arXiv subjects
Publications and source records attributed to M. F. A. da Silva.
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction motion. Our endeavour consists making a thoroughrowly analysis of all the possible geodesics solutions stemming from this spacetime.
We present all possible analytical solutions of the Friedmann-Lemaître-Robertson-Walker metric in Einstein-aether theory for all values of the cosmological constant and spatial curvature with many reasonable values of the equation-of-state parameter. We analyze the dynamics of each model analytically and also graphically by plotting the geometric radius, Hubble and deceleration parameters along with the effective energy conditions. All our results are compared with the corresponding models in General Relativity. The two key results are (i) the aether does not qualitatively change the dynamics of the cosmological models but merely scales the geometric radius, Hubble, and deceleration parameters, and (ii) we found eight models that are entirely void of any aether, meaning in such a universe aether does not play any role cosmologically, although it affects the solar system dynamics.
Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $Ψ(r,t)$ and $H(r,t)$. However, in GR, $Ψ(r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13} \rightarrow 1$ and zero if $c_{13} \rightarrow -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA.
We attempt to answer whether Birkhoff's theorem (BT) is valid in the Einstein-Aether (EA) theory. The BT states that any spherically symmetric solution of the vacuum field equations must be static, unique, and asymptotically flat. For a general spherically symmetric metric with metric functions $A(r,t)$ \& $B(r,t)$, and aether components $a(r,t)$ \& $b(r,t)$, we prove the conditions for the staticity of spacetime using two different methods. We point out that BT is valid in EA theory only for special values of $c_1+c_3$, $c_1+c_4$, and $c_2$, where we can show that all these special cases are asymptotically flat. In particular, when the aether has only a temporal component, i.e., $b(r,t)=0$ and the $c_{14} \neq 0$ case gives us spherically symmetric static black holes without horizons; that is, they have naked singularities, at least for special values of $c_{14}$. Thus, the cosmic censorship conjecture is violated for the case BT holds. However, when we have an aether vector with temporal and radial components, we only prove that the staticity and the flatness at infinity hold for a special metric and particular combination of the aether parameters. For this case, there exist universal horizons instead of naked singularities.
We model a compact radiant star that undergoes gravitational collapse from a certain initial static configuration until it becomes a black hole. The star consists of a fluid with anisotropy in pressures, bulk viscosity, in addition to the radial heat flow. A solution of Einstein's field equations with temporal dependence was presented to study the dynamic evolution of physical quantities, such as the mass-energy function, the luminosity seen by an observer at infinity and the heat flow. We checked the acceptability conditions of the initial static configuration to obtain a range of mass-to-radius ratio in which the presented star model is physically reasonable. The energy conditions were analyzed for the dynamic case, in order to guarantee that the model is composed of a physically acceptable fluid within the range of the mass-to-radius ratio obtained for the static configuration or if they will be modified during the collapse
We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, $c_{2}$, $c_{13}=c_1+c_3$ and $c_{14}=c_1+c_4$, which are: (A) $c_2 \ne 0$ and $c_{13} \ne 0$ and $c_{14}=0$, (B) $c_2 \ne 0$ and $c_{13} = 0$ and $c_{14} = 0$, (C) $c_2 = 0$ and $c_{13} \ne 0$ and $c_{14} = 0$, (D) $c_2 = 0$, $c_{13} = 0$ and $c_{14} \ne 0$, and (E) $c_2 = - c_{13} \ne 0$ and $c_{14} \ne 0$. We present explicit analytical solutions for these five cases. All these cases have singularities at $r=0$ and are asymptotically flat spacetimes and possess both Killing and universal horizons with the universal horizons always being inside the Killing horizons. Finally, we compute the surface gravity, the temperature, the entropy and the first law of thermodynamics for the universal horizons.
In this work we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions in the theory of EA. One of these solutions is the generalization in EA theory of the Levi-Civita (LC) spacetime in General Relativity (GR) theory. We have shown that this generalized LC solution has unusual geodesic properties, depending on the parameter $c_{14}$ of the aether field. The circular geodesics are the same of the GR theory, no matter the values of $c_{14}$. However, the radial and $z$ direction geodesics are allowed only for certain values of $σ$ and $c_{14}$. The $z$ direction geodesics are restricted to an interval of $σ$ different from those predicted by the GR and the radial geodesics show that the motion is confined between the origin and a maximum radius. The latter is not affected by the aether field but the velocity and acceleration of the test particles are Besides, for $0\leqσ<1/2$, when the cylindrical symmetry is preserved, this spacetime is singular at the axis $r=0$, although for $σ>1/2$ exists interval of $c_{14}$ where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis $r=0$ is always singular.
We investigate some models of compact objects in the general relativity theory with cosmological constant $Λ$, based on two density profiles, one of them attributed to Stewart and the other one to Durgapal and Bannerji, proposed in the literature to model "neutron stars". For them, a nonlocal equation of state with cosmological constant is obtained as a consequence of the chosen metric. In another direction, we obtain a solution for configurations with null radial pressure. The first model (based on the Stewart's density profile) turned out to be the most interesting, since surprisingly it admits the presence of dark energy in the interior of the star, in the outermost layers, for a certain range of mass-radius ratio $γ$. This dark energy is independent of the cosmological constant, since it is a consequence of the tangential pressure of the fluid be sufficiently negative. Still in this case, for other values of $γ$, all the energy conditions are satisfied. Another advantage of this model, as well as that based on the density profile of Durgapal and Bannnerji is the existence of intervals of $γ$ compatible with physically acceptable models for $Λ< 0$, $Λ= 0$ and $Λ> 0$, which also allowed us to analyze the influence of $Λ$ on the behavior of the fluid with respect to the energy conditions. The other configuration studied here, $P_r=0$, only allow solutions for $Λ<0$, in order to ensure a positive mass for the object and to satisfy all the energy conditions in a specific range of $γ$.
In the present work we analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether theory with static aether. We show that there are four classes of solutions corresponding to different values of a combination of the free parameters, $c_{14}=c_1+c_4$, which are: $ 0 < c_{14}<2$, $c_{14} < 0$, $c_{14}=2$ and $c_{14}=0$. We present explicit analytical solutions for $c_{14}=3/2, 16/9, 48/25, -16, 2$ and $0$. The first case has some pathological behavior, while the rest have all singularities at $r=0$ and are asymptotically flat spacetimes. For the solutions $c_{14}=16/9, 48/25\, \mathrm{\, and \,}\, -16$ we show that there exist no horizons, neither Killing nor universal horizon, thus we have naked singularities. Finally, the solution for $c_{14}=2$ has a metric component as an arbitrary function of radial coordinate, when it is chosen to be the same as in the Schwarzschild case, we have a physical singularity at finite radius, besides the one at $r=0$. This characteristic is completely different from General Relativity.
We discuss the stability and construct dynamical configurations describing the gravitational collapse of unstable neutron stars with realistic equations of state compatible with the recent LIGO-Virgo constraints. Unlike other works that consider the collapse of a stellar configuration without a priori knowledge if it is stable or unstable, we first perform a complete analysis on stellar stability for such equations of state. Negative values of the squared frequency of the fundamental mode indicate us radial instability with respect to the collapse of the unstable star to a black hole. We find numerical solutions corresponding to the temporal and radial behavior during the evolution of the collapse for certain relevant physical quantities such as mass, luminosity, energy density, pressure, heat flow, temperature and quantities that describe bulk viscous processes. Our results show that the equation of state undergoes abrupt changes close to the moment of event horizon formation as a consequence of dissipative effects. During the collapse process all energy conditions are respected, which implies that our model is physically acceptable.
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general diffeomorphism-invariant action involving a spacetime metric and a vector field. After classifying all the possible nine vacuum solutions with and without cosmological constant in Friedmann-Lema{\^ı}tre-Robertson-Walker (FLRW) cosmology, we show that there exist three singular solutions in the EA theory which are not singular in the General Relativity (GR), all of them for $k=-1$, and another singular solution for $k=1$ in EA theory which does not exist in GR. This result is cross-verified by showing the focusing of timelike geodesics using the Raychaudhuri equation. These new singular solutions show that GR and EA theories can be completely different, even for the FLRW solutions when we go beyond flat geometry ($k=0$). In fact, they have different global structures. In the case where $Λ=0$ ($k=\pm 1$) the vector field defining the preferred direction is the unique source of the curvature.
The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-ρ_0$), and (ii) a fluid with zero energy density ($ρ_0=0$), corresponding to the vacuum solution with and without cosmological constant ($Λ$), respectively. Our solutions show that the EA and GR theories do not differentiate each other only by the coupling constants. This difference is clearly shown because of the existence of singularities that there are not in GR theory. This characteristic appears in the solutions with $p=-ρ_0$ as well as with $ρ_0=0$, where this last one depends only on the aether field. Besides, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on aether field. The solutions admit an expanding or contracting system. A bounce, a singular, a constant and an accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case ($ρ_0=0$), the energy conditions are all satisfied for the aether fluid.
Starting from the stationary cylindrically symmetric solution, but with the coordinates $z$ and $ϕ$ interchanged, and supposing that it could describe the vacuum spacetime of a translating cylinder, we investigate its physical and geometrical properties. This hypothesis is not entirely new since it has already been considered in a previous paper describing a translating source. We show that this metric is geometrically related to the vacuum field produced by a stationary rotating cylindrical source{, known as Lewis solution. However, we find new physical properties, different from those of the Lewis vacuum solution. Moreover, we show that no translating cylindrical dust solution can exist in General Relativity.
Interested in the collapse of a radiating star, we study the temporal evolution of a fluid with heat flux and bulk viscosity, including anisotropic pressure. As a starting point, we adopt an initial configuration that satisfies the regularities conditions as well as the energy conditions to a certain range of the mass-radius ratio for the star, defining acceptable models. For this set of models, we verify that the energy conditions remain satisfied until the black hole formation. Astrophysical relevant quantities, such as the luminosity perceived by an observer at infinity, the time of event horizon formation and the loss of mass during the collapse are presented.
This paper presents a hydrodynamic and thermodynamic treatment of a radiant star model that undergoes a dissipative gravitational collapse, from a certain initial configuration until it becomes a black hole. The collapsing star consists of a locally anisotropic non-perfect fluid, where we explore the consequences of including viscous pressures, both shear and bulk viscosities, as well as radial heat flow. We analyze the temporal evolution of the heat flux, mass function, luminosity perceived by an observer at infinity and the effective surface temperature. It is shown that this simple exact model, satisfying all the energy conditions throughout the interior region of the star and during all the collapse process, provides a physically reasonable behavior for the temperature profile in the context of the extended irreversible thermodynamics.
Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Hořava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null.
We investigate a class of cylindrically symmetric inhomogeneous $Λ$-dust spacetimes which have a regular axis and some zero expansion component. For $Λ\ne 0$, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For $Λ=0$, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.
In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of the Hořava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the post-newtonian approximation (PPN) in the infrared limit. The Newtonian prepotential $φ$ was assumed null. The aim of this work is to know if we can have the same spacetime, as we know in the General Relativity Theory (GRT), in Hořava-Lifshitz Theory (HLT) in this limit. We have shown that there is not an analogy of the dust solution in HLT with the minimally coupling, as in GRT. Using non-minimum coupling with matter, we have shown that the solution admits a process of gravitational collapse, leaving a singularity at the end. This solution has, qualitatively, the same temporal behaviour as the dust collapse in GRT. However, we have also found a second possible solution, representing a bounce behavior that is not found in GRT.