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1. Harmonic functions and gravity localization

   https://doi.org/10.1007/JHEP09(2023)127  

   De Luca, G. Bruno ; De Ponti, Nicolò ; Mondino, Andrea ; Tomasiello, Alessandro ( September 2023 , Journal of High Energy Physics)

   In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes.

   We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string/M-theory solutions with infinite-volume Riemann surfaces; and in a known class of$$ \mathcal{N} $$$N$= 4 models, when the number of NS5- and D5-branes is roughly equal.

    

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2. Gravity from thermodynamics: Optimal transport and negative effective dimensions

   https://doi.org/10.21468/SciPostPhys.15.2.039  

   De Luca, Giuseppe Bruno ; De Ponti, Nicolò ; Mondino, Andrea ; Tomasiello, Alessandro ( January 2023 , SciPost Physics)

   We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory of optimal transport to the Raychaudhuri equation in the internal space, where the warp factor introduces effective notions of curvature and (negative) internal dimension. When the Reduced Energy Condition is satisfied, concavity can be characterized in terms of the cosmological constant\Lambda$\Lambda$; as a consequence, the masses of the spin-two Kaluza-Klein fields obey bounds in terms of\Lambda$\Lambda$alone. We show that some Cheeger bounds on the KK spectrum hold even without assuming synthetic Ricci lower bounds, in the large class of infinitesimally Hilbertian metric measure spaces, which includes D-brane and O-plane singularities. As an application, we show how some approximate string theory solutions in the literature achieve scale separation, and we construct a new explicit parametrically scale-separated AdS solution of M-theory supported by Casimir energy.

    

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3. Gravitational wave bounds on dirty black holes

   https://doi.org/10.1002/asna.201913573  

   Nielsen, A. B. ; Birnholz, O. ( March 2019 , Astronomische Nachrichten)

   Detection of gravitational waves has provided a new way to test black hole (BH) models. We show how simple constraints can be obtained for models that go beyond vacuum Einstein gravity solutions of binary BH mergers. Generic stationary metrics, termed dirty BHs in the literature, are not vacuum solutions of the Einstein equations. These models are, however, general enough to describe BHs surrounded by matter fields. Gravitational wave constraints already rule out certain parts of parameter space for these solutions, including certain parameters describing objects without horizons that have recently been studied in the context of pseudo‐complex general relativity.

    

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4. Low-energy Explosions in a Gravitational Field: Implications for Sub-energetic Supernovae and Fast X-Ray Transients

   https://doi.org/10.3847/1538-4357/ad11f4  

   Paradiso, Daniel A. ; Coughlin, Eric R. ; Zrake, Jonathan ; Pasham, Dheeraj R. ( January 2024 , The Astrophysical Journal)

   Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a “phantom shock breakout”—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst,t_d, and the mean photon energy,kT, are anticorrelated, approximately as$T\propto t_{\mathrm{d}}^{-5/8}$.

    

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5. Geometries with mismatched branes

   https://doi.org/10.1007/JHEP09(2020)166  

   Karch, Andreas ; Randall, Lisa ( September 2020 , Journal of High Energy Physics)

   We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

    

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