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Register a new userTesting the strong equivalence principle with gravitational-wave observations of binary black holes
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Enrico Barausse
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The recent LIGO detection of gravitational waves from black-hole binaries offers the exciting possibility of testing gravitational theories in the previously inaccessible strong-field, highly relativistic regime. While the LIGO detections are so far consistent with the predictions of General Relativity, future gravitational-wave observations will allow us to explore this regime to unprecedented accuracy. One of the generic predictions of theories of gravity that extend General Relativity is the violation of the strong equivalence principle, i.e. strongly gravitating bodies such as neutron stars and black holes follow trajectories that depend on their nature and composition. This has deep consequences for gravitational-wave emission, which takes place with additional degrees of freedom besides the tensor polarizations of General Relativity. I will briefly review the formalism needed to describe these extra emission channels, and show that binary black-hole observations probe a set of gravitational theories that are largely disjoint from those that are testable with binary pulsars or neutron stars.
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We study scalar-tensor theories of gravity which satisfies the strong equivalence principle: the independence of the motion of a self-gravitating body from its internal structure. By solving $eta=4beta-gamma-3=0$ for the coupling function $omega(Phi)$, such a theory is obtained which is different from general relativity and is known as constant-$G$ theory. The theory has peculiar features: the coupling function asymptotes to a conformal coupling ($omegarightarrow -3/2$) for large $Phi$ and the theory is cosmologically attracted toward the conformal coupling.
The low-energy dynamics of any system admitting a continuum of static configurations is approximated by slow motion in moduli (configuration) space. Here, following Ferrell and Eardley, this moduli space approximation is utilized to study collisions of two maximally charged Reissner--Nordstr{o}m black holes of arbitrary masses, and to compute analytically the gravitational radiation generated by their scattering or coalescence. The motion remains slow even though the fields are strong, and the leading radiation is quadrupolar. A simple expression for the gravitational waveform is derived and compared at early and late times to expectations.
We elaborate on the role of higher-derivative curvature invariants as a quantum selection mechanism of regular spacetimes in the framework of the Lorentzian path integral approach to quantum gravity. We show that for a large class of black hole metrics prominently regular there are higher-derivative curvature invariants associated with a singular term in the action. Therefore, according to the finite action principle applied to a general higher-derivative gravity model, not only singular spacetimes but also some of the regular ones seem to not contribute to the path integral.
Today we have quite stringent constraints on possible violations of the Weak Equivalence Principle from the comparison of the acceleration of test-bodies of different composition in Earths gravitational field. In the present paper, we propose a test of the Weak Equivalence Principle in the strong gravitational field of black holes. We construct a relativistic reflection model in which either the massive particles of the gas of the accretion disk or the photons emitted by the disk may not follow the geodesics of the spacetime. We employ our model to analyze the reflection features of a NuSTAR spectrum of the black hole binary EXO 1846-031 and we constrain two parameters that quantify a possible violation of the Weak Equivalence Principle by massive particles and X-ray photons, respectively.
Gravitational waves detected by advanced ground-based detectors have allowed studying the universe in a way which is fully complementary to electromagnetic observations. As more sources are detected, it will be possible to measure properties of the local population of black holes and neutron stars, including their mass and spin distributions. Once at design sensitivity, existing instruments will be able to detect heavy binary black holes at redshifts of $sim 1$. Significant upgrades in the current facilities could increase the sensitivity by another factor of few, further extending reach and signal-to-noise ratio. More is required to access the most remote corners of the universe. Third-generation gravitational-wave detectors have been proposed, which could observe most of the binary black holes merging anywhere in the universe. In this paper we check if and to which extent it makes sense to keep previous-generation detectors up and running once a significantly more sensitive detector is online. First, we focus on a population of binary black holes with redshifts distributed uniformly in comoving volume. We show that measurement of extrinsic parameters, such as sky position, inclination and luminosity distance can significantly benefit from the presence of a less sensitive detector. Conversely, intrinsic parameters such as emph{detector-frame} masses and spins are largely unaffected. Measurement of the emph{source-frame masses} is instead improved, owing to the improvement of the distance measurement. Then, we focus on nearby events. We simulated sources similar to GW150914 and GW151226 and check how well their parameters can be measured by various networks. Here too we find that the main difference is a better estimation of the sky position, although even a single triangular-shaped third-generation detector can estimate their sky position to 1~deg$^2$ or better.
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