We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to non-spinning, quasi-circular binaries with mass ratios ranging from $m_A/m_B = 1$ to $m_A/m_B = 9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order $10^{-5}$ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with non-adiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a re-expansion in terms of the symmetric mass ratio $ν$ does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, $z_A + z_B$, which is symmetric under the exchange of the masses, a re-expansion in $ν$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.
The redshift factor $z$ is an invariant quantity of fundamental interest in post-Newtonian and self-force descriptions of compact binaries. It connects different approximation schemes, and plays a central role in the first law of binary black hole mechanics, which links local quantities to asymptotic measures of energy and angular momentum in these systems. Through this law, the redshift factor is conjectured to have a close relation to the surface gravity of the event horizons of black holes in circular orbits. We propose and implement a novel method for extracting the redshift factor on appa…
In this paper we analyze the frequency shifts of the light emitted by particles describing stable circular geodesics around a static black hole immersed in an external magnetic field of arbitrary strength. This system is represented by the Ernst solution of the Einstein-Maxwell equations. The presence of the magnetic field and its magnitude affects both the geodesics and the red-blueshifts of the light emitted by neutral or charged particles orbiting the black hole. When the magnetic field is turned off we recover the characteristic redshifts coming from particles orbiting a Schwarzschild blac…
In this work we derive some general features of the redshift measured by radially moving observers in the black hole background. Let observer 1 cross the black hole horizon emitting of a photon while observer 2 crossing the same horizon later receives it. We show that if (i) the horizon is the outer one (event horizon) and (ii) it is nonextremal, received frequency is redshifted. This generalizes previous recent results in literature. For the inner horizon (like in the Reissner-Nordström metric) the frequency is blueshifted. If the horizon is extremal, the frequency does not change. We derive …
The Detweiler-Barack-Sago redshift function for particles moving along slightly eccentric equatorial orbits around a Kerr black hole is currently known up to the second order in eccentricity, second order in spin parameter, and the 8.5 post-Newtonian order. We improve the analytical computation of such a gauge-invariant quantity by including terms up to the fourth order in eccentricity at the same post-Newtonian approximation level. We also check that our results agrees with the corresponding post-Newtonian expectation of the same quantity, calculated by using the currently known Hamiltonian f…
We derive closed formulas for the mass and spin parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red-/blue-shifts of photons emitted by massive particles (stars) moving on geodesics around the black hole and their respective orbital radius. It turns out that given a set of two (three) stars revolving around the black hole, these formulas involve just eight (twelve) observational data. For the case of a single star orbiting the black hole we need a minimal set of four observational measurements to analytically determine both parameters.
This paper is dedicated to derive and study binary systems of identical corotating dyonic black holes separated by a massless strut -- two 5-parametric corotating binary black hole models endowed with both electric and magnetic charges-- where the dyonic black holes carrying equal/opposite electromagnetic charges in the first/second model satisfy the extended Smarr formula for the mass including the magnetic charge as a fourth conserved parameter.
Advancements in the black hole shadow observations may allow us not only to investigate physics in the strong gravity regime, but also to use them in cosmological studies. In this paper, we propose to use the shadow of supermassive black holes as a standard ruler for cosmological applications assuming the black hole mass can be determined independently. First, observations at low redshift distances can be used to constrain the Hubble constant independently. Secondly, the angular size of shadows of high redshift black holes is increased due to cosmic expansion and may also be reachable with fut…
A simple estimate is given of gravitational wave memory for the inspiral and merger of a binary black hole system. Here the memory is proportional to the total energy radiated and has a simple angular dependence. This estimate might be helpful as a consistency check for numerical relativity memory waveforms.
We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any boundary conditions in the strong field regime, and offers a holistic (all inclusive) approach to the construction of single and binary black hole initial data. The new implicit solver is extensively tested against known exact black hole solutions and is used to construct initial data for several single and binary black hole configurations.
New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data
Gravitational-wave (GW) observations of binary black holes offer the best probes of the relativistic, strong-field regime of gravity. Gravitational radiation, in the leading order is quadrupolar. However, non-quadrupole (higher-order) modes make appreciable contribution to the radiation from binary black holes with large mass ratios and misaligned spins. The multipolar structure of the radiation is fully determined by the intrinsic parameters (masses and spin angular momenta of the companion black holes) of a binary in quasi-circular orbit. Following our previous work \cite{Dhanpal:2018ufk}, w…
Usually, interpretation of redshift in static spacetimes (for example, near black holes) is opposed to that in cosmology. In this methodological note we show that both explanations are unified in a natural picture. This is achieved if considering the static spacetime one (i) makes a transition to a synchronous frame, (ii) returns to the original frame by means of local Lorentz boost. To reach our goal, we consider a rather general class of spherically symmetric spacetimes. In doing so, we construct frames that generalize the well-known Lemaitre and Painlevé--Gullstand ones and elucidate the re…
We present a research of the time evolution of the redshift of light received from the binary star that moves in the external gravitational field of Kerr black hole. We formulate a method for the solution of inverse problem: calculating of the parameters of relative motion of stars in binary system using the redshift data. The considered formalism has no restrictions on the character of the motion of the center of mass of a compact binary star and can be applied even in the case of binary motion close to the event horizon of a supermassive black hole. The efficiency of the method is illustrate…
Close limit evolution of Kerr-Schild type initial data for binary black holes
我们发展了Bishop {\em et al.}在黑洞彼此靠近的极限。我们提出了一个精确的解决方案的线性化的初始值问题的基础上，他们的建议，并利用最近推出的广义形式主义研究任意坐标系中的Schwarzschild黑洞的扰动执行的演变。通过对黑洞碰撞辐射能量和波形的分析，阐明了初始数据族中自由参数的意义。
Different theories of gravity can admit the same black hole solution, but the parameters usually have different physical interpretations. In this work we study in depth the linear term $βr$ in the redshift function of black holes, which arises in conformal gravity, de Rham-Gabadadze-Tolley (dRGT) massive gravity, $f(R)$ gravity (as approximate solution) and general relativity. Geometrically we quantify the parameter $β$ in terms of the curvature invariants. Astrophysically we found that $β$ can be expressed in terms of the cosmological constant, the photon orbit radius and the innermost stable…
Retrieving the mass of a gravitational-wave (GW) source is a fundamental but difficult problem because the mass is degenerate with redshift. In astronomy, three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but the latter two are normally too weak to affect the observation. In this Letter, we show that the current astrophysical models allow binary black holes (BBHs) to merge within $10$ Schwarzschild radii of a supermassive black hole (SMBH). We find that in this case both the Doppler and gravitational redshift are significant, and in the most extreme condi…
The population-level distributions of the masses, spins, and redshifts of binary black holes (BBHs) observed using gravitational waves can shed light on how these systems form and evolve. Because of the complex astrophysical processes shaping the inferred BBH population, models allowing for correlations among these parameters will be necessary to fully characterize these sources. We hierarchically analyze the BBH population detected by LIGO and Virgo with a model allowing for correlations between the effective aligned spin and the primary mass and redshift. We find that the width of the effect…
One of the goals of gravitational-wave astronomy is to quantify the evolution of the compact binary merger rate with redshift. The redshift distribution of black hole mergers would offer considerable information about their evolutionary history, including their progenitor formation rate, the dependence of black hole formation on stellar metallicity, and the time delay distribution between formation and merger. Efforts to measure the binary redshift distribution are currently limited, however, by the detection range of existing instruments, which can individually resolve compact binary merger e…
We show that the gravitational wave signals from primordial black hole (PBH) binaries at high redshift can be detected. The detectability of PBH binaries is enhanced by redshift bias and more PBH binaries at high redshift. The initial clustering of PBHs is also included and enhances the effectively detectable mass ranges of PBHs at high redshift. Future observations on the gravitational wave at high redshift by space-based detectors such as LISA and SKA can constrain the fraction of PBHs in dark matter and PBHs initial distribution.
Recently, it has been shown that with the inclusion of overtones, the post-merger gravitational waveform at infinity of a binary black hole system is well-modelled using pure linear theory. However, given that a binary black hole merger is expected to be highly non-linear, where do these non-linearities, which do not make it out to infinity, go? We visualize quantities measuring non-linearity in the strong-field region of a numerical relativity binary black hole merger in order to begin to answer this question.
A population of more than 50 binary black hole mergers has now been observed by the LIGO and Virgo gravitational-wave observatories. While neutron stars are known to have large velocities associated with impulsive kicks imparted to them at birth in supernovae, whether black holes receive similar kicks, and of what magnitude, remains an open question. Recently, Callister et al. (2021) analysed the binary black hole population under the hypothesis that they were all formed through isolated binary evolution and claimed that large black hole kicks (greater than 260 km/s at 99% confidence) were req…
We construct from first principles a general relativistic approach to study Schwarzschild black hole (BH) rotation curves and estimate the mass-to-distance ratio of the active galactic nucleus of NGC 4258 in terms of astrophysical observable quantities. The presented method allows one to clearly distinguish and quantify the general and special relativistic contributions to the total redshift expression. The total relativistic redshift/blueshift comprises three components: the gravitational redshift due to the spacetime curvature generated by the mass of the BH in its vicinity, the kinematic sh…
Recent Advanced LIGO detections of binary black hole mergers have prompted multiple studies investigating the possibility that the heavy GW150914 binary system was of primordial origin, and hence could be evidence for dark matter in the form of black holes. We compute the stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the universe and compare it to the similar background spectrum due to binary black hole systems of stellar origin. We investigate the possibility of detecting this background with future gravitational wave detectors…
In the present paper the repulsion of two extreme Kerr black holes arising from their spin-spin interaction is analyzed within the framework of special subfamilies of the well-known Kinnersley-Chitre solution. The binary configurations of both equal and nonequal extreme repelling black holes are considered.
The assembly of massive black holes in the early universe remains a poorly constrained open question in astrophysics. The merger and accretion of light seeds (remnants of Population III stars with mass below $\sim 1000M_{\odot}$) or heavy seeds (in the mass range $10^4-10^6 M_{\odot}$) could both explain the formation of massive black holes, but the abundance of seeds and their merging mechanism are highly uncertain. In the next decades, the gravitational-wave observatories coming online are expected to observe very high-redshift mergers, shedding light on the seeding of the first black holes.…
In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by geodesic massive particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a dista…
The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational-wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within $10$ gravitational radii of a Kerr SMBH to determine the redshift and magnification of t…
Next-generation observations will revolutionize our understanding of binary black holes and will detect new sources, such as intermediate-mass black holes. Primary science goals include: Discover binary black holes throughout the observable Universe; Reveal the fundamental properties of black holes; Uncover the seeds of supermassive black holes.
Gravitational-wave detections of black hole mergers in binary systems offer an excellent opportunity to test the 2nd law of black hole thermodynamics. In this paper, we review how the entropy of any astrophysical black hole is calculated and we use LIGO and VIRGO's mass and spin data measurements from black hole merger events detected over the past years to perform entropy calculations and numerically test the generalized 2nd law of thermodynamics. Besides, we analyze the mathematical correlation between the black hole merger event's initial parameters to prove and conclude that the theorem wi…
We investigate the time evolution of the redshift of the spectrum of electromagnetic radiation that is emitted by the star that moves in the vicinity of supermassive black hole. For the case of Schwarzschild black hole we solve this problem exactly in General Theory of Relativity. Also we formulate an approach that gives possibilities to solve the inverse problem: reconstruction of motion of a star in the vicinity of black hole using the redshift data. This approach consists of two steps. The first step gives possibilities to find unique solution for the integrals of motion of the star by solu…
Gravitational waves from merging binary black holes can be used to shed light on poorly understood aspects of massive binary stellar evolution, such as the evolution of massive stars (including their mass-loss rates), the common envelope phase, and the rate at which massive stars form throughout the cosmic history of the Universe. In this paper we explore the \emph{correlated} impact of these phases on predictions for the merger rate and chirp mass distribution of merging binary black holes, aiming to identify possible degeneracies between model parameters. In many of our models, a large fract…
