Search

We present various post-Newtonian (PN) models for the phase evolution of compact objects moving along quasi-spherical orbits in Kerr spacetime derived by using the 12PN analytic formulas of the energy, angular momentum and their averaged rates of change calculated in the framework of the black hole perturbation theory. To examine the convergence of time-domain PN models (TaylorT families), we evaluate the dephasing between approximants with different PN orders. We found that the TaylorT1 model shows the best performance and the performance of the TaylorT2 is the next best. To evaluate the convergence of frequency-domain PN models (TaylorF families), we evaluate the mismatch between approximants with different orders. We found that the performance of the TaylorF2 model is comparable with the TaylorT2 model. Although the TaylorT2 and TaylorF2 models are not so accurate as the TaylorT1, the fully analytical expressions give us easy-to-handle templates and are useful to discuss effects beyond general relativity., Comment: 27 pages, 14 figures. v2: Problem with not showing the figures resolved

Gravitational wave echo signals have been proposed as evidence for the modification of the spacetime structure near the classical event horizon. These signals are expected to occur after the mergers of compact binaries as a sequence of weak pulse-like signals. Some studies have shown evidence of the echo signals from several binary black hole merger events. On the other hand, the other studies have shown the low significance of such signals from various events in the first, second and third observing runs (O1, O2 and O3). Our previous study also shows the low significance of echo signals from events in O1 and O2, though, we observe that more than half of the events have p-value smaller than 0.1 when the simply modeled waveform is used for the analysis. Since there are only nine events appropriate for this analysis in O1 and O2, it is necessary to analyze more events to evaluate the significance statistically. In this study, we search for echo signals from binary black hole events observed during O3 operated by LIGO, Virgo and KAGRA collaborations. We perform the template-based search by using two different models for echo signal templates: simply modeled one and physically motivated one. Our results show that the distributions of p-values for all events analyzed in this study are consistent with the noise distribution. This means that no significant echo signals are found for both models from O3 events., Comment: 11 pages

In our previous work we investigated the effect of the hypothetical reflecting boundary near the black hole event horizon on the waveform from extreme mass-ratio inspirals (EMRIs). Even if the reflection efficiency is not extremely high, we found that a significant modification of the waveform can be expected. Then, the question is how to implement the search for this signature in the actual data analysis of future space gravitational wave antennas, such as LISA. In this paper we propose a simple but efficient method to detect the signature of the reflecting boundary. The interesting feature of the effect of the reflecting boundary on the orbital evolution of EMRIs is that the energy and angular momentum loss rates periodically oscillate in the frequency domain. The oscillation period is corresponding to the inverse time scale for the round trip of gravitational waves between the hypothetical boundary and the angular momentum barrier. We will show that this peculiar feature allows to detect the signature of the reflecting boundary without much additional computational cost., Comment: 10 pages, 9 figures. v2: 11 pages, 9 figures, accepted version

Scientific analysis for the gravitational-wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary inclination and black hole spin, up to modest eccentricity ($\lesssim 0.3$) and separation ($\gtrsim2$--$10M$ from the last stable orbit). In that regime, our waveforms are accurate at the leading `adiabatic' order, and they approximately capture transient self-force resonances that significantly impact the gravitational-wave phase. The model fills an urgent need for extensive waveforms in ongoing data-analysis studies, and its individual components will continue to be useful in future science-adequate waveforms., Comment: 9+5 pages,4+1 figures,5PN-e10 Teukolsky data are all available at the Black Hole Perturbation Club: https://sites.google.com/view/bhpc1996/data v2:updated references,expanded supplemental discussion of initial phases.v3:contains minor corrections and more references.Matches version published in PRL

Ringdown gravitational waves of compact object binaries observed by ground-based gravitational-wave detectors encapsulate rich information to understand remnant objects after the merger and to test general relativity in the strong field. In this work, we investigate the ringdown gravitational waves in detail to better understand their property, assuming that the remnant objects are black holes. For this purpose, we perform numerical simulations of post-merger phase of binary black holes by using the black hole perturbation scheme with the initial data given under the close-limit approximation, and generate data of ringdown gravitational waves with smaller numerical errors than that associated with currently available numerical relativity simulations. Based on the analysis of the data, we propose an orthonormalization of the quasinormal mode functions describing the fundamental tone and overtones to model ringdown gravitational waves. Finally, through some demonstrations of the proposed model, we briefly discuss the prospects for ringdown gravitational-wave data analysis including the overtones of quasinormal modes., Comment: 30 pages, 14 figures, accepted version

We discuss the energy loss due to gravitational radiation of binaries composed of exotic objects whose horizon boundary conditions are replaced with reflective ones. Our focus is on the extreme mass-ratio inspirals, in which the central heavier black hole is replaced with an exotic compact object. We show, in this case, a modulation of the energy loss rate depending on the evolving orbital frequency occurs and leads to two different types of modifications to the gravitational wave phase evolution; the oscillating part directly corresponding to the modulation in the energy flux, and the non-oscillating part coming from the quadratic order in the modulation. This modification can be sufficiently large to detect with future space-borne detectors., Comment: 5 pages, 3 figures; v2: 8 pages, 3 figures, revised Fig.3, accepted version

The gravitational wave event, GW190521 is the most massive binary black hole merger observed by ground-based gravitational wave observatories LIGO/Virgo to date. While the observed gravitational-wave signal is mainly in the merger and ringdown phases, the inspiral gravitational-wave signal of GW190521-like binary will be more visible by space-based detectors in the low-frequency band. In addition, the ringdown gravitational-wave signal will be more loud with the next generation (3G) of ground-based detectors in the high-frequency band, displaying a great potential of the multiband gravitational wave observations. In this paper, we explore the scientific potential of multiband observations of GW190521-like binaries with milli-Hz gravitational wave observatory: LISA, deci-Hz observatory: B-DECIGO, and (next generation of) hecto-Hz observatories: aLIGO and ET. In the case of quasicircular evolution, the triple-band observation by LISA, B-DECIGO and ET will provide parameter estimation errors of the masses and spin amplitudes of component black holes at the level of order 1% -- 10%. This would allow consistency tests of general relativity in the strong-field at an unparalleled precision, particularly with the "B-DECIGO + ET" observation. In the case of eccentric evolution, the multiband signal-to-noise ratio by "B-DECIGO + ET" observation would be larger than 100 for a five year observation prior to coalescence, even with high final eccentricities., Comment: 26 pages, 2 figures.v2:accepted version.v3:corrects typos in Table.4 (Multiband) and Eq.(A9).References updated

Recently, the possibility of detecting gravitational wave echoes in the data stream subsequent to the binary black hole mergers observed by LIGO was suggested. Motivated by this suggestion, we presented templates of echoes based on black hole perturbations in our previous work. There, we assumed that the incident waves resulting in echoes are similar to the ones that directly escape to the asymptotic infinity. In this work, to extract more reliable information on the waveform of echoes without using the naive assumption on the incident waves, we investigate gravitational waves induced by a point mass plunging into a Kerr black hole. We solve the linear perturbation equation sourced by the plunging mass under the purely outgoing boundary condition at infinity and a hypothetical reflection boundary condition near the horizon. We find that the low frequency component below the threshold of the super-radiant instability is highly suppressed, which is consistent with the incident waveform assumed in the previous analysis. We also find that the high frequency mode excitation is significantly larger than the one used in the previous analysis, if we adopt the perfectly reflective boundary condition independently of the frequency. When we use a simple template in which the same waveform as the direct emissions to infinity is repeated with the decreasing amplitude, the correlation between the expected signal and the template turns out to decrease very rapidly., Comment: 22 pages, 8 figures

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy., Comment: 10 pages, 3 figures

For a Schwarzchild black hole of mass $M$, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius $r=4GM/c^2$. When the particle is endowed with a small mass, $\mu\ll M$, it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to $O(\mu/M)$. Our numerical values are found to be in agreement with estimates first made within the Effective One Body formalism, and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the "light ring", and could thus supply strong-field calibration data for eccentricity-dependent terms in the Effective One Body model of merging binaries., Comment: 29 pages, 6 figures

KAGRA is a new gravitational wave detector which aims to begin joint observation with Advanced LIGO and Advanced Virgo from late 2019. Here, we present KAGRA's possible upgrade plans to improve the sensitivity in the decade ahead. Unlike other state-of-the-art detectors, KAGRA requires different investigations for the upgrade since it is the only detector which employs cryogenic cooling of the test mass mirrors. In this paper, investigations on the upgrade plans which can be realized by changing the input laser power, increasing the mirror mass, and injecting frequency dependent squeezed vacuum are presented. We show how each upgrade affects to the detector frequency bands and also discuss impacts on gravitational-wave science. We then propose an effective progression of upgrades based on technical feasibility and scientific scenarios., Comment: 7 pages, 3 figures, Proceedings for the Fifteenth Marcel Grossmann Meeting, Rome, July 1-7, 2018

We have examined gravitational wave echo signals for nine binary black hole merger events observed by Advanced LIGO and Virgo during the first and second observation runs. To construct an echo template, we consider Kerr spacetime, where the event horizon is replaced by a reflective membrane. We use frequency-dependent reflection rate at the angular potential barrier, which is fitted to the numerical data obtained by solving Teukolsky equations. This reflection rate gives a frequency-dependent transmission rate that is suppressed at lower frequencies in the template. We also take into account the overall phase shift of the waveform as a parameter, which arises when the wave is reflected at the membrane and potential barrier. Using this template based on black hole perturbation, we find no significant echo signals in the binary black hole merger events.

The "flux-balance formulae" that determine the averaged evolution of energy, azimuthal angular momentum, and Carter constant in terms of the averaged asymptotic gravitational-wave fluxes for inspirals of small bodies into Kerr black holes were first derived about 15 years ago. However, this derivation is restricted to the case that the background Kerr geodesics are non-resonant (i.e., the radial and angular motions are always incommensurate), and excludes the resonant case that can be important for the radiative dynamics of extreme mass-ratio inspirals. We give here a new derivation of the flux formulae based on Hamiltonian dynamics of a self-forced particle motion, which is a valuable tool for analyzing self-force effects on generic (eccentric, inclined) bound orbits in the Kerr spacetime. This Hamiltonian derivation using action-angle variables is much simpler than the previous one, applies to resonant inspirals without any complication, and can be straightforwardly implemented by using analytical/numerical Teukolsky-based flux codes., Comment: v2: 27 pages, 0 figures, matches the published version

The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders., Comment: 10 pages, 3 figures

Recently the possibility of detecting echoes of ringdown gravitational waves from binary black hole mergers was shown. The presence of echoes is expected if the black hole is surrounded by a mirror that reflects gravitational waves near the horizon. Here, we present slightly more sophisticated templates motivated by a waveform which is obtained by solving the linear perturbation equation around a Kerr black hole with a complete reflecting boundary condition in the stationary traveling wave approximation. We estimate that the proposed template can bring about $10\%$ improvement in the signal-to-noise ratio., Comment: 10 pages, 5 figures, matches the published version

We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a "first law of mechanics" for black-hole-particle binary systems, at leading order beyond the test-mass approximation., Comment: 55 pages, 0 figures, matches the published version

The cosmological evolution of the binary black hole (BH) merger rate and the energy density of the gravitational-wave (GW) background are investigated. To evaluate the redshift dependence of the BH formation rate, BHs are assumed to originate from low-metallicity stars, and the relations between the star formation rate, metallicity and stellar mass of galaxies are combined with the stellar mass function at each redshift. As a result, it is found that when the energy density of the GW background is scaled with the merger rate at the local Universe, the scaling factor does not depend on the critical metallicity for the formation of BHs. Also taking into account the merger of binary neutron stars, a simple formula to express the energy spectrum of the GW background is constructed for the inspiral phase. The relation between the local merger rate and the energy density of the GW background will be examined by future GW observations., Comment: 10 pages, 10 figures, updated to reflect full results from the first Advanced LIGO Observing Run, accepted for publication in ApJ

The Sasaki-Nakamura transformation gives a short-ranged potential and a convergent source term for the master equation of perturbations in the Kerr space-time. In this paper, we study the asymptotic behavior of the transformation, and present a new relaxed necessary and sufficient condition of the transformation to obtain the short-ranged potential in the assumption that the transformation converges in the far distance. Also, we discuss quasinormal mode frequencies which are determined by the information around the peak of the potential in the WKB analysis. Finally, in the extreme Kerr limit, $a/M \to 1$, where $M$ and $a$ denote the mass and spin parameter of a Kerr black hole, respectively, we find the peak location of the potential, $r_p/M \lesssim 1 + 1.8 \,(1-a/M)^{1/2}$ by using the new transformation. The uncertainty of the location is as large as that expected from the equivalence principle., Comment: 12 pages, 2 figures, added some references, modifications to match the published version in PTEP

We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasi-circular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries., Comment: 8 pages, 6 figures, minor modifications to match the published version in PRD

We calculate the secular changes of the orbital parameters of a point particle orbiting a Kerr black hole, due to the gravitational radiation reaction. For this purpose, we use the post-Newtonian (PN) approximation in the first order black hole perturbation theory, with the expansion with respect to the orbital eccentricity. In this work, the calculation is done up to the fourth post-Newtonian (4PN) order and to the sixth order of the eccentricity, including the effect of the absorption of gravitational waves by the black hole. We confirm that, in the Kerr case, the effect of the absorption appears at the 2.5PN order beyond the leading order in the secular change of the particle's energy and may induce a superradiance, as known previously for circular orbits. In addition, we find that the superradiance may be suppressed when the orbital plane inclines with respect to the equatorial plane of the central black hole. We also investigate the accuracy of the 4PN formulae by comparing to numerical results. If we require that the relative errors in the 4PN formulae are less than $10^{-5}$, the parameter region to satisfy the condition will be $p\gtrsim 50$ for $e=0.1$, $p\gtrsim 80$ for $e=0.4$, and $p\gtrsim 120$ for $e=0.7$ almost irrespective of the inclination angle nor the spin of the black hole, where $p$ and $e$ are the semi-latus rectum and the eccentricity of the orbit. The region can further be extended using an exponential resummation method to $p\gtrsim 40$ for $e=0.1$, $p\gtrsim 60$ for $e=0.4$, and $p\gtrsim 100$ for $e=0.7$. Although we still need the higher order calculations of the PN approximation and the expansion with respect to the orbital eccentricity to apply for data analysis of gravitational waves, the results in this paper would be an important improvement from the previous work at the 2.5PN order, especially for large $p$ region., Comment: 32 pages, 6 figures, minor corrections, minor modifications to match the published version in PTEP added, supplementary data files available at http://www2.yukawa.kyoto-u.ac.jp/~misao.sasaki/BHPC/

The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modelling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods, and can be used to enhance their accuracy, e.g. via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits---specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity $\langle U \rangle$ that generalizes Detweiler's redshift invariant. The functional relationship $\langle U \rangle(\Omega_r,\Omega_\phi)$, where $\Omega_r$ and $\Omega_\phi$ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute $\langle U \rangle(\Omega_r,\Omega_\phi)$ numerically through linear order in the mass ratio $q$, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive $\langle U \rangle(\Omega_r,\Omega_\phi)$ analytically through 3PN order, for an arbitrary $q$, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the $\mathcal{O}(q)$ piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at $\mathcal{O}(q)$., Comment: 44 pages, 2 figures, 4 tables

We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading order orbital evolution is described only by the knowledge of the averaged evolution of the constants of motion, i.e., the energy, azimuthal angular momentum and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiralling orbit may cross a "resonance" point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the 'self-force", which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present a method of computing the averaged rate of change of the Carter constant in a relatively simple manner at the "resonance" point., Comment: 18pages, no figures, matches version published in PTEP

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain "synchronized" in phase., Comment: 11 pages, 8 figures. Updated to reflect published version

The accurate calculation of long-term phase evolution of gravitational wave (GW) forms from extreme (intermediate) mass ratio inspirals (E(I)MRIs) is an inevitable step to extract information from this system. Achieving this goal, it is believed that we need to understand the gravitational self-forces. However, it is not quntatively demonstrated that the second order self-forces are necessary for this purpose. In this paper we revisit the problem to estimate the order of magnitude of the dephasing caused by the second order self-forces on a small body in a quasi-circular orbit around a Kerr black hole, based on the knowledge of the post-Newtonian (PN) approximation and invoking the energy balance argument. In particular, we focus on the averaged dissipative part of the self-force, since it gives the leading order contribution among the various components of them. To avoid the possibility that the energy flux of GWs becomes negative, we propose a new simple resummation called exponential resummation, which assures the positivity of the energy flux. In order to estimate the magnitude of the yet unknown second order self-forces, here we point out the scaling property in the absolute value of the PN coefficients of the energy flux. Using these new tools, we evaluate the expected magnitude of dephasing. Our analysis indicates that the dephasing due to the second order self-forces for quasi-circular E(I)MRIs may be well captured by the 3PN energy flux, once we obtain all the spin dependent terms, except for the case with an extremely large spin of the central Kerr black., Comment: 16 pages, 7 figures. revtex4,v2:added references, and minor modification to clarify the arguments; version published in PRD

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m_1 as it moves along an (unstable) circular geodesic orbit between the innermost stable circular orbit (ISCO) and the light ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we construct the function h_{uu}(x) = h_{\mu\nu} u^{\mu} u^{\nu} (related to Detweiler's gauge-invariant "redshift" variable), where h_{\mu\nu} is the regularized metric perturbation in the Lorenz gauge, u^{\mu} is the four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)\Omega]^{2/3} is an invariant coordinate constructed from the orbital frequency \Omega. In particular, we explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where the circular orbit becomes null. Using the recently discovered link between h_{uu} and the piece a(u), linear in the symmetric mass ratio \nu, of the main radial potential A(u,\nu) of the Effective One Body (EOB) formalism, we compute a(u) over the entire domain 0

We present results from calculations of the orbital evolution in eccentric binaries of nonrotating black holes with extreme mass-ratios. Our inspiral model is based on the method of osculating geodesics, and is the first to incorporate the full gravitational self-force (GSF) effect, including conservative corrections. The GSF information is encapsulated in an analytic interpolation formula based on numerical GSF data for over a thousand sample geodesic orbits. We assess the importance of including conservative GSF corrections in waveform models for gravitational-wave searches., Comment: 4 pages, 3 figures, Fast GSF calculator code available at: http://www.nielswarburton.net/lib_Sch_GSF/

There is a claim that a static charged black hole (Reissner-Nordstr\"{o}m black hole) can be overcharged by absorbing a charged test particle. If it is true, it might give a counter example to the weak cosmic censorship conjecture, which states that spacetime singularities are never observed by a distant observer. However, so far the proposed process has only been analyzed within a test particle approximation. Here we claim that the back reaction effects of a charged particle cannot be neglected when judging whether the suggested process is really a counter example to the cosmic censorship conjecture or not. Furthermore, we argue that all the back reaction effects can be properly taken into account when we consider the trajectory of a particle on the border between the plunge and bounce orbits. In such marginal cases we find that the Reissner-Nordstr\"{o}m black hole can never be overcharged via the absorption of a charged particle. Since all the plunge orbits are expected to have a higher energy than the marginal orbit, we conclude that there is no supporting evidence that indicates the violation of the cosmic censorship in the proposed overcharging process., Comment: 18 pages, revtex4, minor revision and reference added, version to appear in PRD

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black hole binaries with mass ratios 1/8 < m1/m2 < 1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate, and, surprisingly, so also the predictions of self-force theory [replacing m1/m2 --> m1m2/(m1+m2)^2]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches., Comment: 5 pages, 3 figures; v2: new abstract, updated figures correcting minor error, added references, minor changes to match published version; to appear in Phys. Rev. Lett

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass $\mu$ is much smaller than the black hole mass $M$, and explore post-geodesic corrections of $O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge-dependent) semilatus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit "redshift" invariant. We compute the $O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak-field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations., Comment: 29 pages, 4 eps figures, matches PRD version

Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the $O(m)$ conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass $m$ moving around a Schwarzschild black hole of mass ${\mathsf M}\gg m$. Specifically, we study the gauge-invariant function $\rho(x)$, where $\rho$ is defined as the $O(m)$ part of the dimensionless ratio $(\hat\Omega_r/\hat\Omega_{\varphi})^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $x=[Gc^{-3}({\mathsf M}+m)\hat\Omega_{\varphi}]^{2/3}$ is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function $\rho(x)$ in the interval $0

We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett.\ {\bf 102}, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications., Comment: 42 pages. v3 corrects typos in Eqs. (3.11), (3.12), (4.2), (E25) and (E26)

The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M G/c^2$. If the particle is endowed with mass $\mu(\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $\Delta r_{\rm isco}$ and $\Delta\Omega_{\rm isco}$ in the ISCO's radius and frequency, at leading order in the mass ratio $\mu/M$. We obtain, in the Lorenz gauge, $\Delta r_{\rm isco}=-3.269 (\pm 0.003)\mu G/c^2$ and $\Delta\Omega_{\rm isco}/\Omega_{\rm isco}=0.4870 (\pm 0.0006) \mu/M$. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem., Comment: 4 pages. v2: Added clarifications re. the definition of the conservative self-force and the gauge dependence of the frequency; some other minor changes. Accepted for publication in PRL

Recently, two independent calculations have been presented of finite-mass ("self-force") effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult--but also interesting. Barack and Sago [Phys. Rev. D {\bf 75}, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D {\bf 77}, 124026 (2008)] describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge--Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative $O(\mu)$ shift in $u^t$ (where $\mu$ is the particle's mass and $u^t$ is the Schwarzschild $t$ component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of $\sim 10^{-5}$--$10^{-7}$ (depending on the orbital radius)--comparable with the estimated numerical error., Comment: 11 pages; minor typos corrected; final version to be published in PRD

The mode-sum method provides a practical means for calculating the self force acting on a small particle orbiting a larger black hole. In this method, one first computes the spherical-harmonic $l$-mode contributions $F^{\mu}_l$ of the "full force" field $F^{\mu}$, evaluated at the particle's location, and then sums over $l$ subject to a certain regularization procedure. In the frequency-domain variant of this scheme the quantities $F^{\mu}_l$ are obtained by fully decomposing the particle's self field into Fourier-harmonic modes $l m \omega$, calculating the contribution of each such mode to $F^{\mu}_l$, and then summing over $\omega$ and $m$ for given $l$. This procedure has the advantage that one only encounters {\it ordinary} differential equations. However, for eccentric orbits, the sum over $\omega$ is found to converge badly at the particle's location. This problem (reminiscent of the familiar Gibbs phenomenon) results from the discontinuity of the time-domain $F^{\mu}_l$ field at the particle's worldline. Here we propose a simple and practical method to resolve this problem. The method utilizes the {\it homogeneous} modes $l m \omega$ of the self field to construct $F^{\mu}_l$ (rather than the inhomogeneous modes, as in the standard method), which guarantees an exponentially-fast convergence to the correct value of $F^{\mu}_l$, even at the particle's location. We illustrate the application of the method with the example of the monopole scalar-field perturbation from a scalar charge in an eccentric orbit around a Schwarzschild black hole. Our method, however, should be applicable to a wider range of problems, including the calculation of the gravitational self-force using either Teukolsky's formalism, or a direct integration of the metric perturbation equations., Comment: 20 pages, 10 eps figures; version published in PRD

We present a new, simple method for calculating the scalar, electromagnetic, and gravitational self forces acting on particles in orbit around a Kerr black hole. The standard ``mode-sum regularization'' approach for self-force calculations relies on a decomposition of the full (retarded) perturbation field into multipole modes, followed by the application of a certain mode-by-mode regularization procedure. In recent years several groups have developed numerical codes for calculating black hole perturbations directly in 2+1 dimensions (i.e., decomposing the azimuthal dependence into $m$-modes, but refraining from a full multipole decomposition). Here we formulate a practical scheme for constructing the self force directly from the 2+1-dimensional $m$-modes. While the standard mode-sum method is serving well in calculations of the self force in Schwarzschild geometry, the new scheme should allow a more efficient treatment of the Kerr problem., Comment: 17 pages. Minor typos corrected; version to appear in PRD

General orbits of a particle of small mass $\mu$ around a Kerr black hole of mass $M$ are characterized by three parameters: the energy, the angular momentum and the Carter constant. The time-averaged rates of change of the energy and the angular momentum can be obtained by computing the corresponding fluxes of gravitational waves emitted by the particle. By contrast, the time-averaged rate of change of the Carter constant cannot be expressed as a flux of gravitational waves. Recently a method to compute this rate of change was proposed by Mino, and we refined it into a simplified form. In this paper we further extend our previous work to give a new formulation without the aid of expansion in terms of a small inclination angle., Comment: 26pages, to be published in Progress of Theoretical Physics

We discuss the coherent search strategy to detect gravitational waves from inspiraling compact binaries by a network of correlated laser interferometric detectors. From the maximum likelihood ratio statistic, we obtain a coherent statistic which is slightly different from and generally better than what we obtained in our previous work. In the special case when the cross spectrum of two detectors normalized by the power spectrum density is constant, the new statistic agrees with the old one. The quantitative difference of the detection probability for a given false alarm rate is also evaluated in a simple case., Comment: 4 pages, 1 Postscript figures, uses revtex4.sty

We calculate the gravitational self force acting on a pointlike particle of mass $\mu$, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenz-gauge metric perturbation using numerical evolution in the time domain; We then compute the (finite) back-reaction force from each of the multipole modes of the perturbation; Finally, we apply the ``mode sum'' method to obtain the total, physical self force. The {\em temporal} component of the self force (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitational-wave energy radiated to infinity and through the event horizon. The {\em radial} component of the self force (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the $O(\mu)$ correction to the specific energy and angular momentum parameters (in the Lorenz gauge), as well as the $O(\mu)$ shift in the orbital frequency (which is gauge invariant)., Comment: 31 pages, 17 figures. v3 corrects typos in Eqs. (21) and (22). These typos do not propagate, and the rest of the paper remains unaffected

We investigate the adiabatic orbital evolution of a point particle in the Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is enough smaller than the typical timescale of orbits, the evolution of orbits is characterized by the change rates of three constants of motion, the energy $E$, the azimuthal angular momentum $L$, and the Carter constant $Q$. For $E$ and $L$, we can evaluate their change rates from the fluxes of the energy and the angular momentum at infinity and on the event horizon according to the balance argument. On the other hand, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. %and the corresponding conservation law. Recently, Mino proposed a new method of evaluating the averaged change rate of the Carter constant by using the radiative field. In our previous paper we developed a simplified scheme for practical evaluation of the evolution of the Carter constant based on the Mino's proposal. In this paper we describe our scheme in more detail, and derive explicit analytic formulae for the change rates of the energy, the angular momentum and the Carter constant., Comment: 34 pages, no figure

Geodesic motion of a point particle in Kerr geometry has three constants of motion, energy $E$, azimuthal angular momentum $L$, and Carter constant $Q$. Under the adiabatic approximation, radiation reaction effect is characterized by the time evolution of these constants. In this letter we show that the scheme to evaluate them can be dramatically simplified., Comment: 5pages, no figure, accepted for publication in PTP

In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass $\mu$ orbiting a Schwarzschild black hole of mass $M$, where $\mu\ll M$. In our method, we divide the self-force into the $\tilde S$-part and $\tilde R$-part. All the singular behaviors are contained in the $\tilde S$-part, and hence the $\tilde R$-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized $\tilde S$-part and the $\tilde R$-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. For the regularized $\tilde S$-part, we calculate it for circular orbits to 18 post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining $\tilde{R}$-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to $\ell=13$., Comment: 21pages, 12 figures

Gamma-Ray Bursts (GRBs) are now considered as relativistic jets. We analyze the gravitational waves from the acceleration stage of the GRB jets. We show that (i) the point mass approximation is not appropriate if the opening half-angle of the jet is larger than the inverse of the Lorentz factor of the jet, (ii) the gravitational waveform has many step function like jumps, and (iii) the practical DECIGO and BBO may detect such an event if the GRBs occur in Local group of galaxy. We found that the light curve of GRBs and the gravitational waveform are anti-correlated so that the detection of the gravitational wave is indispensable to determine the structure of GRB jets., Comment: Revtex4, 10 pages, 6 figures, Fig.2 and Fig.3 replaced, minor changes to text in Sec.I and Sec.V, typos corrected, some reference added, Version to be published in PRD

We formulate a new analytical method for regularizing the self-force acting on a particle of small mass $\mu$ orbiting a black hole of mass $M$, where $\mu\ll M$. At first order in $\mu$, the geometry is perturbed and the motion of the particle is affected by its self-force. The self-force, however, diverges at the location of the particle, and hence should be regularized. It is known that the properly regularized self-force is given by the tail part (or the $R$-part) of the self-field, obtained by subtracting the direct part (or the $S$-part) from the full self-field. The most successful method of regularization proposed so far relies on the spherical harmonic decomposition of the self-force, the so-called mode-sum regularization or mode decomposition regularization. However, except for some special orbits, no systematic analytical method for computing the regularized self-force has been given. In this paper, utilizing a new decomposition of the retarded Green function in the frequency domain, we formulate a systematic method for the computation of the self-force. Our method relies on the post-Newtonian (PN) expansion but the order of the expansion can be arbitrarily high. To demonstrate the essence of our method, in this paper, we focus on a scalar charged particle on the Schwarzschild background. The generalization to the gravitational case is straightforward, except for some subtle issues related with the choice of gauge (which exists irrespective of regularization methods)., Comment: 17 pages, no figure

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. It is known that the metric perturbation induced by a particle can be divided into two parts, the direct part (or the S part) and the tail part (or the R part), in the harmonic gauge, and the regularized self-force is derived from the R part which is regular and satisfies the source-free perturbed Einstein equations. In this paper, we consider a gauge transformation from the harmonic gauge to the Regge-Wheeler gauge in which the full metric perturbation can be calculated, and present a method to derive the regularized self-force for a particle in circular orbit around a Schwarzschild black hole in the Regge-Wheeler gauge. As a first application of this method, we then calculate the self-force to first post-Newtonian order. We find the correction to the total mass of the system due to the presence of the particle is correctly reproduced in the force at the Newtonian order., Comment: Revtex4, 43 pages, no figure. Version to be published in PRD

The metric perturbation induced by a particle in the Schwarzschild background is usually calculated in the Regge-Wheeler (RW) gauge, whereas the gravitational self-force is known to be given by the tail part of the metric perturbation in the harmonic gauge. Thus, to identify the gravitational self-force correctly in a specified gauge, it is necessary to find out a gauge transformation that connects these two gauges. This is called the gauge problem. As a direct approach to solve the gauge problem, we formulate a method to calculate the metric perturbation in the harmonic gauge on the Schwarzshild backgound. We apply the Fourier-harmonic expansion to the metric perturbation and reduce the problem to the gauge transformation of the Fourier-harmonic coefficients (radial functions) from the RW gauge to the harmonic gauge. We derive a set of decoupled radial equations for the gauge transformation. These equations are found to have a simple second-order form for the odd parity part and the forms of spin $s=0$ and 1 Teukolsky equations for the even parity part. As a by-product, we correct typos in Zerilli's paper and present a set of corrected equations in Appendix., Comment: Revtex4, 13 pages, no figures

A Randall-Sundrum type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum fluctuations of the bulk scalar field $\phi$ with $m^2=V''(\phi)$. We decompose the bulk scalar field into the infinite mass spectrum of 4-dimensional fields; the field with the smallest mass-square, called the zero-mode, and the Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of the classical solution holds if $|m^2|\bar\ell^2\ll1$, where $\bar{\ell}$ is the curvature radius of the effectively anti-de Sitter bulk, but it is violated if $|m^2|\bar\ell^2\gg1$, though the violation is very small. Then we evaluate the vacuum expectation value $<\delta\phi^2>$ on the brane. We find the zero-mode contribution completely dominates if $|m^2|\bar{\ell}^2\ll 1$ similar to the case of classical background. In contrast, we find the Kaluza-Klein contribution is small but non-negligible if the value of $|m^2|\bar{\ell}^2$ is large., Comment: 12pages, 1 figure, typos corrected, a couple of paragraphs modified but no major change in the text, final version to be published in PRD