A quantum bound on the compactness

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

Gravitational self-regularization of quantum fields at Planck scales

Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.

Gravitational Radius in view of Existence and Uniqueness Theorem

Talking about a black hole, one has in mind the process of unlimited self-compression of gravitating matter with a mass greater than critical. With a mass greater than the critical one, the elasticity of neutron matter cannot withstand gravitational compression. However, compression cannot be unlimited, because with increasing pressure, neutrons turn into some other “more elementary” particles. These can be bosons of the Standard Model of elementary particles. The wave function of the condensate of neutral bosons at zero temperature is a scalar field. If instead of the constraint det gik < 0 we use a weaker condition of regularity (all invariants of the metric tensor gik are finite), then there is a regular static spherically symmetric solution to Klein-Gordon and Einstein equations, claiming to describe the state to which the gravitational collapse leads. With no restriction on total mass. In this solution, the metric component grr changes its sign twice: g rr (r) = 0 at r=rg and r=rh > rg . Between these two gravitational radii the signature of the metric tensor gik is (+, +, -, -). Gravitational radius rg inside the gravitating body ensures regularity in the center. Within the framework of the phenomenological model “λψ4 ”, relying on the existence and uniqueness theorem, the main properties of a collapsed black hole are determined. At r = rg a regular solution to Klein-Gordon and Einstein equations exists, but it is not a unique one. Gravitational radius rg is the branch point at which, among all possible continuous solutions, we have to choose a proper one, corresponding to the problem under consideration. We are interested in solutions that correspond to a finite mass of a black hole. It turns out that the density value of bosons is constant at r < rg. It depends only on the elasticity of a condensate, and does not depend on the total mass. The energy-momentum tensor at r ⩽ rg corresponds to the ultra relativistic equation of state p = ɛ/3. In addition to the discrete spectrum of static solutions with a mass less than the critical one (where grr < 0 does not change sign), there is a continuous spectrum of equilibrium states with grr(r) changing sign twice, and with no restriction on mass. Among the states of continuous spectrum, the maximum possible density of bosons depends on the mass of the condensate and on the rest mass of bosons. The rest energy of massive Standard Model bosons is about 100 GeV. In this case, for the black hole in the center of our Milky Way galaxy, the maximum possible density of particles should not exceed 3 × 1081 cm-3.

On the Concept of Gravito-Rotational Acceleration and its Consequences for Compact Stellar Objects

In a previous series of papers relating to the Combined Gravitational Action (CGA), we have exclusively studied orbital motion without spin. In the present paper, we apply CGA to any self-rotating material body, i.e., an axially spinning massive object, which itself may be locally seen as a gravito-rotational source because it is capable of generating the gravito-rotational acceleration, which seems to be unknown to previously existing theories of gravity. The consequences of such an acceleration are very interesting, particularly for Compact Stellar Objects. Independently of the equation of state, it is found that the minimum radius of a stable neutron star is three times its gravitational radius, Rmin = 3GMNS/c2, and its critical and maximum internal magnetic field strength cannot exceed the value of 3&times;1018 G.

EXPLORING THE NATURE OF COMPACT RADIO SOURCES ASSOCIATED TO UCHII REGIONS

We present Very Large Array 7 mm continuum observations of four ultracompact (UC) HII regions, observed previously at 1.3 cm, in order to investigate the nature of the compact radio sources associated with these regions. We detect a total of seven compact radio sources, four of them with thermal emission, and two compact radio sources with clear non- thermal emission. The thermal emission is consistent with the presence of an ionized envelope, either static (i.e., trapped in the gravitational radius of an associated massive star) or flowing away (i.e., a photo-evaporative flow). The nature of the non-thermal sources remains unclear and several possibilities are proposed. The possibility that most of these compact radio sources are photo-evaporating objects, and the remaining ones more evolved objects, is consistent with previous studies on UCHII regions.

How the Limit Values Work

The efficiency of limiting quantities as a tool for describing physics at various spatio-temporal scales is shown. Due to its universality, limit values allow us to establish relationships between, at first glance, distant from each other's characteristics. The article discusses specific examples of the use of limit values to establish such relationships between quantities at different scales. Based on the principle of reaching the limiting values on the event horizons, a connection was obtained between the Planck values and the values of the Universe. The resulting relation can be attributed to relations of the Dirac type - the coincidence of large numbers that emerged from empirical observations. In the article, the relationships between large numbers of the Dirac type are established proceeding, in a certain sense, from physical principles - the existence of limiting values. It is shown that this ratio is observed throughout the evolution of the Universe. An alternative way of solving the problem of the cosmological constant using limiting values and its relation to the minimum spatial scale is discussed. In addition, a one-parameter family of masses was introduced, including the mass of the Universe, the Planck mass and the mass of the graviton, which also establish relationships between quantities differing by 120 orders of magnitude. It is shown that entropic forces also obey the same universal limiting constraints as ordinary forces. Thus, the existence of limiting values extends to informational limitations in the Universe. It is fundamentally important that on any event horizon, regardless of its scale (i.e., its gravitational radius), the universal value of limit force c4/4G is realized. This allows you to relate the characteristics of the Universe related to various stages of its evolution.

A Conceptual Model for the Origin of the Cutoff Parameter in Exotic Compact Objects

A Black Hole (BH) is a spacetime region with a horizon and where geodesics converge to a singularity. At such a point, the gravitational field equations fail. As an alternative to the problem of the singularity arises the existence of Exotic Compact Objects (ECOs) that prevent the problem of the singularity through a transition phase of matter once it has crossed the horizon. ECOs are characterized by a closeness parameter or cutoff, ϵ, which measures the degree of compactness of the object. This parameter is established as the difference between the radius of the ECO’s surface and the gravitational radius. Thus, different values of ϵ correspond to different types of ECOs. If ϵ is very big, the ECO behaves more like a star than a black hole. On the contrary, if ϵ tends to a very small value, the ECO behaves like a black hole. It is considered a conceptual model of the origin of the cutoff for ECOs, when a dust shell contracts gravitationally from an initial position to near the Schwarzschild radius. This allowed us to find that the cutoff makes two types of contributions: a classical one governed by General Relativity and one of a quantum nature, if the ECO is very close to the horizon, when estimating that the maximum entropy is contained within the material that composes the shell. Such entropy coincides with the Bekenstein–Hawking entropy. The established cutoff corresponds to a dynamic quantity dependent on coordinate time that is measured by a Fiducial Observer (FIDO). Without knowing the details about quantum gravity, parameter ϵ is calculated, which, in general, allows distinguishing the ECOs from BHs. Specifically, a black shell (ECO) is undistinguishable from a BH.

Conceptual Model for Cutoff Origin in Exotic Compact Objects

We propose a conceptual model for the closeness parameter $\epsilon$, which characterizes exotic compact objects (ECOs). To estimate $\epsilon$, a thin spherical dust shell is considered, which gravitationally contracts from a specific position $r(t_{0})$ to near its gravitational radius $r(t_{2})=r_{s} + \epsilon$, in a finite time $t_{2}$, measured in the frame of a fiducial observer (FIDO). For an external observer, the shell&rsquo;s kinematics is characterized by two clearly distinguishable phases: one of rapid contraction, where the shell is far away from the gravitational radius, $r(t_{0})\gg r_{s}$, and a second phase quasi-stationary, $r(t)\sim r_{s}$, where all of the shell&rsquo;s mass is concentrated around the associated horizon, such that for a FIDO, a black hole (BH)is undistinguishable from a shell configured as a black shell (BS). \\ In the semi-classical approximation $E\ll \kappa_{0}l_{p}^{2}$ and tends to zero when the observation time of collapse $t_{2}$, measured by FIDO, tends to infinity; $\kappa_{0}$ and $l_{p}$ are surface gravity and Planck length, respectively. The quantum effects are significant when $\epsilon\ll r(t_{2})$ and $\epsilon$ tends to $\kappa_{0}l_{p}^{2}$. \\ Without knowing details on quantum gravity, parameter $\epsilon$ is calculated, which, in general, allows distinguishing the ECOs from BHs. Specifically, a BS (ECO) is undistinguishable from a BH.

Geometry of the X-ray source 1H 0707–495

Aims. We investigate the constraints on the size and location of the X-ray source in 1H 0707–495 determined from the shape of the relativistically smeared reflection from the accretion disc. Methods. We developed a new code to model an extended X-ray source and we applied this code to all archival XMM observations of 1H 0707–495. Results. In contrast to earlier works we find that the relativistic reflection in this source is not consistent with an extended uniform corona. Instead, we find that the X-ray source must be very compact, at most a gravitational radius in size, and located at most a few gravitational radii from the black-hole horizon. A uniform extended corona produces an emissivity that is similar to a twice-broken power-law, but the inner emissivity is fixed by the source geometry rather than being a free parameter. In 1H0707–495, the reflection from the inner disc is much stronger than expected for a uniformly extended source. Including the effect of ionised absorption from the wind does not change this conclusion, but including scattered emission (and more complex absorption) from the wind can dramatically change the reflection parameters.