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N. O. Santos

Publications and source records attributed to N. O. Santos.

At least 73 records · Page 4Linked to original sources
arXiv2000

Parametrization of singularities of the Demiański-Newman spacetimes

We propose a new presentation of the Demiański-Newman (DN) solution of the axisymmetric Einstein equations. We introduce new dimensionless parameters $p$, $q$ and $s$, but keeping the Boyer-Lindquist coordinate transformation used for the Kerr metric in the Ernst method. The family of DN metrics is studied and it is shown that the main role of $s$ is to determine the singularities, which we obtain by calculating the Riemann tensor components and the invariants of curvature. So, $s$ reveals itself as the parameter of the singular rings on the inner ergosphere.

gr-qc↗
arXiv2000

The static cylinder, gyroscopes, the C metric, and all that

The physical meaning of the Levi-Civita spacetime for some "critical" values of the parameter sigma, is discussed in the light of gedanken experiments performed with gyroscopes circumventing the axis of symmetry. The fact that sigma=1/2 corresponds to flat space described from the point of view of an accelerated frame of reference, led us to incorporate the C metric into discussion. The interpretation of phi as an angle variable for any value of sigma, appears to be at the origen of difficulties.

gr-qc↗
arXiv2000

Gyroscope precession in cylindrically symmetric spacetimes

We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable quantities, providing thereby a physical interpretation for those parameters, without specifying the source of the field.

gr-qc↗
arXiv1999

On the Levi-Civita solutions with cosmological constant

The main properties of the Levi-Civita solutions with the cosmological constant are studied. In particular, it is found that some of the solutions need to be extended beyond certain hypersurfaces in order to have geodesically complete spacetimes. Some extensions are considered and found to give rise to black hole structure but with plane symmetry. All the spacetimes that are not geodesically complete are Petrov type D, while in general the spacetimes are Petrov type I.

gr-qc↗
arXiv1998

Geodesics in the Gamma spacetime

Circular and radial geodesics are studied in the spacetime described by the $γ$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry.

gr-qc↗
arXiv1998

Gravitational Collapse of Perfect Fluid

The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the fluid packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similarity, the formation of black holes always starts with a finite non-zero mass. The packet is usually accompanied by a thin matter shell. The effects of the shell on the collapse are also studied.

gr-qc↗
arXiv1998

The Levi-Civita spacetime as a limiting case of the Gamma spacetime

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics.

gr-qc↗
arXiv1998

Gravitational dust collapse with cosmological constant

We study the fate of gravitational collapse in presence of a cosmological constant. The junctions conditions between static and non-static space-times are deduced. Three apparent horizon are formed, but only two have physical significance, one of them being the black hole horizon and the other the cosmological horizon. The cosmological constant term slows down the collapse of matter, limiting also the size of the black hole.

gr-qc↗
arXiv1998

Rotating Cylindrical Systems and Gravitomagnetism

We discuss gravitomagnetism in connection with rotating cylindrical systems. In particular, the gravitomagnetic clock effect is investigated for the exterior vacuum field of an infinite rotating cylinder. The dependence of the clock effect on the Weyl parameters of the stationary Lewis metric is determined. We illustrate our results by means of the van Stockum spacetime.

gr-qc↗
arXiv1997

Stationary and static cylindrically symmetric Einstein spaces of the Lewis form

The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are investigated. It is shown that three of the parameters (and the value of the cosmological constant) are essential, of which one characterizes the local gravitational field and appears in the Cartan scalars, while the remaining two give information about the topological identification made to produce cylindrical symmetry. Other than the cosmological constant, they can be related to the parameters of the vacuum Weyl and Lewis classes, whose interpretation was previously investigated by da Silva et al. (1995a, 1995b).

gr-qc↗
arXiv1997

An exterior for the Gödel spacetime

We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $Λ$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a Gödel universe. There are three cases, depending on the radius of the cylinder. Closed timelike curves are present in the exteriors of some of the solutions. There is a considerable similarity between the spacetimes investigated here and those of van Stockum referring to an infinite cylinder of rotating dust matched to vacuum, with $Λ=0$.

gr-qc↗
arXiv1997

Gravitational collapse of massless scalar field and radiation fluid

Several classes of conformally-flat and spherically symmetric exact solutions to the Einstein field equations coupled with either a massless scalar field or a radiation fluid are given, and their main properties are studied. It is found that some represent the formation of black holes due to the gravitational collapse of the matter fields. When the spacetimes have continuous self-similarity (CSS), the masses of black holes take a scaling form $M_{BH} \propto (P - P^{*})^γ$, where $γ= 0.5$ for massless scalar field and $γ= 1$ for radiation fluid. The reasons for the difference between the values of $γ$ obtained here and those obtained previously are discussed. When the spacetimes have neither CSS nor DSS (Discrete self-similarity), the masses of black holes always turn on with finite non-zero values.

gr-qc↗
arXiv1997

On the sources of static plane symmetric vacuum space-times

The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy conditions, which is consistent with previous studies, while the source for the Rindler solution satisfies the weak and strong energy conditions (but not the dominant one). It is argued that the counterpart of the Einstein theory to the gravitational field of a massive Newtonian plane should be described by the Rindler solution, which represents also a uniform gravitational field.

gr-qc↗
arXiv1997

Geodesics in Lewis Spacetime

The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue.

gr-qc↗
arXiv1996

On parameters of the Levi-Civita solution

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic fluid. The fluid satisfies the energy conditions when the mass parameter $σ$ is in the range $0 \le σ\le 1$. The mass per unit length of the shell is given explicitly in terms of $σ$, which has a finite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out.

gr-qc↗
arXiv1996

On the parameters of Lewis metric for the Weyl class

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cilinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

gr-qc↗
arXiv1996

The Levi-Civita spacetime

We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [1]. For both solutions we studied the junction conditions to the exterior static vacuum Levi-Civita spacetime. From this study we find an upper limit for the energy density per unit length $σ$ of the source equal ${1\over 2}$ for the first case and ${1\over 4}$ for the second one. Thus the homogeneous cluster provides another example [2] where the range of $σ$ is extended beyond the limit value ${1\over 4}$ previously found in the literature [3,4]. Using the Cartan Scalars technics we show that the Levi-Civita spacetime gets an extra symmetry for $σ={1\over 2}$ or ${1\over 4}$. We also find that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density $ρ_0$.

gr-qc↗