes ◽  
Jacobi Equation ◽  
Plasma Frequency ◽  
Conformal Factor ◽  
Matter Content ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Original Procedure ◽  
Hamilton Jacobi Equation

AbstractObtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

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 THERMAL EVOLUTION OF A RADIATING ANISOTROPIC STAR WITH SHEAR

2006 ◽  
Vol 15 (07) ◽  
pp. 1053-1065 ◽  
Author(s):  
N. F. NAIDU ◽  
M. GOVENDER ◽  
K. S. GOVINDER
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Dissipation ◽  
Thermal Evolution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pressure Anisotropy ◽  
Radiating Star ◽  
Anisotropic Star

We study the effects of pressure anisotropy and heat dissipation in a spherically symmetric radiating star undergoing gravitational collapse. An exact solution of the Einstein field equations is presented in which the model has a Friedmann-like limit when the heat flux vanishes. The behavior of the temperature profile of the evolving star is investigated within the framework of causal thermodynamics. In particular, we show that there are significant differences between the relaxation time for the heat flux and the relaxation time for the shear stress.

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.

Spherically symmetric static matter configurations with vanishing radial pressure

2014 ◽  
Vol 24 (01) ◽  
pp. 1550002 ◽  
Author(s):  
S. Thirukkanesh ◽  
M. Govender ◽  
D. B. Lortan
Keyword(s):  
Gravitational Field ◽  
Radial Pressure ◽  
Constant Density ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
New Family ◽  
Generating Method ◽  
Static Solutions ◽  
Special Case

We present a new family of spherically symmetric, static solutions of the Einstein field equations in isotropic, comoving coordinates. The radial pressure at each interior point of these models vanishes yet equilibrium is still possible. The constant density Florides solution which describes the gravitational field inside an Einstein cluster is obtained as a special case of our solution-generating method. We show that our solutions can be utilized to model strange star candidates such as Her. X-1, SAX J1808.4-3658(SS2), SAX J1808.4-3658(SS1) and PSR J1614-2230.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

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