Table of contents

A set of temporal singularities (transients) in the mass-energy density and pressure, bearing a specific mathematical structure which represents a new solution to the continuity equation (i.e. conservation of mass-energy) and satisfying the strong energy condition, is proposed to account for the expansion history of a homogeneous Universe, and the formation and binding of large scale structures as a continuum approximation of their cumulative effects. These singularities are unobservable because they occur rarely in time and are unresolvably fast, and that could be the reason why dark matter and dark energy have not been found. Implication on inflationary cosmology is discussed. The origin of these temporal singularities is unknown, safe to say that the same is true of the moment of the Big Bang itself. This work complements a recent paper, where a topological defect in the form of a spatial, spherical shell of density singularity giving rise to a 1/r attractive force (to test particles of positive mass) but zero integrated mass over a large volume of space, was proposed to solve the dark matter problem in bound structures but not cosmic expansion. The idea also involved a negative density, which is not present in the current model.

We present a comprehensive study of the C-metric in $2+1$ dimensions, placing it within a shell of stress energy and matching it to an exterior vacuum anti-de Sitter metric. The $2+1$ C-metric is not circularly symmetric and hence neither are the constructed shells, which instead take on a cuspoidal or teardrop shape. We interpret the stress energy of the shells as a perfect fluid, calculating the energy density and pressure. For accelerating particles (Class I), we find the stress energy is concentrated on the part of shell farthest from the direction of acceleration and always respects the strong and weak energy conditions. For accelerating black holes (Class I$_{\mathrm{C}}$, II, and III), the shell stress energy may either respect or violate the energy conditions depending on the parameter of the exterior metric—between the two regimes lies a critical value of the external parameter for which the shell stress energy vanishes, leading to new solutions of Einstein's field equations, which fall into three categories: an accelerated black hole pulled by a finite-length string with a point particle at the other end, an accelerated black hole pushed by a finite-length strut with a point particle at the other end, and an accelerated black hole pushed from one side by a finite-length strut and pulled from the other by a finite-length string, each with a point particle at the other end.

We recompute ab initio the drift of comoving sources in axial Bianchi I universes. Our result resolves the long-standing disagreement between the computations by Quercellini et al from 2009 and by Marcori et al from 2018 in favor of the latter. These computations have a potential impact on Gaia data analysis and cosmological parameter estimation.

The Kerr separatrix is a boundary in parameter space that separates bound orbits from plunging orbits in the Kerr black hole space-time. Recently, Stein and Warburton found a polynomial equation for the location of the separatrix, for two different choices of inclination parameter. Following a method of Levin and Perez-Giz developed for the equatorial case, we use a correspondence between homoclinic orbits and unstable spherical orbits to derive explicit solutions to the separatrix polynomials. These solutions are parametrised in terms of the radius of the unstable spherical orbit.

When numerically solving Einstein's equations for the evolution of binary black holes, physical imperfections in the initial data manifest as a transient, high-frequency pulse of 'junk radiation.' This unphysical signal must be removed before the waveform can be used. Improvements in the efficiency of numerical simulations now allow waveform catalogs containing thousands of waveforms to be produced. Thus, an automated procedure for identifying junk radiation is required. To this end, we present a new algorithm based on the empirical mode decomposition (EMD) from the Hilbert–Huang transform. This approach allows us to isolate and measure the high-frequency oscillations present in the measured irreducible masses of the black holes. The decay of these oscillations allows us to estimate the time from which the junk radiation can be ignored. To make this procedure more precise, we propose three distinct threshold criteria that specify how small the contribution of junk radiation has to be before it can be considered negligible. We apply this algorithm to 3403 BBH simulations from the Simulating eXtreme Spacetime catalog to find appropriate values for the thresholds in the three criteria. We find that this approach yields reliable decay time estimates, i.e. when to consider the simulation physical, for $\gt$98.5% of the simulations studied. This demonstrates the efficacy of the EMD as a suitable tool to automatically isolate and characterize junk radiation in the simulation of binary black hole systems.

The sensitivity of the second generation ground-based gravitational-wave detectors is mostly limited by quantum noise (QN). The injection of frequency-dependent squeezed vacuum states into the output port of the interferometer has been shown to reduce QN across the entire detector bandwidth. Frequency dependent squeezed states are generated by reflecting a frequency independent squeezed states off a detuned optical cavity: the phase response of the cavity rotates the squeeze angle as a function of frequency. The precision of the longitudinal control of the such cavity, known as filter cavity, is one of the key parameters affecting the QN suppression factor. The target longitudinal control precision was achieved by simultaneously acting on both the cavity length and the frequency of the squeezing main laser. In this scenario, the analysis of this system requires a Multiple-Input Multiple-Output (MIMO) system model. In this work, we demonstrate that a MIMO model is required and show that a MIMO system identification technique is effective to characterize the system and improve its robustness. Ultimately we show that these techniques allow the design of robust filters that can keep the cavity residual length fluctuations below 1 pm, allowing for a QN reduction of 4.5 dB at high frequencies and 2 dB at low frequencies in the Advanced Virgo interferometer.

We explicitly determine all shear-free null hypersurfaces embedded in an Einstein spacetime, including vacuum asymptotically flat spacetimes. We characterize these hypersurfaces as oriented 3-dimensional manifolds where each is equipped with a coframe basis, a structure group and a connection. Such manifolds are known as null hypersurface structures (NHSs). The coframe and connection one-forms for an NHS appear as solutions to the projection of the Cartan structure equations onto the null hypersurface. We then show that each NHS corresponds to a Carrollian structure equipped with a unique pair of Ehresmann connection and affine connection.

The stochastic gravitational wave (GW) background recently discovered by several pulsar timing array experiments is consistent with arising from a population of coalescing super-massive black hole binaries. The amplitude of the background is somewhat higher than expected in most previous population models or from the local mass density observations. Such binaries are expected to be produced in galaxy mergers, which are also thought to trigger bright quasar activity. Under the assumptions that (i) a fraction $f_{\mathrm{bin}}\sim 1$ of all quasars are associated with mergers, (ii) the typical quasar lifetime is $t_{\mathrm{Q}} \sim 10^8~\textrm{yr}$, and (iii) adopting Eddington ratios $f_{\mathrm{Edd}}\sim 0.25$ for the luminosity of quasars, we compute the GW background associated directly with the empirically measured quasar luminosity function. This approach bypasses the need to model the cosmological evolution of black holes or galaxy mergers from simulations or semi-analytical models. We find the amplitude matching the value measured by NANOGrav. Our results are consistent with most quasars being associated with black hole binaries and being the sources of the GW background, and imply a joint constraint on $t_{\mathrm{Q}}$, $f_{\mathrm{Edd}}$ and the typical mass ratio $q\equiv M_2/M_1$. The signal in this case would be dominated by relatively distant ${\sim}10^9\mathrm{M_\odot}$ sources at $z\approx 2-3$, at the peak of quasar activity. Similarly to other models, our results remain in tension with the local super-massive black hole mass density.

As pulsar timing arrays (PTAs) transition into the detection era of the stochastic gravitational wave background (GWB), it is important for PTA collaborations to review and possibly revise their observing campaigns. The detection of a 'single source' would be a boon for gravitational astrophysics, as such a source would emit gravitational waves for millions of years in the PTA frequency band. Here we present generic methods for studying the effects of various observational strategies, taking advantage of detector sensitivity curves, i.e. noise-averaged, frequency-domain detection statistics. The statistical basis for these methods is presented along with myriad examples of how to tune a detector towards single, deterministic signals or a stochastic background. We demonstrate that trading observations of the worst pulsars for high cadence campaigns on the best pulsars increases sensitivity to single sources at high frequencies while hedging losses in GWB and single source sensitivity at low frequencies. We also find that sky-targeted observing campaigns yield minimal sensitivity improvements compared with other PTA tuning options. Lastly, we show the importance of the uncorrelated half of the GWB, i.e. the pulsar-term, as an increasingly prominent sources of noise and show the impact of this emerging noise source on various PTA configurations.

Tilt-to-length (TTL) noise, caused by angular jitter and misalignment, is a major noise source in the inter-satellite interferometer for gravitational wave detection. However, the required level of axis alignment of the optical components is beyond the current state of the art. A set of optical parallel plates, called beam alignment mechanism (BAM), is proposed by LISA to compensate for the alignment error. In this paper, we show a prototype design of the BAM and demonstrate its performance in a ground-based optical system. We derive the BAM theoretical model, which agrees well with the numerical simulation. Experimental results reveal that the BAM can achieve lateral displacement compensation of the optical axis with a resolution of 1 µm across a range of about 0.5 mm. Furthermore, the TTL coefficient is reduced from about 0.3 mm rad⁻¹ to about 5 µm rad⁻¹, satisfying the preliminary requirements for LISA and TianQin. These findings confirm the efficacy of the BAM in suppressing TTL noise, offering a promising solution for space-based gravitational wave detection.

We present a set of noncommuting tetrad-shift symmetries in 4D gravity in tetrad-connection variables, which allow expressing diffeomorphisms as composite transformations. Working on the phase space level for finite regions, we pay close attention to the corner piece of the generators, discuss various possible charge brackets, relative definitions of the charges, coupling to spinors and relations to other charges. What emerges is a picture of the symmetries and edge modes of gravity that bears local resemblance to a Poincare group $SO(1,3)\ltimes \mathbb{R}^{1,3}$, but possesses structure functions. In particular, we argue that the symmetries and charges presented here are more amenable to discretisation, and sketch a strategy for this charge algebra, geared toward quantum gravity applications.

Fuzzy dark matter (FDM) is among the most suitable candidates to replace WIMPs and to resolve the puzzling mystery of dark matter (DM). A galactic DM halo made of these ultralight bosonic particles leads to the formation of a solitonic core surrounded by quantum interference patterns that, on average, reproduce a Navarro-Frenk-White-like mass density profile in the outskirts of the halo. The structure of such a core is determined once the boson mass and the total mass of the halo are set. We investigated the capability of future astrometric Theia-like missions to detect the properties of such a halo within the FDM model, namely the boson mass and the core radius. To this aim, we built mock catalogs containing three-dimensional positions and velocities of stars within a target dwarf galaxy. We exploited these catalogs using a Markov Chain Monte Carlo algorithm and found that measuring the proper motion of at least 2000 stars within the target galaxy, with uncertainty $\sigma_\textrm{v} \unicode{x2A7D} 3$ km s⁻¹ on the velocity components, will constrain the boson mass and the core radius with 3% accuracy. Furthermore, the transition between the solitonic core and the outermost NFW-like density profile could be detected with an uncertainty of 7%. Such results would not only help to confirm the existence of FDM, but they would also be useful for alleviating the current tension between galactic and cosmological estimations of the boson mass, or demonstrating the need for multiple particles with a broad mass spectrum as naturally arise String Axiverse.

Viscous fluids can dissipate and alter the propagation of gravitational waves (GWs), as well as modify the relaxation and stability properties of self-gravitating fluids. This is particularly relevant in order to understand the relaxation to equilibrium of neutron stars, and their GW emission. Here we study the linearized theory of perturbations of spherically symmetric self-gravitating fluids, treating only the radiative modes. Dissipative effects are included through the hydrodynamics theory of Bemfica, Disconzi, Noronha and Kovtun (BDNK). This theory has been shown to be causal and stable, despite involving only first order gradients. We show how the problem reduces to two coupled wave equations in the axial sector, one of them associated to a novel viscous mode, and including explicitly dissipative terms. In the polar sector we reduce the problem to five coupled wave equations and one additional constraint. We comment on their causal structure, and recover the causality bounds of the BDNK theory.

We investigate the dynamics of fermion localization within the framework of $f(T, B)$ gravity featuring non-minimal couplings. Starting from the Dirac action for a spin-$1/2$ fermion in a five-dimensional spacetime governed by torsional $f(T, B)$ gravity, we derive the Dirac equation and we explore its solutions under various non-minimal coupling functions. We examine two realistic forms of the torsional non-minimal coupling and reveal distinct behaviors that impact the localization of both massless and massive fermionic modes on the brane. Additionally, we employ probabilistic measurements, including Shannon entropy theory, Fisher information theory, and relative probability, to analyze the localization of these fermionic modes. The observed effects offer potential insights into probing torsional modifications.

We analyze scalar field dark energy models minimally and non-minimally coupled to gravity, postulating that a Yukawa-like interacting term is in form equivalent for general relativity, teleparallel and symmetric-teleparallel theories. Our analysis is pursued within two scalar field representations, where a quintessence and phantom pictures are associated with quasiquintessence and quasiphantom exotic fields. In the latter, we suggest how the phion-pressure can be built up without exhibiting a direct kinetic term. Accordingly, the stability analysis reveals that this quasiquintessence field provides a viable description of the Universe indicating, when minimally coupled, how to unify dark energy and dark matter by showing an attractor point where $w_{\phi} = 0$. Conversely, in the non-minimally coupling, the alternative field only leaves an attractor where dark energy dominates, mimicking de facto a cosmological constant behavior. A direct study is conducted comparing the standard case with the alternative one, overall concluding that the behavior of quintessence is well established across all the gravity scenarios. However, considering the phantom field non-minimal coupled to gravity, the results are inconclusive for power-law potentials in Einstein theory, and for the inverse square power potential in both teleparallel and symmetric-teleparallel theories. Finally, we study the growth of matter perturbations and establish that only the fifth power and quadratic potentials, when used to describe quasiphantom field minimally coupled to gravity, exhibit behavior similar to the ΛCDM model.

In a generalized parameter space, regular black holes can be regarded as non-singular solutions under specific parameters in Einstein gravity theory coupled with non-linear electromagnetic fields. Following this concept, we investigate the thermodynamic states and phase transitions of Bardeen–AdS-class black holes, revealing that the system can be classified into two categories, Type I and Type II, based on whether it adopts a pure Bardeen–AdS spacetime without event horizons or a Bardeen–AdS black hole as its phase state, each exhibiting distinct thermodynamic properties. If one includes the Bardeen–AdS black holes in the system (Type I), there will be three distinct black hole states and the phase transitions between them are analogous to the Reissner–Nordstrom–AdS black holes. On the other hand, if the pure Bardeen–AdS spacetime is included (Type II), an additional tiny black hole state emerges. A phase transition reminiscent of the Hawking–Page transition was found. Significantly, in this scenario, thermodynamical characteristic curves exhibit discontinuous behavior, which attributes to the multiple horizons. The presence of a Bardeen–AdS black hole within the phase structure of the Bardeen–AdS-class black hole profoundly modifies the thermodynamical properties of the system, highlighting the novel aspects of regular black holes.

We study the inflationary phenomenology of a rescaled Einstein–Gauss–Bonnet (EGB) gravity. In this framework, the gravitational constant of the Einstein–Hilbert term is rescaled due to effective terms active in the high curvature era. Basically, the total theory is an $F(R,G,\phi)$ theory with the Gauss–Bonnet part contributing only a non-minimal coupling to the scalar field, so it is a theory with string theory origins and with a non-trivial F(R) gravity part. The F(R) gravity part in the high curvature regime contributes only a rescaled Einstein–Hilbert term and thus the resulting theory is effectively a rescaled version of a standard EGB theory. We develop the formalism of rescaled EGB gravity, taking in account the GW170817 constraints on the gravitational wave speed. We show explicitly how the rescaled theory affects directly the primordial scalar and tensor perturbations, and how the slow-roll and observational indices of inflation are affected by the rescaling of the theory. We perform a thorough phenomenological analysis of several models of interest and we show that is it possible to obtain viable inflationary theories compatible with the latest Planck data. Also among the studied models there are cases that yield a relatively large blue tilted tensor spectral index and we demonstrate that these models can lead to detectable primordial gravitational waves in the future gravitational wave experiments. Some of the scenarios examined, for specific values of the reheating temperature may be detectable by SKA, LISA, BBO, DECIGO and the Einstein Telescope.

A novel approach to the class of cosmic barotropic fluids in which the speed of sound squared is defined as a function of the equation of State parameter, so called $c_s^2(w)$ models, is examined. For this class of models, a new analytical reconstruction method is introduced for finding their equivalent purely kinetic k-essence formulation. The method is explicitly demonstrated for several $c_s^2(w)$ models. A distinguished feature of the studied models is a peak in $c_s^2$ during cosmic expansion. A possible role that such model features could play in understanding of so far unexplained aspects of cosmic evolution is discussed. The application of the obtained explicit or closed form solutions in understanding dark sector unification models is outlined.

The connection between classical thermodynamics and black hole horizons is a fundamental topic in gravitational physics, offering a potential pathway to understanding quantum aspects of gravity. However, while black hole mechanics exhibits well-known thermodynamic parallels, a rigorous geometric interpretation of thermodynamic variables directly from the field equations warrants further research. In this manuscript, we present a thermodynamic formulation of the field equations through the decomposition of the Riemann tensor, employing the Geroch-Held-Penrose (GHP) formalism, to clarify a strong correspondence between black hole thermodynamic variables and geometrical quantities derived from horizon geometry. Our analysis reveals an intrinsic connection between the Penrose and Rindler K-curvature and the Smarr relation, motivating a revised definition of both trapping gravity and black hole internal energy. Additionally, we derive through this GHP formalism the Smarr formula for the Reissner–Nördstrom black hole cointained in an AdS spacetime and we explore the implications of this relationship for black holes with exotic topologies and in the context of extended theories, exemplified by f(R) gravity. We also briefly analyze this relation in more general configurations, such as Taub-NUT spacetimes. These findings suggest a deeper geometrical basis for black hole thermodynamics, potentially advancing our understanding of gravitational energy, horizon entropy, and their significance within quantum gravity frameworks.

We present a unitary phenomenological model for black hole (BH) evaporation based on the analogy of the laboratory process of spontaneous parametric down conversion (Alsing 2015 Class. Quantum Grav.32 075010; Alsing and Fanto 2016 Class. Quantum Grav.33 0150005) when the BH (pump) is allowed to deplete to zero mass. The model incorporates an additional new feature that allows for the interior Hawking partner-particles (idlers) behind the horizon to further generate new Hawking particle pairs of lower energy, one of which remains behind the horizon, and the other that adds to the externally emitted Hawking radiation (signals) outside the horizon. This model produces a Page curve for the evolution of the reduced density matrices for the evaporating BH internal degrees of freedom entangled with the generated Hawking radiation pairs entangled across the horizon. The Page curve yields an entropy that rises at early times during the evaporation process as Hawking pairs are generated, reaches a peak midway through the evolution, and then decays to zero upon complete evaporation of the BH. The entire system remains in a pure state at all times undergoing unitary (squeezed state) evolution, with the initial state of the BH modeled as a bosonic Fock state of large, but finite number ${n_{p0}}$ of particles. For the final state of the system, the BH reaches the vacuum state of zero mass, while the external Hawking radiation carries away the total energy of the initial BH. Inside the horizon there remains ${n_{p0}}$ Hawking partner-particles of vanishingly small total energy, reminiscent of the 'soft-hair' (zero energy) qubit model of Hotta et al (2018 Phys. Rev. Lett.120 181301), but now from a Hamiltonian for squeezed state generation perspective. The model presented here can be readily extended to encompass arbitrary initial pure states for the BH, and in falling matter.

No-hair theorems are uniqueness results constraining the form of the metric of black holes in general relativity. These theorems are typically formulated under idealized assumptions, involving a mixture of local (regularity of the horizon) and global aspects (everywhere vacuum spacetime and asymptotic flatness). This limits their applicability to astrophysical scenarios of interest such as binary black holes and accreting systems, as well as their extension to horizonless objects. A previous result due to Gürlebeck constrains the asymptotic multipolar structure of static spacetimes containing black holes surrounded by matter although not revealing the possible structure of the metric itself. In this work, we disentangle some of these assumptions in the static and axisymmetric case. Specifically: (i) we show that only a one-parameter family of black-hole geometries is compatible with a given external gravitational field, (ii) we also analyze the case in which the central object is close to forming an event horizon but is still horizonless and show that the deviations from the natural black-hole shape have to die off as one approaches the black hole limit under the physical principle that curvatures are bounded.

Regular rotating black holes are usually described by a metric of the Kerr–Schild form with a particular mass function that is chosen to avoid the ring singularity of the Kerr metric and which approaches the Kerr metric at the asymptotic limit. However, as is well known, even for a class of well-behaved mass functions, the curvature scalars present a discontinuity in the equatorial plane at the ring. This discontinuity has been associated with the presence of a string of matter that joins the interior and exterior regions along the equatorial plane. By using the Darmois–Israel junction conditions, we analyze all four possible combinations of the normal vector orientations on each side of the ring, construct the complete stress-energy momentum tensor of the string, and interpret each resulting solution. We show that, out of the four possibilities, only one of the four models for the string solution at the ring yields the appropriate asymptotic geometry. In such a case, the string bears a fluid with nonzero pressure, but with a vanishing line energy density, and it does not rotate at all. Finally, taking an appropriate metric for the exterior region, we also discuss a different scenario in which the matter source at the ring is a rotating lightlike fluid.

We study the boson star solutions in a theory involving a complex scalar field in a conical scalar field potential: $V(|\Phi|) : = 2 \lambda |\Phi|$ in the presence of non-minimal gravity given by the term: $(\xi R | \Phi|^2 )$ in the action, where ξ is a constant parameter that couples the complex scalar field Φ with the Ricci scalar R and is treated, in our work, as a free parameter. The theory has one more free parameter denoted by $\alpha : = 8\pi G \lambda^2 / \omega^4$ (where ω is the frequency of the complex scalar field). Here G is the Newton's gravitational constant, λ is a constant used in the definition of the scalar field potential. We find that the acceptable boson star solutions exist in this theory that involves non-minimal gravity as above. For obtaining the acceptable boson star solutions, we obtain the domain of existence of our free parameters ξ and α for which the boson star solutions exist and then study the various properties of the boson star solutions. In our studies, as we trace the evolution of our solutions along the relevant path, emanating from the solutions corresponding to the absence of gravitational field, we observe a steady increase in mass with radius. Employing principles from catastrophe theory, we find that this trajectory remains stable until it reaches the maximum mass value. This leads to the characteristic spiraling behavior of the mass-radius curve, a well-known feature in compact star models signaling the onset of instability.