Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.

Gravitational Wave Glitches in Chaotic Extreme-Mass-Ratio Inspirals

The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a nonintegrable compact object display "glitch" phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity but also of fundamental spacetime symmetries.

Fast Rotating Relativistic Stars: Spectra and Stability without Approximation

We study oscillations and instabilities of relativistic stars using perturbation theory in general relativity and take into account the contribution of a dynamic spacetime. We present the oscillation spectrum as well as the critical values for the onset of the secular CFS instability of neutron stars, and propose universal relations for gravitational wave asteroseismology, which may help constrain the neutron star radius and/or the nuclear equation of state. The results are relevant for all stages during a neutron star's life but especially to nascent or remnant objects following a binary merger.

Spectral Lines of Quantized, Spinning Black Holes and their Astrophysical Relevance

In this Letter, we study black hole area quantization in the context of gravitational wave physics. It was recently argued that black hole area quantization could be a mechanism to produce so-called echoes as well as characteristic absorption lines in gravitational wave observations of merging black holes. One can match the spontaneous decay of these quantum black holes to Hawking radiation calculations. Using some assumptions, one can then estimate the natural widths of these states. As can be seen from a classical paper by Bekenstein and Mukhanov, the ratio between width and spacing of nonspinning black hole states approaches a small constant, which seems to confirm the claim. However, we find that, including the effect of black hole spin, the natural widths increase. To properly address any claim about astrophysical black holes, one should examine the spinning case, as real black holes spin. Thus, the word "spinning" is key to the question of whether or not black holes should have an observable spectrum in nature. Our results suggest that it should be possible to distinguish between any scenarios for which the answer to this question is yes. However, for all of the commonly discussed scenarios, our answer is "almost certainly no."

Tidal Love numbers of neutron stars in f(R) gravity

The recent detection of gravitational waves from a neutron star merger was a significant step towards constraining the nuclear matter equation of state by using the tidal Love numbers (TLNs) of the merging neutron stars. Measuring or constraining the neutron star TLNs allows us in principle to exclude or constraint many equations of state. This approach, however, has the drawback that many modified theories of gravity could produce deviations from General Relativity similar to the deviations coming from the uncertainties in the equation of state. The first and the most natural step in resolving the mentioned problem is to quantify the effects on the TLNs from the modifications of General Relativity. With this motivation in mind, in the present paper we calculate the TLNs of (non-rotating) neutron stars in R 2 -gravity. More precisely, by solving numerically the perturbation equations, we calculate explicitly the polar and the axial l = 2 TLNs for three characteristic realistic equations of state and compare the results to General Relativity. Our results show that while the polar TLNs are slightly influenced by the R 2 modification of General Relativity, the axial TLNs can be several times larger (in terms of the absolute value) compared to the general relativistic case.

f-Mode instability in relativistic neutron stars

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ℓ=m=4 mode) of the order of 10(3)-10(4)  s near the Kepler frequency Ω(K) while the instability is active above ∼0.92  Ω(K) and for temperatures ∼(10(9)-2×10(10))  K, characteristic of newborn neutron stars.

r-Mode Runaway and Rapidly Rotating Neutron Stars

We present a simple spin-evolution model that predicts that rapidly rotating accreting neutron stars will be confined mainly to a narrow range of spin frequencies: P=1.5-5 ms. This is in agreement with current observations of neutron stars in both the low-mass X-ray binaries and the millisecond radio pulsars. The main ingredients in the model are (1) the instability of r-modes above a critical spin rate, (2) the thermal runaway that is due to the heat released as viscous damping mechanisms counteract the r-mode growth, and (3) a revised estimate of the strength of the dissipation that is due to the presence of a viscous boundary layer at the base of the crust in an old and relatively cold neutron star. We discuss the gravitational waves that are radiated during the brief r-mode-driven spin-down phase. We also briefly touch on how the new estimates affect the predicted initial spin periods of hot young neutron stars.

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.