Abstract: We work out the junction conditions for f(R) gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of general relativity and from their metric f(R) counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need not to. We illustrate the relevance of these conditions by considering the properties of stellar surfaces in polytropic models, showing that the range of equations of state with potentially pathological effects is shifted beyond the domain of physical interest. This confirms, in particular, that neutron stars and white dwarfs can be safely modelled within the Palatini f(R) framework.

Abstract: We use the local hidden gauge approach in order to study the B (B) over bar* and B*(B) over bar* interactions for isospin I = 1. We show that both interactions via one light meson exchange are not allowed by the Okubo-ZweigIizuka rule and, for that reason, we calculate the contributions due to the exchange of two pions, interacting and noninteracting among themselves, and also due to the heavy vector mesons. Then, to compare all these contributions, we use the potential related to the heavy vector exchange as an effective potential corrected by a factor which takes into account the contribution of the other light meson exchanges. In order to look for poles, this effective potential is used as the kernel of the Bethe-Salpeter equation. As a result, for the B (B) over bar* interaction we find a loosely bound state with mass in the range 10587-10601 MeV, very close to the experimental value of the Z(b)(10610) reported by the Belle Collaboration. For the B*(B) over bar* case, we find a cusp at 10650 MeV for all spin J = 0, 1, 2 cases.

Abstract: We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. In order to account for the faint and distant binaries, which contribute the most to the SGWB, we extend the merger rate at high redshift assuming that it tracks the star formation rate. We adopt different methods to compute the SGWB signal: we perform an analytical evaluation, we use Monte Carlo sums over the SOBBH population realisations, and we account for the role of the detector by simulating LISA data and iteratively removing the resolvable signals until only the confusion noise is left. The last method allows the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for signal-to-noise ratio thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band agrees with the analytical prediction of a single power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model: at the reference frequency of 0.003 Hz it has an interquartile range of h2ΩGW(f = 3 × 10-3 Hz) ∈ [5.65, 11.5] × 10-13, in agreement with most previous estimates. We then perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate.