Gravitational collapse and dark universe with LTB geometry

2016 ◽  
Vol 26 (06) ◽  
pp. 1750045 ◽  
Author(s):  
M. Zaeem-ul-Haq Bhatti ◽  
Z. Yousaf
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Time Interval ◽  
Curvature Scalar ◽  
Field Equations ◽  
Dark Sector ◽  
Curvature Invariants ◽  
Text Model ◽  
Polynomial Formula ◽  
Electrically Charged

The objective of this paper is to examine the influence of polynomial [Formula: see text] dark sector cosmic terms on the collapse of electrically charged Lemaître–Tolman–Bondi geometry. We explored a class of solutions for [Formula: see text] field equations in the existence of electromagnetic field and under the constraint of constant curvature scalar. The influence of [Formula: see text] model on the dynamics of collapsing object have been discussed by studying its black hole and cosmological horizons. Also, the effects of these dark sources on the time interval between the corresponding singularities and horizons have been studied. We investigated that the process of collapse slows down due to the higher order curvature invariants of polynomial [Formula: see text] model and electromagnetic field.

scholarly journals Discussion of a Possible Corrected Black Hole Entropy

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Miao He ◽  
Ziliang Wang ◽  
Chao Fang ◽  
Daoquan Sun ◽  
Jianbo Deng
Keyword(s):  
Black Hole ◽  
Electromagnetic Field ◽  
Black Hole Entropy ◽  
Einstein Gravity ◽  
Matter Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Corrected Entropy ◽  
Entropy Of Black Hole ◽  
Spherically Symmetric Solution

Einstein’s equation could be interpreted as the first law of thermodynamics near the spherically symmetric horizon. Through recalling the Einstein gravity with a more general static spherical symmetric metric, we find that the entropy would have a correction in Einstein gravity. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, we can also derive the first law in EiBI gravity. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that correction of the entropy could be generalized to EiBI gravity. Furthermore, we point out that the Einstein gravity and EiBI gravity might be equivalent on the event horizon. At last, under EiBI gravity with the electromagnetic field, a specific corrected entropy of black hole is given.

The foundations of a generalization of gravitation theory

1957 ◽  
Vol 53 (2) ◽  
pp. 473-488 ◽  
Author(s):  
John Moffat
Keyword(s):  
Electromagnetic Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Original Form ◽  
Geometric Description ◽  
Field Equations ◽  
Electrically Charged

1. Introduction. Among the more notable attempts to derive a generalization of Einstein's gravitational theory is the recent one of Einstein and Schrodinger ((1)–(8)). This was formulated by dropping the symmetry of the fundamental tensor gμν and the components of the affine connexion. The most serious defect of these non-symmetric theories is that the field equations, in their original form, do not determine the motion of electrically charged particles in an electromagnetic field, as has been proved by Infeld(9), Callaway (10) and Bonnor (n). Together with the lack of an energy-momentum tensor and a geometric description of the paths of charged particles, this seems to indicate that the concept of motion is missing in this type of theory. It is clear that one of the most important results which should follow from a generalization of Einstein's gravitational theory is the correct equations of motion of charged particles in an electromagnetic field.

scholarly journals On the new field theory

1935 ◽  
Vol 148 (864) ◽  
pp. 353-364 ◽  
Keyword(s):  
Electromagnetic Field ◽  
The Self ◽  
Riemannian Curvature ◽  
Curvature Scalar ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Potential Vector ◽  
Fundamental Tensor ◽  
Self Energy ◽  
Field Strengths

In a recent series of articles Born, with Infeld, has developed a theory of the electromagnetic field in which the self-energy of the electron is finite. In II the theory is based upon an unsymmetric fundamental tensor of which the symmetric and antisymmetric parts are identified respectively with the gravitational potentials and the electromagnetic field strengths. The Lagrangian is built up in terms of the determinants of the fundamental unsymmetric tensor and its symmetric part, but field equation of the Lagrangian with respect to the field strengths. One must first assume that these field strengths form the curl of a potential vector, and one must then perform the variation with respect to this vector. Again, though the gravitational g ab enter the Lagrangian, variation with respect to them does not lead to adequate field equations for the gravitational field, so that Born and Infeld have suggested the arbitrary addition of the Riemannian curvature scalar density R√- g to their Lagrangian. In view of these two points it seems desirable to discuss the possible modification of the Born-Infeld theory in terms of the projective theory of relativity since in this way the difficulties mentioned above will be automatically overcome.

Dynamical variables and evolution of the universe

2017 ◽  
Vol 26 (04) ◽  
pp. 1750029 ◽  
Author(s):  
M. Zaeem-ul-Haq Bhatti ◽  
Z. Yousaf
Keyword(s):  
Dust Cloud ◽  
Charged Dust ◽  
Matter Distribution ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Dynamical Equations ◽  
Curvature Invariants ◽  
Imperfect Fluid ◽  
Text Model ◽  
The Universe

One of the striking feature of inhomogeneous matter distribution under the effects of fourth-order gravity and electromagnetic field have been discussed in this manuscript. We have considered a compact spherical celestial star undergoing expansion due to the presence of higher curvature invariants of [Formula: see text] gravity and imperfect fluid. We have explored the dynamical equations and field equations in [Formula: see text] gravity. An explicit expression have been found for Weyl tensor and material variables under the dark dynamical effects. Using a viable [Formula: see text] model, some dynamical variables have been explored from splitting the Riemann curvature tensor. These dark dynamical variables are also studied for charged dust cloud with and without the constraint of constant Ricci scalar.

scholarly journals Plebański–Demiański solution of general relativity and its expressions quadratic and cubic in curvature: Analogies to electromagnetism

2015 ◽  
Vol 24 (10) ◽  
pp. 1550079 ◽  
Author(s):  
Jens Boos
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
General Type ◽  
Coordinate Systems ◽  
Irreducible Decomposition ◽  
Asymptotically Flat ◽  
Type D ◽  
Curvature Invariants ◽  
Free Parameters ◽  
First Time

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution — the exact seven parameter solution of Plebański–Demiański (PD) — to demonstrate these analogies for a physically meaningful spacetime. The two quadratic curvature invariants B2 - E2 and E⋅B are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel–Robinson tensor reads (B2 + E2)2 for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy–momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel–Robinson 3-form, from which the Bel–Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: In the original polynomial PD coordinates and in a modified Boyer–Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.

scholarly journals Electrically charged black hole with scalar hair

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
Cristián Martínez ◽  
Ricardo Troncoso
Keyword(s):  
Black Hole ◽  
Charged Black Hole ◽  
Scalar Hair ◽  
Electrically Charged

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

scholarly journals BORN–INFELD COSMOLOGIES

2000 ◽  
Vol 15 (27) ◽  
pp. 4341-4353 ◽  
Author(s):  
RICARDO GARCÍA-SALCEDO ◽  
NORA BRETÓN
Keyword(s):  
Electromagnetic Field ◽  
Early Universe ◽  
Big Bang ◽  
Linear Case ◽  
Conformal Metric ◽  
Curvature Invariants ◽  
Metric Function ◽  
Big Bang Singularity

We present a model for an inhomogeneous and anisotropic early universe filled with a nonlinear electromagnetic field of Born–Infeld (BI) type. The effects of the BI field are compared with the linear case (Maxwell). Since the curvature invariants are well behaved then we conjecture that our model does not present an initial big bang singularity. The existence of the BI field modifies the curvature invariants at t=0 as well as sets bounds on the amplitude of the conformal metric function.

General form of the analytic function f(T) in diverse dimension for a static planar spacetime

2019 ◽  
Vol 28 (12) ◽  
pp. 1950158 ◽  
Author(s):  
Gamal Nashed
Keyword(s):  
Black Hole ◽  
Analytic Function ◽  
Black Hole Solution ◽  
Static Solution ◽  
Gravitational Theory ◽  
Interesting Property ◽  
Constant Function ◽  
Field Equations ◽  
Adm Mass ◽  
Laws Of Thermodynamics

We derive an exact static solution in diverse dimension, without any constraints, to the field equations of [Formula: see text] gravitational theory using a planar spacetime with two unknown functions, i.e. [Formula: see text] and [Formula: see text]. The black hole solution is characterized by two constants, [Formula: see text] and [Formula: see text], one is related to the mass of the black hole, [Formula: see text], and the other is responsible to make the solution deviate from the teleparallel equivalent of general relativity (TEGR). We show that the analytic function [Formula: see text] depends on the constant [Formula: see text] and becomes constant function when [Formula: see text] which corresponds to the TEGR case. The interesting property of this solution is the fact that it makes the singularity of the Kretschmann invariant much softer than the TEGR case. We calculate the energy of this black hole and show that it is equivalent to ADM mass. Applying a coordinate transformation, we derive a rotating black hole with nontrivial values of the torsion scalar and [Formula: see text]. Finally, we examine the physical properties of this black hole solution using the laws of thermodynamics and show that it has thermodynamical stability.

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