Massive, highly magnetized white dwarfs with fields up to 10 9 G have been observed and theoretically used for the description of a variety of astrophysical phenomena. Ultramagnetized white dwarfs with uniform interior fields up to 10 18 G, have been recently purported to obey a new maximum mass limit, M max ≈ 2.58 M ⊙ , which largely overcomes the traditional Chandrasekhar value, M Ch ≈ 1.44 M ⊙ . Such a much larger limit would make these astrophysical objects viable candidates for the explanation of the superluminous population of type Ia supernovae. We show that several macro and micro physical aspects such as gravitational, dynamical stability, breaking of spherical symmetry, general relativity, inverse β-decay, and pycnonuclear fusion reactions are of most relevance for the self-consistent description of the structure and assessment of stability of these objects. It is shown in this work that the first family of magnetized white dwarfs indeed satisfy all the criteria of stability, while the ultramagnetized white dwarfs are very unlikely to exist in nature since they violate minimal requests of stability. Therefore, the canonical Chandrasekhar mass limit of white dwarfs has to be still applied.

Context. Soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are slow rotating isolated pulsars whose energy reservoir is still matter of debate. Adopting neutron star (NS) fiducial parameters; mass M = 1.4M , radius R = 10 km, and moment of inertia, I = 10 45 g cm 2 , the rotational energy loss,Ė rot , is lower than the observed luminosity (dominated by the X-rays) L X for many of the sources. Aims. We investigate the possibility that some members of this family could be canonical rotation-powered pulsars using realistic NS structure parameters instead of fiducial values. Methods. We compute the NS mass, radius, moment of inertia and angular momentum from numerical integration of the axisymmetric general relativistic equations of equilibrium. We then compute the entire range of allowed values of the rotational energy loss,Ė rot , for the observed values of rotation period P and spin-down rateṖ. We also estimate the surface magnetic field using a general relativistic model of a rotating magnetic dipole. Results. We show that realistic NS parameters lowers the estimated value of the magnetic field and radiation efficiency, L X /Ė rot , with respect to estimates based on fiducial NS parameters. We show that nine SGRs/AXPs can be described as canonical pulsars driven by the NS rotational energy, for L X computed in the soft (2-10 keV) X-ray band. We compute the range of NS masses for which L X /Ė rot < 1. We discuss the observed hard X-ray emission in three sources of the group of nine potentially rotation-powered NSs. This additional hard X-ray component dominates over the soft one leading to L X /Ė rot > 1 in two of them. Conclusions. We show that 9 SGRs/AXPs can be rotation-powered NSs if we analyze their X-ray luminosity in the soft 2-10 keV band. Interestingly, four of them show radio emission and six have been associated with supernova remnants (including Swift J1834.9-0846 the first SGR observed with a surrounding wind nebula). These observations give additional support to our results of a natural explanation of these sources in terms of ordinary pulsars. Including the hard X-ray emission observed in three sources of the group of potential rotation-powered NSs, this number of sources with L X /Ė rot < 1 becomes seven. It remains open to verification 1) the accuracy of the estimated distances and 2) the possible contribution of the associated supernova remnants to the hard X-ray emission.

There is solid observational evidence on the existence of massive, M ∼ 1 M , highly magnetized white dwarfs (WDs) with surface magnetic fields up to B ∼ 10 9 G. We show that, if in addition to these features, the star is fast rotating, it can become a rotation-powered pulsar-like WD and emit detectable high-energy radiation. We infer the values of the structure parameters (mass, radius, moment of inertia), magnetic field, rotation period and spin-down rates of a WD pulsar death-line. We show that WDs above the death-line emit blackbody radiation in the soft X-ray band via the magnetic polar cap heating by back flowing pair-created particle bombardment and discuss as an example the X-ray emission of soft gamma-repeaters and anomalous X-ray pulsars within the WD model.

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We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor, which is zero for FRW model. We study some consequences of this Weyl tensor in the GDE.

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