scholarly journals Static spherical perfect fluid stars with finite radius in general relativity: a review

2021 ◽  
Vol 18 (2 Jul-Dec) ◽  
pp. 020208
Author(s):  
E. Chávez Nambo ◽  
O. Sarbach
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Uniqueness Of Solutions ◽  
Finite Radius ◽  
Relativistic Euler Equations ◽  
Gaseous Stars ◽  
Systematic Derivation ◽  
Tov Equation

In this article, we provide a pedagogical review of the Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe static, spherically symmetric gaseous stars in general relativity. Our discussion starts with a systematic derivation of the TOV equation from the Einstein field equations and the relativistic Euler equations. Next, we give a proof for the existence and uniqueness of solutions of the TOV equation describing a star of finite radius, assuming suitable conditions on the equation of state characterizing the gas. We also prove that the compactness of the gas contained inside a sphere centered at the origin satisfies the well-known Buchdahl bound, independent of the radius of the sphere. Further, we derive the equation of state for an ideal, classical monoatomic relativistic gas from statistical mechanics considerations and show that it satisfies our assumptions for the existence of a unique solution describing a finite radius star. Although none of the results discussed in this article are new, they are usually scattered in different articles and books in the literature; hence it is our hope that this article will provide a self-contained and useful introduction to the topic of relativistic stellar models.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Mass-radius relation of compact objects

2019 ◽  
Vol 15 (S356) ◽  
pp. 383-384
Author(s):  
Seman Abaraya ◽  
Tolu Biressa
Keyword(s):  
Numerical Analysis ◽  
Equation Of State ◽  
Compact Objects ◽  
Mass Limit ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Formation And Evolution ◽  
Active Research ◽  
Compact Sources ◽  
Astrophysical Research

AbstractCompact objects are of great interest in astrophysical research. There are active research interests in understanding better various aspects of formation and evolution of these objects. In this paper we addressed some problems related to the compact objects mass limit. We employed Einstein field equations (EFEs) to derive the equation of state (EoS). With the assumption of high densities and low temperature of compact sources, the derived equation of state is reduced to polytropic kind. Studying the polytropic equations we obtained similar physical implications, in agreement to previous works. Using the latest version of Mathematica-11 in our numerical analysis, we also obtained similar results except slight differences in accuracy.

scholarly journals "Gravitationally Lensed Gravitation" (GLG)

2021 ◽  
Author(s):  
Andreas Boenke
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Free Fall ◽  
Gravitational Effect ◽  
Gravitational Lens ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Optical Illusions ◽  
Spacetime Curvature ◽  
Background Object

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

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.

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

Stability of anisotropic perturbed Einstein universe in f(R) gravity

2020 ◽  
Vol 35 (18) ◽  
pp. 2050152
Author(s):  
M. Sharif ◽  
Sana Saleem
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
State Parameter ◽  
Field Equations ◽  
Static Universe ◽  
Scale Factors ◽  
Static Solutions ◽  
Equation Of State Parameter ◽  
Specific Formula ◽  
Einstein Static Universe

The aim of this paper is to investigate the existence of stable modes of the Einstein static universe in the background of [Formula: see text] theory. For this purpose, we take homogeneous anisotropic perturbations in scale factors as well as matter contents. We construct static and perturbed field equations that are further parameterized by linear equation of state parameter. We obtain the Einstein static solutions for two specific [Formula: see text] models and graphically analyze their stable regions. It is concluded that contrary to general relativity, there exists stable Einstein static universe with anisotropic perturbations.

scholarly journals Gravitational waves — A review on the theoretical foundations of gravitational radiation

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1830013 ◽  
Author(s):  
Alain Dirkes
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Wave Zone ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiative Losses ◽  
Zone Field ◽  
Theoretical Foundations

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

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