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Register a new userAnisotropic compact stars: Constraining model parameters to account for physical features of tidal Love numbers
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In this paper, we develop a new class of models for a compact star with anisotropic stresses inside the matter distribution. By assuming a linear equation of state for the anisotropic matter composition of the star we solve the Einstein field equations. In our approach, for the interior solutions we use a particular form of the ansatz for the metric function $g_{rr}$. The exterior solution is assumed as Schwarzschild metric and is joined with the interior metric obtained across the boundary of the star. These matching of the metrices along with the condition of the vanishing radial pressure at the boundary lead us to determine the model parameters. The physical acceptability of the solutions has verified by making use of the current estimated data available from the pulsar 4U1608-52. Thereafter, assuming anisotropy due to tidal effects we calculate the Love numbers from our model and compare the results with the observed compact stars, viz. KS 1731- 260,4U 1608- 52,4U 1724- 207,4U 1820- 30,SAX J1748.9-2021 and EXO 1745-268. The overall situation confirms physical viability of the proposed approach,which can shed new light on the interior of the compact relativistic objects.
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We investigate the properties of relativistic stars made of dark energy. We model stellar structure assuming i) isotropic perfect fluid and ii) a dark energy inspired equation of state, the generalized equation of state of Chaplygin gas, as we will be calling it. The mass-to-radius profiles, the tidal Love numbers as well as the ten lowest radial oscillation modes are computed. Causality, stability and energy conditions are also discussed.
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
For a variety of fully relativistic polytropic neutron star models we calculate the stars tidal Love number k2. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n~0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l=2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second order differential equation for the perturbation to the metric coefficient g_tt, and matching the exterior solution to the asymptotic expansion of the metric in the stars local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to ~24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.
The tidal Love numbers (TLNs) encode the deformability of a self-gravitating object immersed in a tidal environment and depend significantly both on the objects internal structure and on the dynamics of the gravitational field. An intriguing result in classical general relativity is the vanishing of the TLNs of black holes. We extend this result in three ways, aiming at testing the nature of compact objects: (i) we compute the TLNs of exotic compact objects, including different families of boson stars, gravastars, wormholes, and other toy models for quantum corrections at the horizon scale. In the black-hole limit, we find a universal logarithmic dependence of the TLNs on the location of the surface; (ii) we compute the TLNs of black holes beyond vacuum general relativity, including Einstein-Maxwell, Brans-Dicke and Chern-Simons gravity; (iii) We assess the ability of present and future gravitational-wave detectors to measure the TLNs of these objects, including the first analysis of TLNs with LISA. Both LIGO, ET and LISA can impose interesting constraints on boson stars, while LISA is able to probe even extremely compact objects. We argue that the TLNs provide a smoking gun of new physics at the horizon scale, and that future gravitational-wave measurements of the TLNs in a binary inspiral provide a novel way to test black holes and general relativity in the strong-field regime.
Ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, low frequency portion of the signal of detected neutron star - neutron star inspirals. In this early adiabatic regime, the influence of a neutron stars internal structure on the phase of the waveform depends only on a single parameter lambda of the star related to its tidal Love number, namely the ratio of the induced quadrupole moment to the perturbing tidal gravitational field. We analyze the information obtainable from gravitational wave frequencies smaller than a cutoff frequency of 400 Hz, where corrections to the internal-structure signal are less than 10 percent. For an inspiral of two non-spinning 1.4 solar mass neutron stars at a distance of 50 Mpc, LIGO II detectors will be able to constrain lambda to lambda < 2.0 10^{37} g cm^2 s^2 with 90% confidence. Fully relativistic stellar models show that the corresponding constraint on radius R for 1.4 solar mass neutron stars would be R < 13.6 km (15.3 km) for a n=0.5 (n=1.0) polytrope.
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