Slowly rotating supercompact Schwarzschild stars

Observations have found black holes spanning 10 orders of magnitude in mass across most of cosmic history. The Kerr black hole solution is, however, provisional as its behavior at infinity is incompatible with an expanding universe. Black hole models with realistic behavior at infinity predict that the gravitating mass of a black hole can increase with the expansion of the universe independently of accretion or mergers, in a manner that depends on the black hole’s interior solution. We test this prediction by considering the growth of supermassive black holes in elliptical galaxies over 0 < z ≲ 2.5. We find evidence for cosmologically coupled mass growth among these black holes, with zero cosmological coupling excluded at 99.98% confidence. The redshift dependence of the mass growth implies that, at z ≲ 7, black holes contribute an effectively constant cosmological energy density to Friedmann’s equations. The continuity equation then requires that black holes contribute cosmologically as vacuum energy. We further show that black hole production from the cosmic star formation history gives the value of ΩΛ measured by Planck while being consistent with constraints from massive compact halo objects. We thus propose that stellar remnant black holes are the astrophysical origin of dark energy, explaining the onset of accelerating expansion at z ∼ 0.7.

In selective laser melting (SLM) the variation of process parameters significantly impacts the resulting workpiece characteristics. In this study, AISI 316L was manufactured by SLM with varying laser power, layer thickness, and hatch spacing. Contrary to most studies, the input energy density was kept constant for all variations by adjusting the scanning speed. The varied parameters were evaluated at two different input energy densities. The investigations reveal that a constant energy density with varying laser parameters results into considerable differences of the workpieces’ roughness, density, and microhardness. The density and the microhardness of the manufactured components can be improved by selecting appropriate parameters of the laser power, the layer thickness, and the hatch spacing. For this reason, the input energy density alone is no indicator for the resulting workpiece characteristics, but rather the ratio of scanning speed, layer thickness, or hatch spacing to laser power. Furthermore, it was found that the microhardness of an additively manufactured material correlates with its relative density. In the parameter study presented in this paper, relative densities of the additively manufactured workpieces of up to 99.9% were achieved.

We investigate the properties of relativistic star spheres made of an electrically charged incompressible fluid, generalizing, thus, the Schwarzschild interior solution. The investigation is carried by integrating numerically the hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff (TOV) equation, with the hypothesis that the charge distribution is proportional to the energy density. We match the interior to a Reissner-Nordstr\"om exterior, and study some features of these star spheres such as the total mass $M$, the radius $R$, and the total charge $Q$. We also display the pressure profile. For star spheres made of a perfect fluid there is the Buchdahl bound, $R/M\ensuremath{\ge}9/4$, a compactness bound found from generic principles. For the Schwarzschild interior solution there is also the known compactness limit, the interior Schwarzschild limit where the configurations attain infinite central pressure, given by $R/M=9/4$, yielding an instance where the Buchdahl bound is saturated. We study this limit of infinite central pressure for the electrically charged stars and compare it with the Buchdahl-Andr\'easson bound, a limit that, like the Buchdahl bound for the uncharged case, is obtained by imposing some generic physical conditions on charged configurations. We show that the electrical interior Schwarzschild limit of all but two configurations is always below the Buchdahl-Andr\'easson limit, i.e., we find that the electrical interior Schwarzschild limit does not generically saturate the Buchdahl-Andr\'easson bound. We also find that the quasiblack hole limit, i.e., the extremal most compact limit for charged incompressible stars, is reached when the matter is highly charged and the star's central pressure tends to infinity. This is one of the two instances where the Buchdahl-Andr\'easson bound is saturated, the other being the uncharged, interior Schwarzschild solution.

The contents of this paper refers to following main subjects: numerical adaptation of our cosmological parameters recently used within the framework of the Projective Unified Field Theory [1] to the new measured values of the Wilkinson Microwave Anisotropy Probe (WMAP) published by Ch.L. Bennett et al. [2]; study of the resulting consequences for our cosmological model of a closed homogeneous isotropic cosmos; approximate treatment of a quasi-static spherically symmetric perfect fluid sphere (interior and exterior solution) being under the adiabatic influence of the expanding cosmos; application of these results to sun-like and earth-like cosmic bodies; time dependence of the “empirical gravitational constant”; treatment of the Einstein effects, particularly of the periastron (perihelion) motion of an orbiting body (mercury) about a central body (sun) with a mass quadrupole moment and calculation of its numerical value for the sun. Further cosmological and astrophysical applications. An appendix points to a different set of parameters.

Inertial reference frames spanning approximately 10°–30° square on the sky and capable of locating objects to few-hundred microarcsecond accuracies are useful for a broad class of astrometric measurements. Deep space tracking and general relativistic angular deflection experiments are examples of astrometric measurements which can profitably reference the positions and/or motions of objects to a field of radio sources in a local frame. A method for defining local inertial reference frames has been developed based on Very Long Baseline Interferometry (VLBI) measurements of extragalactic radio sources. By observing the radio emission from the object to be located in the frame, as well as that from about five radio sources which define the frame, dominant systematic astrometric errors can be minimized through parameter estimation. The entire reference frame measurement is of the order of 30 minutes including all the sources in a frame. The limiting error for single-epoch position determination in a local frame is the unknown structure of both target and reference objects. Structure can cause systematic milliarcsecond-level errors. The limiting error for epoch-to-epoch differential position measurements is tropospheric fluctuations, assuming that the radio source structures do not change from one epoch to the next. Preliminary results of an epoch-to-epoch measurement of relativistic gravitational deflection by Jupiter, in which the total deflection was about 600 microarcseconds, suggest that the local reference frame is stable at the 240-microarcsecond level over twelve days. Data have been taken at longer time intervals to determine the annual stability of the frames. At the time of preparation of these proceedings, those data have not yet been analyzed.

We present a detailed Hamiltonian treatment of an inhomogeneous fermionic perturbation propagating on a closed Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime quantized via loop quantum cosmology. Expanding the fermion in spinor harmonics on a spatial three-sphere and truncating at quadratic order, we derive a decoupled, mode-by-mode Hamiltonian, where each mode behaves as a time-dependent Fermi oscillator. This framework naturally facilitates a Schr\"odinger-picture evolution for fermionic perturbations on a quantum-corrected background. Under the test-field approximation, each massive mode sees its own ``dressed metric,'' akin to bosonic perturbations, but with distinctive Planck-scale modifications in both temporal and spatial components. Massless modes, by contrast, experience only an equivalent class of conformally invariant backgrounds: quantum corrections drop out of the spatial sector, while the temporal component alone is dressed by quantum gravity corrections. Extending beyond the test-field regime via a Born-Oppenheimer approximation, we incorporate fermionic backreaction self-consistently. Each mode's energy (depending on the either vacuum or pair states they occupied) sources a mode-dependent shift of the background Hamiltonian, resulting in a ``rainbow metric.'' In the deep Planck regime, vacuum occupation yields a positive fermionic perturbation term in the Hamiltonian, raising the effective minisuperspace potential and delaying the bounce to higher density in the contracting branch. Excited occupation flips the perturbation sign, lowering the barrier and advancing the bounce to lower density and larger volume. At large volumes, massive fermion backreaction settles into a constant energy density---an emergent cosmological constant---capable of driving late-time acceleration, whereas massless modes remain dynamically inert postbounce. These effects break the exact time-reversal symmetry of the quantum bounce, modify the critical density condition, and generate asymmetric pre- and postbounce trajectories. Our results highlight the crucial role that fermionic degrees of freedom---through both their two-state spectrum and quantum gravity couplings---play in shaping Planck-era and subsequent cosmological dynamics.

We investigate the hyperbolic scattering of test particles, spinning test particles and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.

The multipole moments and the tidal Love numbers of neutron stars and quark stars satisfy certain relations which are almost insensitive to the star's internal structure. A natural question is whether the same relations hold for different compact objects and how they possibly approach the black-hole limit. Here we consider "gravastars", which are hypothetical compact objects sustained by their internal vacuum energy. Such solutions have been proposed as exotic alternatives to the black-hole paradigm because they can be as compact as black holes and exist in any mass range. By constructing slowly-rotating, thin-shell gravastars to quadratic order in the spin, we compute the moment of inertia $I$, the mass quadrupole moment $Q$, and the tidal Love number $\lambda$ in exact form. The $I$-$\lambda$-$Q$ relations of a gravastar are dramatically different from those of an ordinary compact star, but the black-hole limit is continuous, i.e. these quantities approach their Kerr counterparts when the compactness is maximum. Therefore, such relations can be used to discern a gravastar from an ordinary compact star, but not to break the degeneracy with the black-hole case. Based on these results, we conjecture that the full multipolar structure and the tidal deformability of a spinning, ultracompact gravastar are identical to those of a Kerr black hole. The approach to the black-hole limit is nonpolynomial, thus differing from the critical behavior recently found for strongly anisotropic neutron stars.

We consider a particle falling into a rotating black hole. Such a particle makes an infinite number of revolutions $n$ from the viewpoint of a remote observer who uses the Boyer-Lindquist type of coordinates. We examine the behavior of $n$ when it is measured with respect to a local reference frame that also rotates due to dragging effect of spacetime. The crucial point consists here in the observation that for a nonextremal black hole, the leading contributions to $n$ from a particle itself and the reference frame have the same form being in fact universal, so that divergences mutually cancel. As a result, the relative number of revolutions turns out to be finite. For the extremal black hole this is not so, $n$ can be infinite. Different choices of the local reference frame are considered, the results turn out to be the same qualitatively. For illustration, we discuss two explicit examples - rotation in the flat spacetime and in the Kerr metric.

We derive the classical gravitational radiation from an aligned spin binary black hole on closed orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a graviton. We show explicitly the agreement of the transverse-traceless components of the radiative linear metric perturbations — and the corresponding gravitational wave energy flux — at future null infinity, derived from the scattering amplitude and those derived utilizing an effective worldline action in conjunction with multipolar post-Minkowskian matching. At the tree-level, this result holds at leading orders in the black holes’ velocities and up to quadratic order in their spins. At sub-leading order in black holes’ velocities, we demonstrate a matching of the radiation field for quasi-circular orbits in the no-spin limit. At the level of the radiation field, and to leading order in the velocities, there exists a one-to-one correspondence between the binary black hole mass and current quadrupole moments, and the scalar and linear-in-spin scattering amplitudes, respectively. Therefore, we show explicitly that waveforms, needed to detect gravitational waves from inspiraling binary black holes, can be derived consistently, to the orders considered, from the classical limit of quantum scattering amplitudes.

We find a class of solutions to the Einstein field equations with constant vacuum energy density (''cosmological constant'') that has a similarity symmetry of the second kind. We show this symmetry to be a global conformal symmetry. Nontrivial analytic solutions are given and one in particular (exhibiting intrinsic symmetry) is shown to evolve to a nonempty Robertson-Walker space-time with ''steady-state'' metric. This is found to be due to particle production associated with the negative matter pressure that is required by the assumed symmetry. These models can describe, classically, an origin of the Universe in terms of particle production from the vacuum, driving an exponential (de Sitter) expansion. This solution is inhomogeneous and anisotropic, but tends to homogeneity and isotropy at early times and large distances, and at late times and small distances. The solution therefore corresponds to the outward motion of a spherical disturbance which distorts the local homogeneity and isotropy in an asymptotically homogeneous and isotropic universe. The limiting homogeneous and isotropic forms are discussed.

Laser powder bed fusion of AlSi10Mg: Influence of energy intensities on spatter and porosity evolution, microstructure and mechanical properties

How to Accomplish Inflation and a Constant Dark Energy Density

For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior solution, defines the most compact state of distribution while the other end is marked by the Finch-Skea model, and all the other physically tenable models lie in between these two limiting distributions.

Usually it is demanded that the metric and its 1st derivatives have to match at the boundary of two adjacent regions which are solutions to Einstein’s field equation. We propose a new linking condition concerning gravitational models based on surfaces which could be embedded into a higher dimensional flat space. We probe this condition for the Schwarzschild interior and exterior solution.