Modifcations to gravitational waves due to matter shells

As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies.

Black shells and naked shells

In this paper, we study the collapse of a thin dust shell from the point of view of the horizon dynamics. We identify the critical surfaces at which time and space coordinates interchange their roles and investigate their properties by using the formalism of trapped surfaces. We show the existence of marginally outer trapped surfaces that are associated with the presence of quasi-local horizons. A particular shell configuration that avoids the formation of horizons is interpreted as naked shell.

Quantum radiation of a collapsing shell in three-dimensional AdS spacetime revisited

In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and the radiation temperature is in agreement with the Hawking temperature, irrespective of the specific choice of the interior geometries.

Non-stoichiometric amorphous magnesium-iron silicates in circumstellar dust shells

Aims. We study the growth of dust in oxygen-rich stellar outflows in order to find out to which extent dust growth models can quantitatively reconcile with the quantities and nature of dust as derived from observations of the infrared emission from circumstellar dust shells. Methods. We use a set of nine well-observed massive supergiants with optically thin dust shells as testbeds because of the relatively simple properties of the outflows from massive supergiants, contrary to the case of AGB stars. Models of the infrared emission from their circumstellar dust shells are compared to their observed infrared spectra to derive the essential parameters that rule dust formation in the extended envelope of these stars. The results are compared with a model for silicate dust condensation. Results. For all objects, the infrared emission in the studied wavelength range, between 6 and 25 μm, can be reproduced rather well by a mixture of non-stoichiometric iron-bearing silicates, alumina, and metallic iron dust particles. For three objects (μ Cep, RW Cyg, and RS Per), the observed spectra can be sufficiently well reproduced by a stationary and (essentially) spherically symmetric outflow in the instantaneous condensation approximation. For these objects, the temperature at the onset of massive silicate dust growth is of the order of 920 K and the corresponding outflow velocity of the order of the sound velocity. This condensation temperature is only somewhat below the vapourisation temperature of the silicate dust and suggests that the silicate dust grows on the corundum dust grains that formed well inside of the silicate dust shell at a much higher temperature. The low expansion velocity at the inner edge of the silicate dust shell further suggests that, for these supergiants, the region inside the silicate dust shell has an only subsonic average expansion velocity, though a high degree of supersonic turbulence is indicated by the widths of spectral lines. Conclusions. Our results suggest that for the two major problems of dust formation in stellar outflows, that is (i) formation of seed nuclei and (ii) their growth to macroscopic dust grains, we are gradually coming close to a quantitative understanding of the second item.

Dynamical transition from a naked singularity to a black hole

We show that a Reissner–Nordström (RN) black hole can be formed by dropping a charged thin dust shell onto a RN naked singularity. This is in contrast to the fact that a RN naked singularity is prohibited from forming by dropping a charged thin dust shell onto a RN black hole. This implies the strong tendency of the RN singularity to be covered by a horizon in favor of cosmic censorship. We show that an extreme RN black hole can also be formed from a RN naked singularity by the same process in a finite advanced time. We also discuss the evolution of the charged thin dust shells and the causal structure of the resultant space–times. a a The statements expressed in this paper are those of the authors and do not represent the views of Sumitomo Mitsui Banking Corporation or its staff.

Conceptual Model for Cutoff Origin in Exotic Compact Objects

We propose a conceptual model for the closeness parameter $\epsilon$, which characterizes exotic compact objects (ECOs). To estimate $\epsilon$, a thin spherical dust shell is considered, which gravitationally contracts from a specific position $r(t_{0})$ to near its gravitational radius $r(t_{2})=r_{s} + \epsilon$, in a finite time $t_{2}$, measured in the frame of a fiducial observer (FIDO). For an external observer, the shell’s kinematics is characterized by two clearly distinguishable phases: one of rapid contraction, where the shell is far away from the gravitational radius, $r(t_{0})\gg r_{s}$, and a second phase quasi-stationary, $r(t)\sim r_{s}$, where all of the shell’s mass is concentrated around the associated horizon, such that for a FIDO, a black hole (BH)is undistinguishable from a shell configured as a black shell (BS). \\ In the semi-classical approximation $E\ll \kappa_{0}l_{p}^{2}$ and tends to zero when the observation time of collapse $t_{2}$, measured by FIDO, tends to infinity; $\kappa_{0}$ and $l_{p}$ are surface gravity and Planck length, respectively. The quantum effects are significant when $\epsilon\ll r(t_{2})$ and $\epsilon$ tends to $\kappa_{0}l_{p}^{2}$. \\ Without knowing details on quantum gravity, parameter $\epsilon$ is calculated, which, in general, allows distinguishing the ECOs from BHs. Specifically, a BS (ECO) is undistinguishable from a BH.

Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

We perform Hamiltonian reduction of a model in which 2 + 1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of ADS2—both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of ADS2 momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

Collapsing Wormholes Sustained by Dustlike Matter

It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is “exotic”—i.e., violates a number of energy conditions. For this reason, it is impossible to construct static wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman’s solution describes the collapsing dust ball; the inner space-time structure of the ball corresponds to the Friedmann universe filled by a dust. In the present work we use the general Tolman’s solution in order to construct a dynamic spherically symmetric wormhole solution in GR with dust-like matter. The solution constructed represents the collapsing dust ball with the inner wormhole space-time structure. It is worth noting that, with the dust-like matter, the ball is made of satisfies the usual energy conditions and cannot prevent the collapse. We discuss in detail the properties of the collapsing dust wormhole.