Scalar Stochastic Gravitational-Wave Background in Brans-Dicke Theory of Gravity

We study the scalar stochastic gravitational-wave background (SGWB) from astrophysical sources, including compact binary mergers and stellar collapses, in the Bras-Dicke theory of gravity. By contrast to tensor waves, we found the scalar SGWB to predominantly arise from stellar collapses. These collapses not only take place at higher astrophysical rates, but emit more energy. This is because, unlike tensor radiation, which mainly starts from quadrupole order, the scalar perturbation can be excited by changes in the monopole moment. In particular, in the case of stellar collapse into a neutron star or a black hole, the monopole radiation, at frequencies below 100\,Hz, is dominated by the memory effect. At low frequencies, the scalar SGWB spectrum follows a power law of $\Omega_\text{S}\propto f^\alpha$, with $\alpha = 1$. We predict that $\Omega_\text{S}$ is inversely proportional to the square of $\omega_{\rm BD}+2$, with $\quad(\omega_{\rm BD}+2)^2\Omega_S(f=25\,{\rm Hz}) = 2.8\times 10^{-6}$. We also estimate the detectability of the scalar SGWB for current and third-generation detector networks, and the bound on $\omega_{\rm BD}$ that can be imposed from these observations.Comment: 9 pages, 8 figure

Searching for near-horizon quantum structures in the binary black-hole stochastic gravitational-wave background

It has been speculated that quantum gravity corrections may lead to modifications to space-time geometry near black hole horizons. Such structures may cause reflections to gravitational waves, causing {\it echoes} that follow the main gravitational waves from binary black hole coalescence. We show that such echoes, if exist, will give rise to a stochastic gravitational-wave background, which is very substantial if the near-horizon structure has a near unity reflectivity for gravitational waves, readily detectable by Advanced LIGO. In case reflectivity is much less than unity, the background will mainly be arising from the first echo, with a level proportional to the power reflectivity of the near-horizon structure, but robust against uncertainties in the location of the structure --- as long as it is very close to the horizon. Sensitivity of third-generation detectors allows the detection of a background that corresponds to power reflectivity $\sim 10^{-3}$, if the uncertainties in the binary black-hole merger rate can be removed. We note that the echoes do alter the $f^{2/3}$ power law of the background spectra at low frequencies, which is rather robust against the uncertainties.Comment: 5 pages, 5 figure

Fundamental Physics Through Gravitational Waves: From No-Hair Theorem to Quantum Structures of Black Holes

In general relativity, black hole is the simplest macroscopic object in the universe: any black hole can be completely described by its mass, charge and angular mo- mentum. However, such a simple picture might be changed if the gravitational field equations are modified or quantum effects are taken into consideration. These additional hairs of black hole, if exist, may provide valuable information to reveal the deepest mystery of the universe: quantum theory of gravity. In this thesis, we try to relate the hypothetical extra hairs of black hole with the ob- servational evidence as gravitational waves – another prediction of general relativity and are recently detected. In Chapter I, we provide a pedagogical introduction to the black hole hairs introduced by modified gravity and quantum mechanics, and lay out a mathematical framework to describe the gravitational wave emission with the existence of near-horizon quantum hair. In Chapter II we show that in scalar-tensor theory of gravity, the formation process of a black hole from gravitational collapse is accompanied with the emission of scalar hair. This mechanism gives rise to a scalar type memory effect of gravitational wave, which does not exist in general relativity. This phenomenon can further be used to study the parameter space of the scalar-tensor theory. In Chapter III, we find the scalar gravitational memory effect from stellar collapses provide the strongest sources for the stochastic gravita- tional wave background with scalar polarization in Brans-Dicke theory. The energy density spectrum for this background is provided and its model dependencies are studied. In Chapter IV, we provide a Green’s function method to study the echoes, which are the gravitational waves reflected by the quantum hair near the event hori- zon of a black hole. In Chapter V, we build phenomenological models to describe the near-horizon quantum hair and predict its implication to the binary black hole stochastic gravitational wave background. Our study indicates that the existence of the quantum hair will significantly increases such a background and pins down the most relevant model parameter to be the area under the effective potential. Further, we also demonstrate that the result is rather robust against the uncertainties about the nature of the near-horizon quantum hair. In the end, a field theory based treatment to the gravitational waves in general relativity is provided as the appendix.</p

Scalar stochastic gravitational-wave background in Brans-Dicke theory of gravity

We study the scalar stochastic gravitational-wave background (SGWB) from astrophysical sources, including compact binary mergers and stellar collapses, in the Brans-Dicke theory of gravity. By contrast to tensor waves, the scalar SGWB predominantly arises from stellar collapses. These collapses not only take place at higher astrophysical rates but also emit more energy. This is because, unlike tensor radiation which mainly starts from quadrupole order, the scalar perturbation can be excited by changes in the monopole moment. In particular, in the case of stellar collapse into a neutron star or a black hole, the monopole radiation, at frequencies below 100 Hz, is dominated by the memory effect. At low frequencies, the scalar SGWB spectrum follows a power law of Ω_S ∝ f^α, with α = 1. We predict that Ω_S is inversely proportional to the square of ω_(BD) + 2, with (ω_(BD) + 2)^2Ω_S (f = 25 Hz) = 2.8 × 10^(−6). We also estimate the detectability of the scalar SGWB for current and third-generation detector networks and the bound on ω_(BD) that can be imposed from these observations

A recipe for echoes from exotic compact objects

Gravitational wave astronomy provides an unprecedented opportunity to test the nature of black holes and search for exotic, compact alternatives. Recent studies have shown that exotic compact objects (ECOs) can ring down in a manner similar to black holes, but can also produce a sequence of distinct pulses resembling the initial ringdown. These “echoes” would provide definite evidence for the existence of ECOs. In this work we study the generation of these echoes in a generic, parametrized model for the ECO, using Green’s functions. We show how to reprocess radiation in the near-horizon region of a Schwarzschild black hole into the asymptotic radiation from the corresponding source in an ECO spacetime. Our methods allow us to understand the connection between distinct echoes and ringing at the resonant frequencies of the compact object. We find that the quasinormal mode ringing in the black hole spacetime plays a central role in determining the shape of the first few echoes. We use this observation to develop a simple template for echo waveforms. This template preforms well over a variety of ECO parameters, and with improvements may prove useful in the analysis of gravitational waves

Gravitational wave memory: A new approach to study modified gravity

It is well known that two types of gravitational wave memory exist in general relativity (GR): the linear memory and the nonlinear, or Christodoulou, memory. These effects, especially the latter, depend on the specific form of the Einstein equation. It can then be speculated that, in modified theories of gravity, the memory can differ from the GR prediction and provides novel phenomena to study these theories. We support this speculation by considering scalar-tensor theories, for which we find two new types of memory: the T memory and the S memory, which contribute to the tensor and scalar components of a gravitational wave, respectively. Specifically, the former is caused by the burst of energy carried away by scalar radiation, while the latter is intimately related to the no scalar hair property of black holes in scalar-tensor gravity. We estimate the size of these two types of memory in gravitational collapses and formulate a detection strategy for the S memory, which can be singled out from tensor gravitational waves. We show that (i) the S memory exists even in spherical symmetry and is observable under current model constraints, and (ii) while the T memory is usually much weaker than the S memory, it can become comparable in the case of spontaneous scalarization

Searching for Near-Horizon Quantum Structures in the Binary Black-Hole Stochastic Gravitational-Wave Background

Quantum gravity corrections have been speculated to lead to modifications to space-time geometry near black-hole horizons. Such structures may reflect gravitational waves, causing echoes that follow the main gravitational waves from binary black-hole coalescence. By studying two phenomenological models of the near-horizon structures under the Schwarzschild approximation, we show that such echoes, if they exist, will give rise to a stochastic gravitational-wave background, which is very substantial if the near-horizon structure has a near-unity reflectivity for gravitational waves, readily detectable by Advanced LIGO. In case the reflectivity is much less than unity, the background will mainly be arising from the first echo, with a level proportional to the power reflectivity of the near-horizon structure, but robust against uncertainties in the location and the shape of the structure—as long as it is localized and close to the horizon. Sensitivity of third-generation detectors allows the detection of a background that corresponds to power reflectivity ∼3×10^(−3), if uncertainties in the binary black-hole merger rate can be removed. We note that the echoes do alter the f^(2/3) power law of the background spectra at low frequencies, which is rather robust against uncertainties