arXiv subjects
Publications and source records attributed to Amir H. Abbassi.
It is shown that the field equations of general relativity in the Einstein tensor form and the unimodular theory of gravity do not fulfill the correspondence principle commitment completely. The consistent formalisms are briefly discussed.
A more rigorous treatment of the Schwarzschild metric by making use of the energy-momentum tensor of a single point particle as source term shows that $g_{00}=-\{1-\frac{2GM}{c^2r}-\frac{8G^2 M^2}{c^4 r^2}(θ(r)-1)\}\exp [2(θ(r)-1)]$ $g_{rr}=\{1-\frac{2GM}{c^2r}-\frac{8G^2 M^2}{c^4 r^2}(θ(r)-1)\}^{-1}$ The existence of a discontinuity at r=0 leads to an infinite repulsive force that will change the ultimate fate of a free fall test particle to a bouncing state.
Space-time is spherically symmetric if it admits the group of SO(3) as a group of isometries,with the group orbits spacelike two-surfaces. These orbits are necessarily two-surface of constant positive curavture. One commonly chooses coordinate ${t,r,θ,ϕ}$ so that the group orbits become surfaces ${t,r = const.}$ and the radial coordinate r is defined by the requirment that $4πr^2$ is the area of these spacelike two-surfaces with the range of zero to infinity. According to the Birkhoff's theorem upon the above assumptions, the Schwarzschild metric is the only soltion of the vacuum Einstein field equations. Our aim is to reconsider the solution of the sperically symmetric vacuum Einstein field equtions by regarding a weaker requirement. We admit the evident fact that in the completely empty sace the radial coordinate r may be defined so that $4πr^2$ becomes the area of spacelike two-surfaces ${t,r = const.}$ with the range of zero to infinity. This is not necessarily to be true in the presence of a material point mass M. It turns out that inspite of imposing asymptotically flatness and staticness as initial conditions the equations have general classes of solutions which the Schwarzschild metric is the only member of them which has an intrinsic singularity at the location of the point mass M. The area of ${t,r = const.}$ is $4π(r +αM)^2$ in one class and $4π(r^2 + a_1 Mr +a_2 M^2)$ in the other class while the center of symmetry is at r = 0.
It is discussed that the usual Heisenberg commutation relation (CR) is not a proper relation for massless particles and then an alternative is obtained. The canonical quantization of the free electromagnetic(EM)fields based on the field theoretical generalization of this alternative is carried out. Without imposing the normal ordering condition,the vacuum energy is automatically zero.This can be considered as a solution to the EM fields vacuum catastrophe and a step toward managing the cosmologial constant problem at least for the EM fields contribution to the state of vacuum.
1- It is shown that the upper bound for $α$ in the general solutions of spherically symmetric vacuum field equations(gr-qc/9812081,$Λ$=0) is nearly 10^3.This has been obtained by comparing the theoretical prediction for bending of light and precession of perihelia with observation. For a significant range of possible values of$α$ ($α$ >2) the metric is free of coordinate singularity. 2- It is checked that the singularity in the non-static spherically symmetric solution of Einstein field equations with $Λ$ (JHEP04(1999)011,$α$ = 0)at the origin is intrinsic. 3- Using the techniques of these two works, ageneral class of non-static solutions is presented. They are smooth and finite everywhere and have an extension larger than Schwarzschild metric. 4- The geodesic equations of a freely material particle for the general case are solved which reveals a Schwarzschild -deSitter type potential field.
A specific form of the inertial law is presented by which we can have some deeper insight into the essence of mass and inertia. In this modified theory, there is no need to keep the concept of absolute space and Newton's third law as principles. By introducing a convenient form for gravitational law the coupling constant G becomes a function of inertial parameters of the universe.
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that these equations have general solutions with the Schwarzschild metric as merely a special and simplest form of them. It is possible to have perfect and smooth metrics with the same Newtonian and post-Newtonian limits of Schwarzschild by a convenient and correct selection.
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world the Schwarzschild type coordinate systems are disqualified by redshift-magnitude test as a proper frame of reference(gr-qc/9812092). We derive the solution in a FRW type coordinate system which is qualified according to the mentioned test. Asymptotically it approachs to the non-static form of deSitter metric. The obtained metric is transformable to Schwarzschild-deSitter metric. It is an analytic function of $r$ for all values except $r=0$which is singular. This is carried out with no making use of Eddington-Finkelstein coordinates and without entering any cross term in the metric.