In this paper we study the propagation in a de Sitter universe of gravitational waves generated by perturbating some unspecified spherical astrophysical object in the frequencies domain. We obtain the axial and polar perturbation equations in a cosmological de Sitter universe in the usual comoving coordinates, the coordinates we occupy in our galaxy. We write down the relevant equations in terms of Laplace transform with respect to the comoving time $t$ instead of the usual Fourier one that is no longer available in a cosmological context. Both axial and polar perturbation equations are expressed in terms of a non trivial mixture of retarded-advanced metric coefficients with respect to the Laplace parameter $s$ (complex translation). The axial case is studied in more detail. In particular, the axial perturbations can be reduced to a master linear second-order differential equation in terms of the Regge-Wheeler function $Z$ where a coupling with a retarded $Z$ with respect to the cosmological time $t$ is present. It is shown that a de Sitter expanding universe can change the frequency $ω$ of a gravitational wave as perceived by a comoving observer. The polar equations are much more involved. Nevertheless, we show that also the polar perturbations can be expressed in terms of four independent integrable differential equations.
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
Three exact solutions say $ϕ_0$ of massless scalar theories on Euclidean space, i.e. $D=6 ϕ^3$, $D=4 ϕ^4$ and $D=3 ϕ^6$ models are obtained which share similar properties. The information geometry of their moduli spaces coincide with the Euclidean ${AdS}_7$, ${AdS}_5$ and ${AdS}_4$ respectively on which $ϕ_0$ can be described as a stable tachyon. In D=4 we recognize that the SU(2) instanton density is proportional to $ϕ_0^4$. The original action $S[ϕ]$ written in terms of new scalars ${\tilde ϕ}=ϕ-ϕ_0$ is shown to be equivalent to an interacting scalar theory on $D$-dimensional de Sitter backg…
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $Λ$. These solutions approach asymptotically the anti-de Sitter spacetime and possess a regular event horizon. A discussion of the main properties of the solutions and the differences with respect to the asymptotically flat case is presented. The mass of these configurations is computed by using a counterterm method. We note that the $Λ=-3$ configurations have an higher dimensional interpretation in context of $d=11$ supergravity. The existen…
The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on uncharged and non-rotating black holes, we extend the results to spacetimes including a cosmological constant, which have so far mostly been investigated numerically from this perspective.
In this work we have constructed axially symmetric vacuum solutions of the gravitational field equations in a Randall-Sundrum brane. A non-null effective cosmological constant is considered, and asymptotically de Sitter and anti-de Sitter spacetimes are obtained. The solutions describe rotating black holes in a four-dimensional brane. Optical features of the solutions are treated, emphasizing the rotation of the polarization vector along null congruences.
We investigate vortex solutions to the Abelian Higgs field equations in a four dimensional de Sitter spacetime background. We obtain both static and dynamic solutions with axial symmetry that are generalizations of the Nielsen-Olesen gauge vortices in flat spacetime. The static solution is located in the static patch of de Sitter space. We numerically solve the field equations in an inflationary (big bang) patch and find a time dependent vortex soution, whose effect to create a deficit angle in the spacetime. We show that this solution can be interpreted in terms of a renormalization group flo…
We discuss solution generating techniques treating stationary and axially symmetric metrics in the presence of a cosmological constant. Using the recently found extended form of Ernst's complex equation, which takes into account the cosmological constant term, we propose an extension of spheroidal coordinates adapted to asymptotically de-Sitter and anti de-Sitter static spacetimes. In the absence of a cosmological constant we show in addition that any higher dimensional metric parametrised by a single angular momentum can be given by a 4 dimensional solution and Weyl potentials parametrising t…
We study gravitational perturbations of electrically charged black holes in (3+1)-dimensional Einstein-Born-Infeld gravity with a positive cosmological constant. For the axial perturbations, we obtain a set of decoupled Schrodinger-type equations, whose formal expressions, in terms of metric functions, are the same as those without cosmological constant, corresponding to the Regge-Wheeler equation in the proper limit. We compute the quasi-normal modes (QNMs) of the decoupled perturbations using the Schutz-Iyer-Will's WKB method. We discuss the stability of the charged black holes by investigat…
Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity and non-stationarity of these two different forms are traced back to the noncomoving and comoving nature of the corresponding coordinate systems. In this paper using the quasi-Maxwell form of the Einstein field equations and a definition of static spacetimes based upon them, we look at these two different forms of the same solution from a new perspective whi…
We present a comprehensive study of the massless scalar field perturbation in the Reissner-Nordstrom anti-de Sitter (RNAdS) spacetime and compute its quasinormal modes (QNM). For the lowest lying mode, we confirm and extend the dependence of the QNM frequencies on the black hole charge got in previous works. In near extreme limit, under the scalar perturbation we find that the imaginary part of the frequency tends to zero, which is consistent with the previous conjecture based on electromagnetic and axial gravitational perturbations. For the extreme value of the charge, the asymptotic field de…
We study scalar, electromagnetic and gravitational perturbations of a Reissner-Nordström-anti-de Sitter (RN-AdS) spacetime, and compute its quasinormal modes (QNM's). We confirm and extend results previously found for Schwarzschild-anti-de Sitter (S-AdS) black holes. For ``large'' black holes, whose horizon is much larger than the AdS radius, different classes of perturbations are almost exactly {\it isospectral}; this isospectrality is broken when the black hole's horizon radius is comparable to the AdS radius. We provide very accurate fitting formulas for the QNM's, which are valid for black…
In this paper we continue the investigation concerning the propagation of gravitational waves in a cosmological background using Laplace transform \cite{A}. We analyze the possible physical consequences of the result present in \cite{A} where it is argued that a non-vanishing positive abscissa of convergence caused by the de Sitter expansion factor $a(t)=e^{Ht}$ implies a shift in the frequencies domain of a traveling gravitational waves as measured by a comoving observer. In particular, we show that in a generic asymptotically de Sitter cosmological universe this redshift effect does also ari…
Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravitational sector, where spherical symmetry is necessarily broken. In \cite{Bizon:2011gg} the onset of such nonlinear instability was associated with the existence of irremovable secular resonances at third order in perturbation theory. Furthermore, it was also conjectured in \cite{Bizon:2011gg} that certain very fine tuned initial data would not collapse. Such solutions, upon linearisation, correspond…
We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincare or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltr…
The recent reported gravitational wave detection motivates one to investigate the properties of different black hole models, especially their behavior under (axial) gravitational perturbation. Here, we study the quasinormal modes of black holes in Weyl gravity. We derive the master equation describing the quasinormal radiation by using a relation between the Schwarzschild-anti de Sitter black holes and Weyl solutions, and also the conformal invariance property of the Weyl action. It will be observed that the quasinormal mode spectra of the Weyl solutions deviate from those of the Schwarzschild…
We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtaine…
