Neutrino radiation in spherically-symmetric gravitational fields I. The energy-momentum tensor for the one-neutrino and many-particle neutrino field

1973 ◽  
Vol 4 (5) ◽  
pp. 361-370 ◽  
Author(s):  
J. B. Griffiths
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Neutrino Radiation ◽  
Neutrino Field ◽  
The One

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Charged gravastars in f(R,T,RμνTμν) gravity

2021 ◽  
pp. 2150084
Author(s):  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Equations Of State ◽  
Mathematical Formulation ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
De Sitter ◽  
The Stability ◽  
Physical Features ◽  
Modified Theory

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

Study of gravitational decoupled anisotropic solution

2019 ◽  
Vol 28 (16) ◽  
pp. 2040004
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Anisotropic Model ◽  
Field Equations ◽  
Anisotropic Solution ◽  
Spherically Symmetric Solution ◽  
Gravitational Source ◽  
The Stability

This paper formulates the exact static anisotropic spherically symmetric solution of the field equations through gravitational decoupling. To accomplish this work, we add a new gravitational source in the energy–momentum tensor of a perfect fluid. The corresponding field equations, hydrostatic equilibrium equation as well as matching conditions are evaluated. We obtain the anisotropic model by extending the known Durgapal and Gehlot isotropic solution and examined the physical viability as well as the stability of the developed model. It is found that the system exhibits viable behavior for all fluid variables as well as energy conditions and the stability criterion is fulfilled.

scholarly journals SPHERICALLY SYMMETRIC GRAVITATIONAL COLLAPSE

2009 ◽  
Vol 24 (19) ◽  
pp. 1533-1542 ◽  
Author(s):  
M. SHARIF ◽  
KHADIJA IQBAL
Keyword(s):  
Surface Energy ◽  
Gravitational Collapse ◽  
Curvature Tensor ◽  
Energy Momentum Tensor ◽  
Extrinsic Curvature ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Tangential Pressure ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with g00 = 1. Israel's junction conditions are used to develop this formalism. The formulas for extrinsic curvature tensor are obtained. The general form of the surface energy–momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.

scholarly journals Spinor field in Bianchi type-IX space–time

2018 ◽  
Vol 96 (10) ◽  
pp. 1074-1084
Author(s):  
Bijan Saha
Keyword(s):  
Spinor Field ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Early Stage ◽  
Momentum Tensor ◽  
Space Time ◽  
Rapid Expansion ◽  
Coupling Constant ◽  
The One

Within the scope of Bianchi type-IX cosmological model we have studied the role of spinor field in the evolution of the Universe. It is found that unlike the diagonal Bianchi models in this case the components of energy–momentum tensor of spinor field along the principal axis are not the same (i.e., [Formula: see text]), even in the absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy–momentum tensor of the spinor field imposes severe restrictions both on geometry of space–time and on the spinor field itself. As a result the space–time turns out to be either locally rotationally symmetric or isotropic. In this paper we considered the Bianchi type-IX space–time both for a trivial b, that corresponds to standard Bianchi type-IX and the one with a non-trivial b. It was found that a positive self-coupling constant λ1 gives rise to an oscillatory mode of expansion, while a trivial λ1 leads to rapid expansion at the early stage of evolution.

scholarly journals MATTER INHERITANCE SYMMETRIES OF SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2006 ◽  
Vol 21 (12) ◽  
pp. 2645-2657 ◽  
Author(s):  
M. SHARIF
Keyword(s):  
Energy Momentum Tensor ◽  
Complete Classification ◽  
Momentum Tensor ◽  
Conformal Killing ◽  
Spherically Symmetric ◽  
Metric Tensor ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Conformal Killing Vectors ◽  
Static Space

In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static space–times by their matter inheritance symmetries. It is shown that when the energy–momentum tensor is degenerate, most of the cases yield infinite dimensional matter inheriting symmetries. It is worth mentioning here that two cases provide finite dimensional matter inheriting vectors even for the degenerate case. The nondegenerate case provides finite dimensional matter inheriting symmetries. We obtain different constraints on the energy–momentum tensor in each case. It is interesting to note that if the inheriting factor vanishes, matter inheriting collineations reduce to be matter collineations already available in the literature. This idea of matter inheritance collineations turn out to be the same as homotheties and conformal Killing vectors are for the metric tensor.

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

scholarly journals Inverse problem: What can we tell about the matter and energy in our Universe from its dimensionality and evolution

2018 ◽  
Vol 27 (07) ◽  
pp. 1841005
Author(s):  
Hanna Makaruk ◽  
James Langenbrunner
Keyword(s):  
Energy Momentum Tensor ◽  
Physical Space ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Time Dimension ◽  
Superstring Theory ◽  
Anisotropic Energy ◽  
The One ◽  
Multidimensional Models ◽  
Additional Space

The most popular theories of everything are various versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in [Formula: see text] space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and [Formula: see text]-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of [Formula: see text]-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.

Supersymmetry anomalies and analytic regularization

1988 ◽  
Vol 66 (5) ◽  
pp. 419-427 ◽  
Author(s):  
H. C. Lee ◽  
Q. Ho-Kim ◽  
F. Q. Liu
Keyword(s):  
Energy Momentum Tensor ◽  
Axial Current ◽  
Momentum Tensor ◽  
Tensor Algebras ◽  
Loop Level ◽  
Analytic Regularization ◽  
The One

The method of analytic regularization in which the number of dimensions is not generalized is shown to preserve the supersymmetry identity relating the anomalies of the supersymmetry current, the trace of the energy–momentum tensor, and the divergence of the axial current at the one-loop level. Explicit counterterms needed for the identity to hold are constructed. The method preserves Dirac and all other tensor algebras in D = 4 space and renders the computation of anomalies straightforward and simple.

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