In this paper we will explore two different proposals for the action for causal sets: the Benincasa–Dowker action [1], and a modified version of the chain action [2]. We propose a variational principle for two-dimensional causal sets and use it for both actions to determine which causal sets at least on average satisfy a discrete version of the Einstein equation. Specifically, we test this method on

We report the mirror suspension design for large-scale cryogenic gravitational wave telescope, KAGRA, during bKAGRA phase 1. Mirror thermal noise is one of the fundamental noises for room-temperature gravitational-wave detectors such as Advanced LIGO and Advanced Virgo. Thus, reduction of thermal noise is required for further improvement of their sensitivity. One effective approach for reducing thermal

An accelerated boundary correspondence (i.e. a flat spacetime accelerating mirror trajectory) is derived for the Kerr spacetime, with a general formula that ranges from the Schwarzschild limit (zero angular momentum) to the extreme maximal spin case (yielding asymptotic uniform acceleration). The beta Bogoliubov coefficients reveal the particle spectrum is a Planck distribution at late times with temperature

In four dimensions complexified general relativity (GR) can be non-trivially deformed: there exists an (infinite-parameter) set of modifications all having the same count of degrees of freedom. It is trivial to impose reality conditions that give versions of the deformed theories corresponding to Riemannian and split metric signatures. We revisit the Lorentzian signature case. To make the problem tractable

Theories of quantum gravity based on the holographic principle predict the existence of quantum fluctuations of distance measurements that accumulate and exhibit correlations over macroscopic distances. This paper models an expected signal due to this phenomenology, and details the design and estimated sensitivity of co-located twin table-top 3D interferometers being built to measure or constrain it

In this work, the field of a gravitational shockwave generated by a massless point-like particle is calculated at the event horizon of a stationary Kerr–Newman black hole. Using the geometric framework of generalized Kerr–Schild deformations in combination with the spin-coefficient formalism of Newman and Penrose, it is shown that the field equations of the theory, at the event horizon of the black

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyse the future asymptotics of models which exhibit oscillatory behaviour, we provide a theorem concerning the large-time behaviour for solutions of a general class of systems. We thus propose our result to be applicable to a wide range of problems in spatially homogenous cosmology

The apparent missing mass in Galaxies and Galaxy clusters, commonly viewed as evidence for dark matter, could possibly originate from gradients in the gravitational coupling parameter, G, and active gravitational mass, M act, rather than hypothetical beyond-the-standard-model particles. We argue that in (the weak field limit of) a Weyl-invariant extension of general relativity, one can simply affect

In the context of the weak gravity conjecture the notion of quasi-extremality for black holes and branes was recently defined as the property of having either vanishing horizon size or surface gravity. It was derived that such objects obey a no-force condition. In this short note I present a simplified derivation that is essentially present in the formalism of timelike reduction pioneered by Breitenlohner

Recently, a generalised solution for Einstein equations for a rotating black hole, surrounded by matter field was proposed, which is the Kerr–Newman spacetime with an anisotropic matter [Phys. Rev. D. 101 064067]. Due to the negative radial pressure of the anisotropic matter, the solution possesses an additional hair along with the conventional mass, charge and spin. In this article we show that, this

The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a solution with a late-time permanent spike. We achieve this by applying Stephani’s transformation with the rotational Killing vector field (KVF) of the locally rotationally

It is known that the regular Hayward black hole is an exact solution of the Einstein equations which describes a non-rotating magnetic monopole governed by a non linear Lagrangian. We consider the problem of electromagnetic perturbations of such an object in order to study its stability.

A numerical study of the Einstein field equations, based on the 3 + 1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the Arnowitt–Deser–Misner (ADM) and the conformal Baumgarte–Shapiro–Shibata–Nakamura (BSSN) approach. The numerical code is based on the Fourier decomposition, accompanied by different

The gravitational deflection of light in the strong field limit is an important test for alternative theories of gravity. However, solutions for the metric that allow for analytic computations are not always available. We implement a hybrid analytic-numerical approximation to determine the deflection angle in static, spherically symmetric spacetimes. We apply this to a set of numerical black hole solutions

We propose a new approach to find magnetically-dominated force-free (FF) magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular FF magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength.

Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the (quasi-)position representation acquires numerous issues, source of misunderstandings. In this work, we review these issues, clarifying some of the aspects of minimal

The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone have previously been studied, the present work continues along this path by providing explicit cosmological applications of the Hawking energy associated with a lightcone. Firstly, it is shown

We consider the inspiral of black holes carrying U(1) charge that is not electromagnetic, but corresponds to some dark sector. In the weak-field, low-velocity regime, the components follow Keplerian orbits. We investigate how the orbital parameters evolve for dipole-dominated emission and find that the orbit quickly circularises, though not as efficiently as for a gravitationally dominated emission

We consider the chiral cosmological model consisting of two scalar fields minimally coupled to gravity. In the context of a Friedmann–Lematre–Robertson–Walker (FLRW) spacetime, and for massless fields in the presence of a cosmological constant, we present the general solution of the field equations. The minisuperspace configuration that possesses maximal symmetry leads to scenarios which—depending

Numerical simulations of extreme mass ratio inspirals, the most important sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations of the self-force acting on point particles orbiting supermassive black holes. Such equations are distributionally sourced, and

The Tolman–Oppenheimer–Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center. Hence, the thermodynamic consistency

We perform a detailed analysis of the dynamics of a chiral-like cosmological model where the scalar fields can have negative kinetic terms. In particular, we study the asymptotic dynamics for the gravitational field equations for four different models in a spatially flat Friedmann–Lematre–Robertson–Walker (FLRW) background space. When one of the scalar fields is phantom, we show that the cosmological

Advanced Virgo end benches were a significant source of scattered light noise during the third observing run that lasted from April 1 2019 until March 27 2020. We describe how that noise could be subtracted using auxiliary channels during the online strain data reconstruction. We model in detail the scattered light noise coupling and demonstrate that further noise subtraction can be achieved. We also

Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, , of finite volume equals the Einstein Hilbert action of plus the volume of the co-dimension 2 intersection of the future boundary with the past boundary. We give the heuristic argument for this conjecture and analyse some examples

The gravitational-wave detectors outputs from the LIGO and Virgo collaborations have been a source of scientific results of prime importance in various domains such as astrophysics, cosmology or fundamental physics. With the upgrades of the detectors and their improved sensitivities, new challenges are set for these instruments calibration. A calibration method based on the local variations of the

Solitons in space-time capable of transporting time-like observers at superluminal speeds have long been tied to violations of the weak, strong, and dominant energy conditions of general relativity. The negative-energy sources required for these solitons must be created through energy-intensive uncertainty principle processes as no such classical source is known in particle physics. This paper overcomes

We describe a non-minimal higher-derivative extension of Einstein–Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static, spherically symmetric solution of this theory that reduces to the Reissner–Nordstrm one at weak coupling, but in which the singularity at r = 0 is regularized for arbitrary

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are potentially interesting ingredients in the construction of quantum curvature observables. Motivated by recent developments in nonperturbative quantum gravity, we establish

KAGRA is an underground interferometric gravitational wave detector which is currently being commissioned. This detector relies on high-performance vibration-isolation systems to suspend its key optical components. These suspensions come in four different configurations, of which the type-B is used for the beam splitter and signal recycling mirrors. The type-B suspension comprises the payload, three

Einstein–Rosen waves with two polarizations are cylindrically symmetric solutions to vacuum Einstein equations. Einstein equations in this case reduce to an integrable system. In 1971, Geroch has shown that this system admits an infinite-dimensional group of symmetry transformations known as the Geroch group. The phase space of this system can be parametrized by a matrix-valued function of spectral

As the sensitivities of LIGO, Virgo and KAGRA detectors improve, calibration of the interferometers (ITFs) output is becoming more and more important and may impact scientific results. For the observing run O3, Virgo used for the first time photon calibrators (PCals) to calibrate the ITF, using radiation pressure of a modulated auxiliary laser beam impinging on the Advanced Virgo end mirrors. Those

The approach of extended irreversible thermodynamics consists of promoting the dissipative fluxes to non-equilibrium thermodynamic variables. In a relativistic context, this naturally leads to the formulation of the theory of Israel and Stewart (1979), which is, to date, one of the most successful theories for relativistic dissipation. Although the generality of the principle makes it applicable to

We investigate the effect of spatial compactification on the transition rate of an inertial or accelerated Unruh–Dewitt detector coupled to an untwisted or twisted massless quantum scalar field. Four typical cases of the detector’s motion in the compactified Minkowski spacetime are considered respectively. Our results indicate that the detector’s transition rates are crucially dependent on the spatial

We prove that the surface gravity of a compact non-degenerate Cauchy horizon in a smooth vacuum spacetime, can be normalized to a non-zero constant. This result, combined with a recent result by Oliver Petersen and Istvn Rcz, end up proving the Isenberg–Moncrief conjecture on the existence of Killing fields, in the smooth differentiability class. The well known corollary of this, in accordance with

In this work by using a numerical analysis, we investigate in a quantitative way the late-time dynamics of scalar coupled gravity. Particularly, we consider a Gauss–Bonnet term coupled to the scalar field coupling function ξ(ϕ), and we study three types of models, one with f(R) terms that are known to provide a viable late-time phenomenology, and 2 Einstein–Gauss–Bonnet types of models. Our aim is

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random 3-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that the Hausdorff and spectral dimensions of the model approach 1 in the joint classical-thermodynamic limit and we argue that the scaling limit of the model is the circle

We recast the well known Israel–Darmois matching conditions for locally rotationally symmetric (LRS-II) spacetimes using the semitetrad 1 + 1 + 2 covariant formalism. This demonstrates how the geometrical quantities including the volume expansion, spacetime shear, acceleration and Weyl curvature of two different spacetimes are related at a general matching surface inheriting the symmetry, which can

We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables

Reconstruction process of scalar field models (quintessence, tachyon, dilaton and K-essence), which can be performed by making use of some dark energy density definitions such as holographic, Ricci, new agegraphic and ghost types proposals, has been an interesting and very attractive area to many physicists in literature. In this work, in a five-dimensional framework, we establish a correspondence

We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges

In this paper we generalize the off-shell Abbott–Deser–Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most

We study the bootstrapped Newtonian potential generated by a localised source in one and two spatial dimensions, and show that both cases naturally lead to finite spatial extensions of the outer vacuum. We speculate that this implies the necessary existence of a cosmological (particle) horizon associated with compact sources. In view of the possible dimensional reduction occurring in ultra-high energy

It is shown that the generalized Collins–Stewart radiation and Milne solutions are attractors of the massless Einstein–Vlasov system for Bianchi types II and V spacetimes, respectively. The proof is based on an energy method and bootstrap argument which are used to determine the decay rates of the perturbations away from the attractors.

It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein–Gauss–Bonnet (EGB) gravity. This motivates the questions: in EGB does the conformal flatness criterion yield the Schwarzschild metric? Does the assumption of constant density generate the Schwarzschild interior spacetime? The answer

We propose a toy model for the origin of the Universe, where the scale-invariant fluctuations are generated together with the quantum creation process of the Universe. The fluctuations arise inside an instanton in the Euclidean domain of time. In the Lorentzian point of view, the Universe emerges with passive, coherent and scale-invariant fluctuations present from the beginning, without the need of

In this work we have obtained a charged black hole solution in the presence of perfect fluid dark matter (PFDM) and discuss its energy conditions. The metric corresponding to the rotating avatar of this black hole solution is obtained by incorporating the Newman–Janis algorithm. We then compute two types of circular geodesics, namely, the null geodesics and time-like geodesics for this rotating spacetime

Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have

In the Hamiltonian formulation, it is not a priori clear whether a symmetric configuration will keep its symmetry during evolution. In this paper, we give precise requirements of when this is the case and propose a symmetry restriction to the phase space of the symmetric variables. This can often ease computation, especially when transcending from the infinite dimensional phase space of a field theory

The endpoint theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It plays a fundamental role in the theory of the abstract boundary as it implies that there is always an abstract boundary point to represent the endpoint of such sequences

The Einstein–Hilbert action with a cosmological constant is the most general local four-dimensional action leading to second-order derivative equations of motion that are symmetric and divergence free. In higher dimensions, additional terms can appear. We investigate a generalised metric decomposition involving a scalar degree of freedom to express the higher-dimensional action as an effective four-dimensional

In this paper, we prove that lightlike geodesics of a pseudo-Finsler manifold and its focal points are preserved up to reparametrization by anisotropic conformal changes, using the Chern connection and the anisotropic calculus developed in [11, 12] and the fact that geodesics are critical points of the energy functional and Jacobi fields, the kernel of its index form. This result has applications to

We study the quantum evolution of the early Universe, its semi-classical analogue together with inflationary regime, in view of a generalized modified theory of gravity. The action is built by supplementing the non-minimally coupled scalar–tensor theory of gravity with scalar curvature squared term and a Gauss–Bonnet-dilatonic coupled term. It is generalized, since all the parameters are treated as

We characterize in an analytical way the general conditions that a choice of vacuum state for the cosmological perturbations must satisfy to lead to a power spectrum with no scale-dependent oscillations over time. In particular, we pay special attention to the case of cosmological backgrounds governed by effective loop quantum cosmology and in which the Einsteinian branch after the bounce suffers a

Noise due to scattered light has been a frequent disturbance in the advanced LIGO gravitational wave detectors, hindering the detection of gravitational waves. The non stationary scatter noise caused by low frequency motion can be recognized as arches in the time-frequency plane of the gravitational wave channel. In this paper, we characterize the scattering noise for LIGO and Virgo’s third observing

It has recently been suggested that ‘gravity is the weakest force’ in any theory with a suitable UV completion within quantum gravity. One formulation of this statement is the scalar weak gravity conjecture (WGC), which states that gravity is weaker than the force originating from scalar fields. We study the scalar WGC in de Sitter (dS) space, and discuss its low-energy consequences in light of the

In this article, we discuss propagation expressions for polar gravitational waves in the spatially flat Friedmann–Lemaitre–Robertson–Walker spacetime dominated by a perfect fluid in the Rastall theory. We perturb the spatially flat spacetime description by making use of Regge–Wheeler perturbations inducing the polar gravitational waves and formulate the corresponding field equations for both unperturbed

We compute the vacuum polarization for a massless, conformally coupled scalar field on the covering space of global, four-dimensional, anti-de Sitter space-time. Since anti-de Sitter space is not globally hyperbolic, boundary conditions must be applied to the scalar field. We consider general Robin (mixed) boundary conditions for which the classical evolution of the field is well-defined and stable

We propose that several of the anomalies that have been observed at large angular scales in the CMB have a common origin in a cosmic bounce that took place before the inflationary era. The bounce introduces a new physical scale in the problem, which breaks the almost scale invariance of inflation. As a result, the state of scalar perturbations at the onset of inflation is no longer the Bunch–Davies

We consider the high spin expansion for the null geodesics in the Kerr spacetime. We expand the null geodesic equation successively to higher orders in deviation from extremality. Via the method of matched asymptotic expansion, the radial integrals are obtained analytically. It turns out that the analytic expressions are very sensitive to the value of the shifted Carter constant q. We show that for

Fully non-linear equations of motion for dissipative general relativistic multi-fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation—like the famous Mller–Israel–Stewart model—are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here