General Relativity and Quantum Cosmology (gr-qc)

Abstract: Ultralight bosons are well-motivated particles from various physical and cosmological theories, and can be spontaneously produced during the superradiant process, forming a dense hydrogen-like cloud around the spinning black hole. After the growth saturates, the cloud slowly depletes its mass through gravitational-wave emission. In this work we study the orbit dynamics of a binary system containing such a gravitational atom saturated in various spin-0,1,2 superradiant states, taking into account both the effects of dynamical friction and the cloud mass depletion. We estimate the significance of mass depletion, finding that although dynamical friction could dominate the inspiral phase, it typically does not affect the outspiral phase driven by the mass depletion. Focusing on the large orbit radius, we investigate the condition to observe the outspiral, and the detectability of the cloud via pulsar-timing signal in the case of black hole-pulsar binary.

Abstract: Interspacecraft ranging is crucial for the suppression of laser frequency noise via time-delay interferometry (TDI). So far, the effect of on-board delays and ambiguities in the LISA ranging observables was neglected in LISA modelling and data processing investigations. In reality, on-board delays cause offsets and timestamping delays in the LISA measurements, and PRN ranging is ambiguous, as it only determines the range up to an integer multiple of the pseudo-random noise (PRN) code length. In this article, we identify the four LISA ranging observables: PRN ranging, the sideband beatnotes at the interspacecraft interferometer, TDI ranging, and ground-based observations. We derive their observation equations in the presence of on-board delays, noise, and ambiguities. We then propose a three-stage ranging sensor fusion to combine these observables in order to gain optimal ranging estimates. We propose to calibrate the on-board delays on ground and to compensate the associated offsets and timestamping delays in an initial data treatment (stage 1). We identify the ranging-related routines, which need to run continuously during operation (stage 2), and implement them numerically. Essentially, this involves the reduction of ranging noise, for which we develop a Kalman filter combining the PRN ranging and the sideband beatnotes. We further implement crosschecks for the PRN ranging ambiguities and offsets (stage 3). We show that both ground-based observations and TDI ranging can be used to resolve the PRN ranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN ranging offsets.

Abstract: We re-analyze the far zone contribution to the two-body conservative dynamics arising from interaction between radiative and longitudinal modes, the latter sourced by mass and angular momentum, which in the mass case is known as tail process. We verify the expected correspondence between two loop self-energy amplitudes and the gluing of two classical (one leading order, one at one loop) emission amplitudes. In particular we show that the factorization of the self-energy amplitude involving the angular momentum is violated when applying standard computation procedures, due to a violation of the Lorentz gauge condition commonly adopted in perturbative computations. We show however that a straightforward fix exists, as the violation corresponds to a consistent anomaly, and it can be re-absorbed by the variation of a suitable action functional.

Abstract: Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR). We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also discuss some specific combinations of these three terms whose investigation might deserve priority from the quantum-gravity perspective.

Abstract: We consider the equations of linearised gravity on the Schwarzschild spacetime in a double null gauge. Applying suitably commuted versions of the conservation laws derived in earlier work of the second author we establish control on the gauge invariant Teukolsky quantities $\alpha^{[\pm 2]}$ without any reference to the decoupled Teukolsky wave equation satisfied by these quantities. More specifically, we uniformly bound the energy flux of all first derivatives of $\alpha^{[\pm 2]}$ along any outgoing cone from an initial data quantity at the level of first derivatives of the linearised curvature and second derivatives of the linearised connection components. Analogous control on the energy fluxes along any ingoing cone is established a posteriori directly from the Teukolsky equation using the outgoing bounds.

Abstract: In this paper, we study the canonical energy associated with solutions to the linearised vacuum Einstein equation on a stationary spacetime. The main result of this paper establishes, in the context of the $4$-dimensional Schwarzschild exterior, a direct correspondence between the conservation law satisfied by the canonical energy and the conservation laws deduced by Holzegel for gravitational perturbations in double null gauge. Since the latter exhibit useful coercivity properties (leading to energy and pointwise boundedness statements) we obtain coercivity results for the canonical energy in the double null gauge as a corollary. More generally, the correspondence suggests a systematic way to uncover coercivity properties in the conservation laws for the canonical energy on Kerr.