scholarly journals Spherically Symmetric Geometries inf(T)andf(R)Gravitational Theories

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Ricci Scalar ◽  
Spherically Symmetric ◽  
Total Derivative ◽  
Torsion Scalar ◽  
Gravitational Theories ◽  
Derivative Term ◽  
Total Derivative Term ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

Using the well know relation between Ricci scalar,R, and torsion scalar,T, that is,R=-T-2∇αTα, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is,T=TμναSαμν=0or (ii) total derivative term, that is,∇αTαwithTαis the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution forf(T)andf(R)gravitational theories.

scholarly journals Anisotropic compact stars in higher-order curvature theory

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
G. G. L. Nashed ◽  
S. D. Odintsov ◽  
V. K. Oikonomou
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Higher Order ◽  
Specific Form ◽  
Ricci Scalar ◽  
Spherically Symmetric ◽  
Curvature Theory ◽  
Anisotropic Star ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

AbstractIn this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the $${{\mathrm {f(R)}}}$$ f ( R ) type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $${{\mathrm {f(R)}}}$$ f ( R ) theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of $${{\mathrm {f(R)}}}$$ f ( R ) that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $${\mathrm {f(R)}}$$ f ( R ) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $$\textit{Her X--1}$$ Her X - - 1 , which has an estimated mass and radius $$(mass = 0.85 \pm 0.15M_{\circledcirc }\ and\ radius = 8.1 \pm 0.41~\text {km}$$ ( m a s s = 0.85 ± 0.15 M ⊚ a n d r a d i u s = 8.1 ± 0.41 km ). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.

scholarly journals Perihelion Precession and Deflection of Light in the General Spherically Symmetric Spacetime

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ya-Peng Hu ◽  
Hongsheng Zhang ◽  
Jun-Peng Hou ◽  
Liang-Zun Tang
Keyword(s):  
Solar System ◽  
Theoretical Result ◽  
Master Equation ◽  
Electric Charge ◽  
Spherically Symmetric ◽  
Experiment Data ◽  
Perihelion Precession ◽  
Deflection Of Light ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

The perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the master equation is obtained. As the application of this master equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution inf(R)gravity have been taken as examples. We find that both the electric charge andf(R)gravity can affect the perihelion precession and deflection of light, while the cosmological constant can only effect the perihelion precession. Moreover, we clarify a subtlety in the deflection of light in the solar system that the possible sun’s electric charge is usually used to interpret the gap between the experiment data and theoretical result. However, after also considering the effect from the sun’s same electric charge on the perihelion precession of Mercury, we can find that it is not the truth.

scholarly journals Schrödinger-like quantum dynamics in loop quantized black holes

2016 ◽  
Vol 25 (08) ◽  
pp. 1642006 ◽  
Author(s):  
Rodolfo Gambini ◽  
Javier Olmedo ◽  
Jorge Pullin
Keyword(s):  
Black Holes ◽  
Quantum Theory ◽  
Quantum Dynamics ◽  
Local Information ◽  
Quantum States ◽  
Spherically Symmetric ◽  
Definition Of ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in [R. Gambini, J. Olmedo and J. Pullin, Class. Quantum Grav. 31 (2014) 095009.] that this setting admits a Schrödinger-like picture. More precisely, the technique adopted there for the definition of parametrized Dirac observables (that codify local information of the quantum theory) can be extended in order to accommodate different pictures. In this new picture, the quantum states are parametrized in terms of suitable gauge parameters and the observables constructed out of the kinematical ones on this space of parametrized states.

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