Thermodynamics of scalar-tensor theory with non-minimally derivative coupling

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we show that the unified first law on the apparent horizon is equivalent to the Friedmann equation for the scalar--tensor theory with non-minimally derivative coupling. The second law of thermodynamics on the apparent horizon is also satisfied. The results support a deep and fundamental connection between gravitation, thermodynamics, and quantum theory.Comment: 12 pages, no figure, minor correction

Static spherical vacuum solutions in the bumblebee gravity model

The bumblebee gravity model is a vector-tensor theory of gravitation where the vector field nonminimally couples to the Ricci tensor. By investigating the vacuum field equations with spherical symmetry, we find two families of black-hole (BH) solutions in this model: one has a vanishing radial component of the vector field and the other has a vanishing radial component of the Ricci tensor. When the coupling between the vector field and the Ricci tensor is set to zero, the first family becomes the Reissner-Nordstr\"om solution while the second family degenerates to the Schwarzschild solution with the vector field being zero. General numerical solutions in both families are obtained for nonzero coupling between the vector field and the Ricci tensor. Besides BH solutions, we also reveal the existence of solutions that have a nonvanishing $tt$-component of the metric on the supposed event horizon where the $rr$-component of the metric diverges while the curvature scalars are finite. These solutions are not supported by existing observations but present certain properties that are of academic interests. We conclude the study by putting the BH solutions into tests against the Solar-system observations and the images of supermassive BHs.Comment: 19 pages, 10 figure

Importance of including higher signal harmonics in the modeling of extreme mass-ratio inspirals

Extreme mass-ratio inspirals (EMRIs) are the most potential sources detectable by the Laser Interferometer Space Antenna (LISA). To analyze the influence of higher harmonics on parameter estimation for EMRIs efficiently, we use the waveform model that the phase trajectories are relativistic flux-based adiabatic trajectories and the waveforms are constructed by the augmented analytic kludge method. We perform a Fisher-matrix error analysis of the EMRI parameters using signals taking into account the motion of the LISA constellation and higher harmonics of gravitational waves. Our results demonstrate that including higher harmonics greatly reduces the errors on the exterior parameters such as inclination angle $\iota$, the luminosity distance $d_L$, the polarization angle $\psi$, and the initial phase $\Phi_0$, except for source localization $\Delta \Omega$ when EMRIs face us. However, the influence of higher harmonics on parameters $(\iota,d_L,\psi,\Phi_0)$ can be negligible when the inclination angle is above $1.0$. For intrinsic parameters such as the spin of central black and the masses of binaries, the influence of higher harmonics can be negligible for any inclination angle. Our findings are independent of the mass or spin of the EMRI system.Comment: 23 pages, 6 figures; PRD accepte

Frequency response of space-based interferometric gravitational-wave detectors

Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $\ln(f)/f^2$.Comment: V3: minor corrections. PRD in pres

Gravitational waves from eccentric extreme mass-ratio inspirals as probes of scalar fields

We study eccentric orbits of the Schwarzschild spacetime for extreme mass ratio system (EMRI) in modified gravity theories with additional scalar fields. Due to the additional energy and angular momentum carried away by the scalar field, the orbit of the EMRI in modified gravity decays faster than that in general relativity. The time that it takes the eccentricity $e$ to reach the minimum is smaller and the values of the semi-latus rectum $p$ and $e$ at the turning point when $e$ reaches the minimum are bigger for larger scalar charge $d$. In addition to the calculation of energy fluxes with numerical method, we also use the Post-Newtonian expansion of the rate of energy carried away by the scalar field in eccentric orbits to understand the behaviors of the energy emission. By adding the scalar flux to the open code FastEMRIWaveforms of the Black Hole Perturbation Toolkit, we numerically generate fast gravitational waveforms for eccentric EMRIs with scalar fields and use the faithfulness between waveforms with and without the scalar charge to discuss the detection of scalar charge $d$. The detection error of the scalar charge is also estimated with method of Fisher information matrix.Comment: 26 pages, 13 figures, 1 table; accepted for publication by JCA

Extended thermodynamics of the bumblebee black holes

As a vector-tensor theory including nonminimal coupling between the Ricci tensor and a vector field, the bumblebee gravity is a potential theory to test Lorentz symmetry violation. Recently, a new class of numerical spherical black holes in the bumblebee theory was constructed. In this paper, we investigate the associated local thermodynamic properties. By introducing a pair of conjugated thermodynamic quantities $X$ and $Y$, which can be interpreted as an extension of electric potential and charge of the Reissner Nordstr\"om black holes, we numerically construct a new first law of thermodynamics for bumblebee black holes. We then study the constant-$Y$ processes in the entropy-charge parameter space. For the constant-$Y$ processes, we also calculate the heat capacity to study the local thermodynamic stability of the bumblebee black holes. For a negative nonminimal coupling coefficient $\xi$, we find both divergent and smooth phase transitions. For a positive but small $\xi$, only a divergent phase transition is found. It turns out that there is a critical value $0.4\kappa <\xi_c < 0.5\kappa$ such that when $\xi_c < \xi<2\kappa$, even the divergent phase transition disappears and the bumblebee black holes thus become locally thermodynamically unstable regardless of the bumblebee charge. As for $\xi>2\kappa$, the smooth phase transition arises again but there no longer exists any discontinuous phase transition for the bumblebee black holes.Comment: 10 pages, 3 figures; accepted for publication in PR