We apply the Darmois and the $C^3$ matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect flui
d solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all three cases whereas the $C^3$ conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.
In this work, a new approach is presented with the aim of showing a simple way of unifying the classical formulas for the forces of the Coulombs law of electrostatic interaction ($F_C$) and the Newtons law of universal gravitation $(F_G)$. In this ap
proach, these two forces are of the same nature and are ascribed to the interaction between two membranes that oscillate according to different curvature functions with the same spatial period $xipi/k$ where $xi$ is a dimensionless parameter and $k$ a wave number. Both curvature functions are solutions of the classical wave equation with wavelength given by the de Broglie relation. This new formula still keeps itself as the inverse square law, and it is like $F_C$ when the dimensionless parameter $xi =274$ and like $F_G$ when $xi = 1.14198$x$10^{45}$. It was found that the values of the parameter $xi$ quantize the formula from which $F_C$ and $F_G$ are obtained as particular cases.
We present an analysis of DES17X1boj and DES16E2bjy, two peculiar transients discovered by the Dark Energy Survey (DES). They exhibit nearly identical double-peaked light curves which reach very different maximum luminosities (M$_mathrm{r}$ = -15.4 a
nd M$_mathrm{r}$ = -17.9, respectively). The light curve evolution of these events is highly atypical and has not been reported before. The transients are found in different host environments: DES17X1boj was found near the nucleus of a spiral galaxy, while DES16E2bjy is located in the outskirts of a passive red galaxy. Early photometric data is well fitted with a blackbody and the resulting moderate photospheric expansion velocities (1800 km/s for DES17X1boj and 4800 km/s for DES16E2bjy) suggest an explosive or eruptive origin. Additionally, a feature identified as high-velocity CaII absorption (v $approx$ 9400km/s) in the near-peak spectrum of DES17X1boj may imply that it is a supernova. While similar light curve evolution suggests a similar physical origin for these two transients, we are not able to identify or characterise the progenitors.
In the Introduction we briefly recall our previous results on stationary electromagnetic fields on black-hole backgrounds and the use of spin-weighted spherical harmonics. We then discuss static electric and magnetic test fields in a Schwarzschild ba
ckground using some of these results. As sources we do not consider point charges or current loops like in previous works, rather, we analyze spherical shells with smooth electric or magnetic charge distributions as well as electric or magnetic dipole distributions depending on both angular coordinates. Particular attention is paid to the discontinuities of the field, of the 4-potential, and their relation to the source.
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in
terms of oblate spheroidal coordinates. Furthermore, the solutions are asymptotically flat and regular everywhere, as it is shown by computing all the curvature scalars. These solutions describe an infinite family of thin dust disks with a central inner edge, whose energy densities are everywhere positive and well behaved, in such a way that their energy-momentum tensor are in fully agreement with all the energy conditions. Now, although the disks are of infinite extension, all of them have finite mass. The superposition of the first member of this family with a Schwarzschild black hole was presented previously [G. A. Gonzalez and A. C. Gutierrez-Pi~neres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent paper a detailed analysis of the corresponding superposition for the full family will be presented.
The first fully integrated explicit exact solution of the Einstein field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite annular thin dis
k (a disk with an inner edge) around the Schwarszchild black hole. The mass of the disk is finite and the energy-momentum tensor agrees with all the energy conditions. Furthermore, the total mass of the disk when the black hole is present is less than the total mass of the disk alone. The solution can also be interpreted as describing a thin disk made of two counterrotanting dust fluids that are also in agreement with all the energy conditions. Additionally, as we will show shortly in a subsequent paper, the above solution is the first one of an infinite family of solutions.
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having f flips.
There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.
