Speakers

I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalization of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.

Recently in paper [1] we considered the effective potential of a scalar-tensor model of gravity with quartic self-interaction of the scalar field. In this report we extend that study for the case of the scalar Higgs field of the Standard Model. The current best fit of the Higgs potential [2] shows that it has the second more deep minimum which leads to metastability of the universe. This potential also violates the weak energy condition of general relativity and can potentially lead to instabilities induced by gravity. We consider evolution of small perturbations of the scalar Higgs field in the gravitational field of a Schwarzschild black hole or a heavy star. Differential equations for the evolution of perturbations in time are constructed. The equations are analyzed and solved numerically following the methods described in [3].

We have shown that the mechanism of gravitational baryogenesis leads to a strong instability of the curvature scalar, resulting in its boundless exponential rise [1,2]. This instability appears because the coupling of the curvature to baryonic current leads to the fourth order differential equation of motion for the curvature scalar, instead of the algebraic one in conventional General Relativity (GR). It is shown that in the case of \( R^2 \)-gravity the non-linear in curvature term transforms the exponential rise into high frequency oscillations of \( R \) [3]. These oscillations create an efficient particle production possibly contributing into high energy cosmic rays. As a result the oscillation amplitude would be noticeably diminished.

The Advanced LIGO and Advanced Virgo detectors have commenced observations through three observation periods. Gravitational waves from the mergers of compact binary systems have been observed. A major goal for LIGO and Virgo will be to detect or set limits on a stochastic background of gravitational waves [1]. A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved cosmological and/or astrophysical sources. A cosmologically produced background would carry unique signatures from the earliest epochs in the evolution of the Universe. Similarly, an astrophysical background would provide information about the astrophysical sources that generated it. The observation of gravitational waves from compact binary systems implies that there will be a stochastic background from these sources that could be observed by Advanced LIGO and Advanced Virgo in the near future. The LIGO and Virgo search for a stochastic background should probe interesting regions of the parameter space for numerous astrophysical and cosmological models. Presented here is an outline of LIGO and Virgo’s search strategies for a stochastic background of gravitational waves, including the search for gravitational wave polarizations outside of what is predicted from general relativity [2]. Also discussed is how global electromagnetic noise (from the Schumann resonances) could affect this search [3] possible strategies to monitor and subtract this potential source of correlated noise in a the global detector network are explained. The results from the Advanced LIGO and Advanced Virgo observing run O3 are presented [4], along with the implications of the gravitational wave detections. The future goals for Advanced LIGO and Advanced Virgo are explained.

The cancellation of infrared (IR) divergences is an old topic in quantum field theory whose main results are condensed into the celebrated Kinoshita-Lee-Nauenberg (KLN) theorem. We consider mass-suppressed corrections to the leading (i.e.double-logarithmic) IR divergences in the context of spontaneously broken gauge theories.

One of the challenges in describing dark energy as a dynamical field is that we do not see any sign of it in local tests of gravity. Moreover, all gravitational wave events detected so far are in very good agreement with General Relativity predictions. In this talk I will discuss about kinetic screening as a way to overcome this dichotomy and I will present our recent results in testing it with black hole collapse, and the late inspiral and merger of binary neutron stars.

The multi-messenger detection of gravitational waves (GW) from the merger of the binary neutron star system GW170817 by the LIGO and Virgo interferometers ushered a new chapter in the determination of the expansion history of the Universe [1]. However, the majority of GW signals detected to date come from merging binary black holes [2,3], for which no electromagnetic counter-part is expected. Nonetheless, methods to infer the Hubble constant have been proposed that rely on either the statistical association of a GW signal to its host galaxy~[4] or on the knowledge of the intrinsic astrophysical distribution of merging binaries [5]. In this talk, I will review the main methodologies and their application to the latest GW catalog [6]. I will also discuss some of the longer term perspectives as well as some of the problems to be solved for their success.

We review the concept of accidental symmetry with a couple of examples from classical physics to SM. Then we approach the flavor puzzle by studying models in which an accidental PQ symmetry arises in a natural way.

A review of recent observations of the early universe at redshifts of order 10 is presented The available data from JWST, HST, and some other instruments, such as e.g. ALMA are analysed. Special attention is payed to identification of spectral lines emitted by different heavy elements in the early universe, that allows to precisely fix the redshifts of the observed objects. Possible resolution of discovered inconsistency of the unexpectedly dense population of the early universe with the standard Friedmann cosmology is discussed.

Special relativity is counterintuitive. More than a century after its discovery, it still seems to have some surprises in store for us. In this talk, which is based on [1], I will present a new theorem, which states that thermodynamic irreversibility is compatible with Lorentz covariance if and only if the principle of causality holds (i.e. information cannot travel faster than light). This fundamental result finally explains why many relativistic hydrodynamic theories happen to be unstable [2], and it can be used as a guiding principle in the search for reliable fluid theories. Applications to viscous cosmology [3] are discussed in detail.

After more than two years of scanning the sky the eROSITA X-ray telescope aboard SRG orbital observatory produced the best ever X-ray maps of the sky and discovered more than three million X-ray sources, of which about 20% are stars with active coronas in the Milky Way, and most of the rest are galaxies with active nuclei, quasars and clusters of galaxies. eROSITA detected over \( \sim 10^3 \) sources that changed their luminosity by more than an order of magnitude, including about a hundred tidal disruption events. Two tidal disruption events are associated with IceCube neutrinos. SRG/eROSITA samples of quasars and galaxy clusters will make it possible to study the large-scale structure of the Universe at \( z\sim 1 \) and measure its cosmological parameters. I will review some of the SRG/eROSITA results in the Eastern Galactic hemisphere and future prospects.

In this talk, based on [1,2], we will study massive non-linear gauge theories with mass added by hand. The standard perturbative methods indicate that the massless limit is not smooth. By considering the massive Yang-Mills theory and self-interacting theories of Proca, Kalb-Ramond, and three-form fields, we will show that this is due to those degrees of freedom that are absent in the corresponding massless theories. We will further show that these degrees of freedom become strongly coupled at the Vainshtein scale, beyond which they decouple from the remaining ones. As a result, we will find that the apparent discontinuity is just an artifact of the perturbation theory and discuss the implications of massless limits on theories that are claimed to be dual.

I review the observational evidence for primordial black holes (PBHs) from a variety of lensing, dynamical, accretion and gravitational-wave effects. This is a shift from the usual emphasis on PBH constraints. Microlensing observations of stars and quasars suggest that PBHs of around \( 1 \,M_{\odot} \) could provide most of the dark matter in galactic halos and intergalactic space, especially if they have an extended mass spectrum. In this case, the Poisson fluctuations associated with the PBHs could generate the first bound objects at a much earlier epoch than in the standard cosmological scenario and this could explain the recent detection of high redshift ultra-faint dwarf galaxies. LIGO/Virgo observations of coalescing compact objects may provide evidence for PBHs, since they encompass the mass gaps not usually associated with stellar remnants, but those dominating the detection rate have tens of solar masses and could only provide a small fraction of the dark matter. PBHs could explain various other observational conundra and sufficiently large ones could provide seeds for the supermassive black holes in galactic nuclei. even if their density is tiny. The strength of the evidence for PBHs is independent of any specific model for their formation. However, the sound-speed naturally undergoes a series of dips at around the QCD epoch and this motivates a scenario in which the PBH mass function exhibits a number of distinct bumps, allowing PBHs to play many of the rôles discussed above.

The deflection of light in the gravitational field of the Sun is one of the most fundamental con- sequences for general relativity as well as one of its classical tests first performed by Eddington a century ago. However, despite its center stage role in modern physics, no experiment has tested it in an ostensibly quantum regime where both matter and light exhibit non-classical features. This paper shows that the interaction which gives rise to the light-bending also induces photon-matter entanglement as long as gravity and matter are treated at par with quantum mechanics. The quantum light-bending interaction within the framework of perturbative quantum gravity highlights this point by showing that the entangled states can be generated already with coherent states of light and matter exploiting the non-linear coupling induced by graviton exchange. Furthermore, the quantum light-bending interaction is capable of discerning between the spin-2 and spin-0 gravitons thus also providing a test for alternative theories of gravity at short distances and at the quantum level. We will conclude by estimating the order of magnitude of the entanglement generated by employing the linear entropy. In particular, we find that a ring cavity of radius 0.25 m placed around a 10 kg mechanical oscillator operating at 150 Hz (0.1 Hz), could be used to generate linear entropy of order unity using a petawatt (megawatt) laser source at optical wavelengths, see [1,2].

We will discuss some surprising features of k-essential FRW models related to ramified equations of state.

The late-time Universe features nonlinear local deviations from strict homogeneity and isotropy as matter structures develop. These may have a non-negligible impact (dark energy– or dark matter–like “backreaction” effects) on the expansion at the largest scales. Those effects can be described, in a general-relativistic picture, by explicitly coarse-graining the smaller-scale inhomogeneities using a spatial averaging scheme. Applying it to specific spacetime models or simulations then generally requires a special attention to the choice of spatial slices.

I will show how rather simple averaging frameworks (see~[1]) can be extended to the description of general fluid sources in any spatial slices~[2]. I will then discuss the resulting effective dynamics and backreaction terms, and how their dependence in the spatial frames can be kept under control. I will also show how this formalism can be applied to evaluate backreaction using relativistic cosmological simulations, such as~[3].

Many dark energy (DE) models are based on a scalar field with timelike gradient. In this talk we begin with a review of the systematic construction of the effective field theory (EFT) describing perturbations around the Minkowski background with a timelike scalar profile and its extension to cosmological backgrounds, i.e. the ghost condensation and the EFT of inflation/DE. If one hopes to learn something about the EFT of DE from black holes (BHs) then one needs to consider BH solutions with timelike scalar profiles. We thus extend the EFT to arbitrary backgrounds~[1]. Finally, as an application of the general EFT, we study odd-parity perturbations around a spherically symmetric, static black hole background with a timelike scalar field responsible for DE~[2] and compute quasi-normal mode frequencies~[3].

The space-borne interferometer LISA will be sensitive to a variety of mechanisms sourcing gravitational waves in the late and early universe. In this talk we present the status of the LISA mission and summarize the science that LISA will achieve. We discuss in some detail the measurements that will allow LISA to probe BSM physics and cosmology [1, 2, 3]. Particular attention will be devoted to the gravitational-wave signatures predicted in models with first-order phase transitions, and how LISA can exploit these signatures to put constraints on BSM models in synergy with future colliders [4, 5].

We investigate how the Standard Model parity symmetry \( \mathcal P \), as restored in Left-Right symmetric theories, may arise as a discrete remnant of a unified gauge symmetry. This leads to a high-energy unification that necessarily includes the gauging of the Lorentz symmetry, bringing into the game gravitational interactions, and leading to a gravi-GUT scheme. Parity emerges unbroken below the Planck scale, and can be broken spontaneously at lower energies making contact with the Standard Model. This framework motivates the spontaneous origin of parity violation as in Left-Right symmetric theories with \( \mathcal P \). The possible unifying gauge groups are identified as \( SO(1,7) \) for gravitational and weak interactions, or \( SO(7,7) \) for a complete unification. Talk based on [1].

We analyze the cosmological implications of a theory of a spinor field in which the Lagrangian contains a non-linear function of the kinetic term. We show that, if the spinor field is subject to a Heisenberg potential, then there are cases in which a perfect fluid of matter generates a bouncing.

This talk is based on articles [1,2]. Equation for gravitational wave (GW) propagation over arbitrary curved spacetime is considered. A new term is found which absent in the conventional homogeneous and isotropic Friedmann cosmology. This term, under certain conditions, can significantly change the character of solutions. The assumption is that the term may also be the cause of relic GWs amplitude suppression. Two realistic phenomena are discussed, which can probably provide this suppression.

A minor population of antistars in galaxies has been predicted by some of the non-standard models of nucleosynthesis in the early Universe and their presence is not yet excluded by the currently available observations. Detection of anti-nuclei in cosmic rays can provide the unique information on the baryogenesis scenarios in the early Universe and serve as a test of heavy dark matter models. Recent report of AMS-02 collaboration on the tentative detection of a few anti-helium nuclei in GeV cosmic rays provided a great hope on the progress in this issue.

We discuss possible sources of anti-nuclei in cosmic rays from anti-stars which are predicted in a modified Afflek-Dyne baryogenesis scenario by Dolgov and Silk. The model allows us to estimate the expected fluxes of the heavy anti-nuclei in the GeV regime cosmic rays from the anti-star composition models.

A direct observational evidence of antistars can also be obtained from X-ray spectroscopic observations of narrow emission lines produced in cascade decays of exotic atoms (protonium and antihelium-proton) atoms that should be formed before hadronic annihilation in interactions of antimatter ejected from antistars with the surrounding interstellar medium.

We place constraints on the normalised energy density in gravitational waves from first-order phase transitions~[1], focusing on transitions characterised by strong supercooling, and then from the formation of primordial black holes~[2] using data from Advanced LIGO and Virgo's first, second and third observing runs. First, adopting a broken power law model, we place 95 % confidence level upper limits simultaneously on the gravitational-wave energy density at 25 Hz from unresolved compact binary mergers and first-order phase transitions. As an application of our analysis, we determine bounds on the parameter space of two representative particle physics models. We also comment on the expected reach of third-generation detectors in probing supercooled phase transitions. We then do a similar search assuming a background sourced by the formation of primordial black holes and unresolved compact binary mergers. For a very generic spectrum describing the primordial black hole background, we place 95 % confidence level upper limits on the gravitational-wave energy density at 25 Hz.

The stochastic gravitational wave background (SGWB) produced at the electroweak phase transition is expected to be peaking within LISA's sensitivity frequency range, being a promising test of high energy physics and beyond Standard Model extensions. The contribution of magnetohydrodynamic (MHD) turbulence to the cosmological SGWB is one of the least understood sources due to the necessity, in general, to perform large-scale numerical simulations solving MHD equations. In this talk, I will review recent numerical simulations that have addressed this issue and studied the potential detectability of the resulting SGWB and its polarization by space-based GW detectors like LISA [1,2]. I will focus on magnetically dominated MHD turbulence and compare to astrophysical constraints that can provide a multi-messenger study of primordial magnetic fields. In particular, I will present the SGWB produced by decaying MHD turbulence, which has been validated by numerical simulations for a particular range of parameters [3]. This model has been recently used to constrain the characteristics of a primordial magnetic field produced at the QCD phase transition with the common-spectrum process reported by the different pulsar timing array collaborations in the last few years.

The origin of the small parameters with the aim of explaining the Hierarchy problem is discussed. %The flexible extra dimensions and background scalar fields are essential tools. The evolution of a multidimensional metric starts at the Planck scale and is completed with the static extra-dimensional metric and the 4-dim de Sitter space at high energies, where the exponential production of causally disconnected universes begins [1]. Quantum fluctuations distort the metric within these universes, causing some of them tend towards low energy states [2]. The effective parameter reduction applied to the Higgs sector of the Standard Model is explained by the presence of small-amplitude distributions of a scalar field in a fraction of these universes.

To recover the 21 cm hydrogen line, it is essential to separate the cosmological signal from the much stronger foreground contributions at radio frequencies. The BINGO (Baryon Acoustic Oscillations from Integrated Neutral Gas Observations) radio telescope is designed to 1 cm line and measure the 2 detect Baryon Acoustic Oscillations (BAOs) using the intensity mapping technique. I will present the performance of the Generalized Needlet Internal Linear Combination (GNILC) method [1], combined with a power spectrum debiasing procedure. The method was applied to a simulated BINGO emission on, bu previous work from the collaboration. It compares two different synchrotron emission models and different instrumental configurations, in addition to the combination with ancillary data to optimize both the foreground removal and recovery of the 21 cm signal across the full BINGO frequency band, as well as to determine an optimal number of frequency bands for the signal recovery [2].

We present our definition of minimal symmetry breaking of the cosmological principle. For comoving dust, the definition leads uniquely to the axial Bianchi IX universes with positive curvature and their flat Bianchi I limits. We discuss the direction dependent Lemaitre-Hubble diagram of these universes and its future observational tests. In view of promised promising data from the Vera Rubin Observatory, the James Webb Space Telescope and the Chinese Space Station Telescope, we plead for an immediate preparation of a joint analysis with data from SuperNovae 1a, Cosmic Microwave Background, drift of radio sources and Baryonic Acoustic Oscillations.

Gamma-ray telescopes Tibet ASgamma, HAWC and LHASSO discovered number of PeVatron sources in the 100 TeV energy range. Moreover, Tibet ASgamma and LHASSO see diffuse emission from cosmic rays in the Galaxy in this energy range. Finally, recently it was found evidence of excess in the IceCube data in 20 degrees around Galactic plane at the same energies.

In this talk I’ll review status of experimental data and discuss how we can use it to learn about cosmic rays in our Galaxy at multi-PeV energies. I’ll present anisotropic cosmic ray diffusion model at PeV energies and show how this model can explain existing data. Also I’ll show how future data of LHAASO, SWGO and CTA experiments together with km3 and IceCube neutrino telescopes will help to resolve 100 year old puzzle of cosmic ray sources.

Axion-like particles (ALPs) are dark matter candidates and can form small scale structures in the form of condensates, mini-clusters and solitons, the latter also known as ALP-stars. If ALPs couple to photons, through mergers, interactions with other objects or accretion, these structures can give rise to astrophysical and cosmological signatures such as ALP conversion into photons and thus an injection of electromagnetic energy. If, for example, the ALP mass is in the micro-electron volt range, which is well motivated by scenarios in which the QCD axion contributes to the dark matter, this will manifest as radio signals. We will give an overview over such radio signatures which can be in the form of radio lines from local discrete sources [1] or they can form a diffuse cosmological radio glow with a broader spectrum. Future prospects for their detectability will also be discussed.

I will discuss the requirements of a successful simultaneous solution to the Hubble and the S8 tension and why New Early Dark Energy (NEDE) is a particularly simple and minimalistic framework for such solutions. I will then explain why this class of successful solutions to the tensions implies a more blue initial spectrum of primordial curvature perturbations favouring the simplest curvaton model over the Starobinsky inflation model. I will also discuss how this can be tested by future stronger constraints or measurements of local non-gaussiandity and the tensor-to-scalar ratio. The presentation is based on new results of [1] to appear soon, and our previous work on NEDE [2 ,3,5,4,6,7,8].

Since duration of the inflationary epoch was finite inside our past light-cone, it is natural to think what could be before it. I discuss different possibilities proposed historically with the main emphasis on isotropic bounce due to positive spatial curvature [1], or even in its absence [2], or alternatively, generic anisotropic singularity with curvature much exceeding that during the observable part of inflation [3,4,5].

The rate of thermal bubble nucleation of a quantum field is usually calculated using an instanton with periodic boundary conditions. Setting out from the definition of the decay rate in terms of field-space probabilities, I sketch how a full expression for the rate of bubble nucleation at finite temperature can be derived, which reproduces the familiar result at leading order. This procedure can be applied to describe tunneling out of an arbitrary initial state. I then discuss the high-temperature limit characterized by temperatures much larger than the scalar field's effective mass. I will show that the parameter that controls this expansion also multiplies the contributions of a possible Euclidean time-dependence of the instanton. This provides an analytical justification for the common assumption of a time-independent instanton, and allows us to quantify the resulting error. Furthermore, I show that the standard procedure of determining the instanton from the effective action can be performed in a way that still allows a consistent perturbative analysis of one-loop corrections, if the quartic coupling of the scalar field is sufficiently small, and demonstrate that this is indeed the case for the Standard Model. Lastly, I present numerical results for the bubble nucleation rate of the electroweak vacuum at temperatures above \( 10^{12} \) GeV, as would have been relevant in the early universe.

Future lepton colliders at the \( t\bar t \) can establish if the Standard Model Higgs potential is unstable when extrapolated at ultra-high energies. I show that the Higgs vacuum instability, if triggered, would not self-quench gravitationally. However, spontaneous vacuum decay, thermal effects, primordial black holes and collisions of few particles (such as colliders and cosmic rays) trigger the Higgs vacuum instability with exponentially suppressed and thereby negligible rates. A system of futuristic ultra-high energy colliders could artificially trigger the Higgs vacuum instability. I wildly speculate how the resulting true-vacuum bubble could be controlled arguing that vacuum energy, at least in theory, could be an energy source.

In this talk we will discuss the most general scalar-tensor theories of gravity which contain the only single scalar degree of freedom. These theories, known as Degenerate Higher-Order Scalar-Tensor (DHOST) theories, include Horndeski and Beyond Horndeski theories. More details, we will focus on the particular subclass of models, known as the theory of gravity with non-minimal derivative coupling, and consider isotropic and anisotropic cosmological models in such the theory [1,2,3,4,5,6,7]. As well, we will shortly discuss compact astrophysical objects (black holes, wormholes, neutron stars) in the theory of gravity with non-minimal derivative coupling [8,9].

Black holes are exceptional due to their time evolution and information processing. However, these properties are generic for objects, the saturons, that attain the maximal entropy permitted by unitarity. We verify this connection within a renormalizable \( SU(N) \) invariant theory [1]. We show that the spectrum of the theory contains a tower of bubbles representing bound states of \( SU(N) \) Goldstone. Despite the absence of gravity, a saturated bound state exhibits a striking correspondence with a black hole: Its entropy is given by the Bekenstein-Hawking formula; semiclassically, the bubble evaporates at a thermal rate with a temperature equal to its inverse radius; the information retrieval time is similar to Page's time. We will discuss the implications of the black hole–saturon correspondence for black hole physics, both fundamental and observational.

Just like light, gravitational waves can be lensed if there is a massive object, such as a galaxy, in the path from source to observer. In the case of strong lensing the "images" take the form of copies of the original signal, with the same frequency evolution, but (de)magnified, and arriving at the observer at times that differ by minutes to months. It seems plausible that lensed gravitational waves will be observed in the next few years, and they are actively being searched for. In this talk I explain the challenges that the searches pose, but also the considerable scientific pay-off in terms of astrophysics, fundamental physics, and cosmology. Gravitational wave lensing may be the only way to localize stellar mass binary black hole mergers, and it will allow for high-redshift Hubble constant measurements with gravitational waves. In terms of fundamental physics, it will enable stringent tests of the polarization content of gravitational waves, and of the way they propagate over cosmological distances.

I will present a new cosmological model in which the expansion is no longer affected by spatial curvature (i.e. \( \Omega = 1, \ \forall \Omega_K \)), while the measure of distances still requires this curvature [3]. The model originates from a modification of Einstein's equation in which a term related to the topology of the Universe is added. First, I will present the main motivation for this modification, which is related to the existence of the non-relativistic limit for any topology [2]. Then, I will present the model and discuss its consequences on the value of the spatial curvature inferred from observations, in particular with respect to the recent “curvature tension” [1].

We start by reviewing magnetic monopole solutions in gauge field theories. The known magnetic solutions in the electroweak theory are the embedded monopoles of Dirac, the Nambu monopole, and the Cho-Maison monopole. We then present new results on stability of these solutions, according to which the Cho-Maison monopole is stable but all Dirac monopoles are unstable. It seems that the Dirac monopoles decay via condensing to stable non-Abelian configurations without spherical symmetry, hence the electroweak theory admits infinitely many unknown non-Abelian monopole solutions. To confirm this, we present new non-Abelian solutions with higher magnetic charges in the axially-symmetric sector. They are strongly squashed and show inside a bubble of symmetric phase filled with a U(1) hypercharge field produced by a pointlike magnetic charge at the origin. The bubble is surrounded by a large ring of broken phase containing a magnetically charged W-condensate, and in the far field region there remains only the magnetic field supported by the total magnetic charge contained at the origin and in the magnetic ring. All electroweak monopoles have infinite energy due to the pointlike U(1) charge at the origin, but the energy becomes finite when gravity is taken into account, which provides a cutoff via creating an event horizon.

The presence of backreaction effects is investigated in the spherically symmetric Lemaître-Tolman-Bondi dust model and its generalisation including pressure, the Lemaître model. An averaging scheme based on a weighting by rest mass is applied. The mass-weighted effective scale factor derived from the inhomogeneous model is found to obey a modified Friedmann equation involving a coefficient that depends on the two-point density correlation function. This coefficient amplifies the matter contribution to the effective expansion rate and thus induces a 'missing mass' effect, similar to the heuristic approach undertaken in [1] in the Newtonian setting. In addition, pressure gradients which can arise from structure formation are found to be able to induce local acceleration, similar to a local dark energy. Inhomogeneities and pressure gradients produce deviations from a Friedmann evolution even in the Newtonian limit, meaning that both effects on the expansion could be non-relativistic, which is an uncommon feature in backreaction scenarios, such as in the Buchert formalism.

We consider general radially moving frames realized in the background of nonextremal black holes having causal structure similar to that of the Schwarzschild metric. In doing so, we generalize the Lemaitre approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy \( e_{0} \) including \( e_{0} \) and a special case \( e_{0} \). The general formula of 3-velocity of a freely falling particle with the specific energy e with respect to a frame with \( e_{0} \) is presented. We point out the relation between the properties of considered frames near a horizon and the Banados-Silk-West effect of an indefinite growth of energy of particle collisions. Using our radially moving frames, we consider also nonradial motion of test particles including the regions near the horizon and singularity. We also point out the properties of the Lemaitre time at horizons depending on the frame and sign of particle energy.