Narrow Results

In this work, the analysis of the behavior of an interior solution in the frame of Einstein’s general theory of relativity is reported. Given the possibility that, for greater densities than the nuclear density, the matter presents anisotropies in the pressures and that these are the orders of density present in the interior of the compact stars, the solution that is discussed considers that the interior region contains an anisotropic fluid, i.e. $P_r\ne P_t$. The compactness value, where $u=\frac{GM}{c^{2}R}$, for which the solution is physically acceptable is $u\le 0.23577$ as such the graphic analysis of the model is developed for the case in which the mass $M=(0.85\pm 0.15)M_{\odot }$ and the radius $R=8.1\pm 0.41\mathrm{\text{km}}$ which corresponds to the star Her X-1, with maximum compactness $u_{max}=0.1919$, although for other values of compactness $u\le 0.23577$ the behavior is similar. The functions of density and pressures are positive, finite and monotonically decreasing, also the solution is stable according to the cracking criteria and the range of values is consistent with what is expected for these type of stars.

An anisotropic fluid with variable energy density and negative pressure is proposed, both outside and inside stars. The gravitational field is constant everywhere in free space (if we neglect the local contributions) and its value is of the order of g = 10 ^-8cm/s², in accordance with MOND model. With ρ, p ∝ 1/r, the acceleration is also constant inside stars but the value is different from one star to another and depends on their mass M and radius R. In spite of the fact that the spacetime is of Rindler type and curved even far from a local mass, the active gravitational energy on the horizon is -1/4g, as for the flat Rindler space, excepting the negative sign.

Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks. Although initial results indicated this scenario as being unphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such an unphysical situation may not always be necessarily true. In this paper, we present solutions of the Einstein equations using the original Alcubierre warp drive metric endowed with various matter-energy sources, namely dust, perfect fluid, anisotropic fluid, and perfect fluid within a cosmological constant spacetime. A connection of some of these solutions featuring shock waves described by the Burgers equation is also shown.

A certain type of matter with anisotropic pressures can add to the Reissner-Nordström metric a term proportional to a power of the radial coordinate. Using the standard method of separating variables for the Hamilton-Jacobi equation, we study the shadow of the corresponding rotating solution, obtained through the Newman-Janis algorithm. We define and calculate three observables in order to characterize the position, size and shape of the shadow.