A GENERAL RELATIVISTIC THOMAS FERMI TREATMENT OF NEUTRON STAR CORES II: GENERALIZED FERMI ENERGIES AND BETA EQUILIBRIUM

2012 ◽  
Vol 12 ◽  
pp. 198-202
Author(s):  
D. PUGLIESE ◽  
JORGE A. RUEDA ◽  
R. RUFFINI ◽  
S.S. XUE
Keyword(s):  
General Relativity ◽  
Ground State ◽  
Meson Exchange ◽  
Strong Interactions ◽  
Equilibrium Equations ◽  
Rho Meson ◽  
Self Consistent ◽  
General Relativistic ◽  
Walecka Model ◽  
Thermodynamic Equilibrium Condition

We formulate the set of self-consistent ground-state equilibrium equations of a system of degenerate neutrons, protons and electrons in beta equilibrium taking into account quantum statistics, electro-weak, and strong interactions, within the framework of general relativity. The strong interaction between nucleons is modeled through sigma-omega-rho meson exchange in the context of the extended Walecka model, all duly expressed in general relativity. We demonstrate that, as in the non-interacting case, the thermodynamic equilibrium condition given by the constancy of the Fermi energy of each particle-specie can be properly generalized to include the contribution of all fields.

scholarly journals NEUTRON STAR CORES IN THE GENERAL RELATIVISTIC THOMAS-FERMI TREATMENT

2013 ◽  
Vol 23 ◽  
pp. 185-192
Author(s):  
RICCARDO BELVEDERE ◽  
JORGE A. RUEDA ◽  
REMO RUFFINI
Keyword(s):  
General Relativity ◽  
Neutron Stars ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Strong Interactions ◽  
Spherically Symmetric ◽  
The Core ◽  
General Relativistic ◽  
The Mean

We introduce a new set of equations to describe the equilibrium of the core of neutron stars, composed by self-gravitating degenerate neutrons, protons and electrons in β-equilibrium. We take into account strong, weak, electromagnetic and gravitational interactions within the framework of general relativity. We extend the conditions of equilibrium based on the constancy of the Klein potentials to the strongly interactive case. The strong interactions between nucleons are modeled through the exchange of the σ, ω and ρ virtual mesons. The equations are solved numerically in the case of zero temperatures and for a non-rotating spherically symmetric neutron stars in the mean-field approximation.

MASS, RADIUS AND MOMENT OF INERTIA OF NEUTRON STARS

2011 ◽  
Vol 20 (supp01) ◽  
pp. 208-213
Author(s):  
RICCARDO BELVEDERE ◽  
JORGE ARMANDO RUEDA ◽  
REMO RUFFINI
Keyword(s):  
Neutron Star ◽  
Strong Interactions ◽  
Nuclear Model ◽  
Equilibrium Equations ◽  
Equilibrium Conditions ◽  
Neutron Star Mass ◽  
Equilibrium Configurations ◽  
General Relativistic ◽  
System Of Equilibrium Equations ◽  
Relativistic Fermi

We construct the ground-state equilibrium configurations of neutron star cores. The system of equilibrium equations, taking into account quantum statistics, electro-weak, and strong interactions, is formulated within the framework of general relativity both in the rotating and non-rotating spherically symmetric case. The core is assumed to be composed of interacting degenerate neutrons, protons and electrons in beta equilibrium. The strong interaction between nucleons is mediated by the sigma-omega-rho virtual mesons. The mass-radius relation for neutron star cores is obtained for various parametrizations of the nuclear model. The equilibrium conditions are given by our recently developed theoretical framework based on the Einstein-Maxwell-Thomas-Fermi equations along with the constancy of the general relativistic Fermi energies of particles, the "Klein potentials", throughout the configuration. These equations are here solved numerically in the case of zero temperatures and for selected parameterizations of the nuclear model. We present here the new neutron star mass-radius relation.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

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.

Correlation in the Ground State of He Atom

1981 ◽  
Vol 36 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Zero Order ◽  
Consistent Variation ◽  
Hartree Fock ◽  
Perturbation Procedure ◽  
Self Consistent ◽  
He Atom ◽  
Atomic Parameters

It is possible to reproduce the entire results of Pekeris et al. of different atomic parameters for the He atom by introducing (ll) type correlation in a self consistent variation perturbation procedure using the Hartree-Fock (HF) wavefunction as the zero-order wavefunction

Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

2004 ◽  
Vol 17 (1-2) ◽  
pp. 165-197 ◽  
Author(s):  
Erhard Scholz
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
A Priori ◽  
Group Extension ◽  
Central Idea ◽  
German Word ◽  
General Relativistic ◽  
Empirical Turn ◽  
Relativistic Framework ◽  
Internal Symmetries

Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.

All classical predictions of general relativity from special relativistic Hamiltonian dynamics

2018 ◽  
Vol 33 (29) ◽  
pp. 1850169
Author(s):  
J. H. Field
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Hamiltonian Dynamics ◽  
Gravitational Redshift ◽  
Newtonian Mechanics ◽  
Light Deflection ◽  
Schwarzschild Metric ◽  
Related Literature ◽  
General Relativistic ◽  
Relativistic Hamiltonian Dynamics

Previous special relativistic calculations of gravitational redshift, light deflection and Shapiro delay are extended to include perigee advance. The three classical, order G, post-Newtonian predictions of general relativity as well as general relativistic light-speed-variation are therefore shown to be also consequences of special relativistic Newtonian mechanics in Euclidean space. The calculations are compared to general relativistic ones based on the Schwarzschild metric equation, and related literature is critically reviewed.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

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