Black hole in balance with dark matter

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040050
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Phase Equilibrium ◽  
Vector Field ◽  
Scalar Field ◽  
Total Mass ◽  
Metric Tensor ◽  
Static Solutions ◽  
Tensor Formula ◽  
Galaxy Rotation Curves

Equilibrium of a gravitating scalar field inside a black hole compressed to the state of a boson matter, in balance with a longitudinal vector field (dark matter) from outside is considered. Analytical consideration, confirmed numerically, shows that there exist static solutions of Einstein’s equations with arbitrary high total mass of a black hole, where the component of the metric tensor [Formula: see text] changes its sign twice. The balance of the energy-momentum tensors of the scalar field and the longitudinal vector field at the interface ensures the equilibrium of these phases. Considering a gravitating scalar field as an example, the internal structure of a black hole is revealed. Its phase equilibrium with the longitudinal vector field, describing dark matter on the periphery of a galaxy, determines the dependence of the velocity on the plateau of galaxy rotation curves on the mass of a black hole, located in the center of a galaxy.

scholarly journals Static State of a Black Hole Supported by Dark Matter

Universe ◽  
2019 ◽  
Vol 5 (9) ◽  
pp. 198 ◽  
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Scalar Field ◽  
Rotation Curve ◽  
Vector Fields ◽  
Tensor Component ◽  
Einstein Equations ◽  
Metric Tensor ◽  
Static State ◽  
Static Solutions

The possibility of an equilibrium state of a gravitating scalar field (describing ordinary matter) inside a black hole, compressed to the state of boson condensate, in balance with a longitudinal vector field (describing dark matter) from the outside, is considered. Analytical analysis, confirmed numerically, shows that there are regular static solutions to the Einstein equations with no limitation on the mass of a black hole. The metric tensor component grr(r) changes sign twice. The behavior of the gravitational field and material fields in the vicinity of these two Schwarzschild radii were studied in detail. The equality of the energy–momentum tensors of the scalar and longitudinal vector fields at the interface supports the phase equilibrium of a black hole and dark matter. Considering the gravitating scalar field as an example, a possible internal structure of a black hole and its influence on the dark matter at the periphery of a galaxy are clarified. In particular, the speed on the plateau of a galaxy rotation curve as a function of a black hole’s mass is determined.

scholarly journals Guessing the Riddle of a Black Hole

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 113
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Standard Model ◽  
Total Mass ◽  
Milky Way ◽  
Einstein Equations ◽  
Black Hole Mass ◽  
Static Solutions ◽  
The Standard Model ◽  
Black Hole Masses

A static structure of matter, extremely compressed to the state of a Bose–Einstein condensate by its own gravitational field, is considered. Instead of the widely spread restriction detgik<0, I used a weaker condition of regularity: all invariants of gik are finite. This makes it possible to find regular static solutions to Einstein equations for a spherically symmetric distribution of matter with no restriction on total mass. In these regular static solutions, the metric component grr changes its sign twice: grr(r)=0 at r=rg and at r=rh>rg. The signature of the metric tensor is changed to (+,+,−,−) within the spherical layer rg<r<rh. Though the gravitation dominates at extremely high density, I assume that it does not violate the exchange interaction of elementary particles of the Standard Model. The found regular static solution to Einstein equations, having no limitation on mass, pretends to describe the state of a black hole to which the gravitational collapse leads. The features of a collapsed black hole, its internal composition depending on total mass and the relation with surrounding dark matter, are considered. An astrophysical application: The pressure balance at the interface between a black hole and dark matter determines the plateau velocity of a galaxy rotation curve as a function of the black hole mass. The plateau velocity is inversely proportional to the black hole mass. The speed of rotation of a star at the periphery of a galaxy is proportional to the square root of the black hole mass (direct attraction to the center) and inversely proportional to the mass of the same black hole (as the influence of dark matter). For a condensate of massive bosons in the Standard Model, the direct attraction to the black hole and the influence of dark matter are equal if the black hole mass is about M˜ ∼ 4.24×1037 g. In galaxies with black hole masses M≳M⊙=1.989×1033 g (like UMa: NGC 3726 and UMa: NGC 3769 of the Ursa Major cluster), the motion of stars is driven by dark matter. Their rotation curves should have a well-defined plateau. On the contrary, in galaxies with black hole masses M>>M˜ (like in our Milky Way with the black hole mass M=8.6×1039 g), the motion of stars is regulated by the black hole in the center. Dark matter does not play a significant role in our Milky Way Galaxy.

Real scalar field solutions of the EKG equations including matter

2020 ◽  
pp. 2150009
Author(s):  
A. Cabo Montes de Oca ◽  
D. Suarez Fontanella
Keyword(s):  
Dark Matter ◽  
Gravitational Field ◽  
Scalar Field ◽  
Scalar Fields ◽  
Stationary Solutions ◽  
Field Interaction ◽  
Small Bodies ◽  
Real Scalar ◽  
Static Solutions ◽  
Klein Gordon

Static (not stationary) solutions of the Einstein–Klein–Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated.

scholarly journals Oscillating Universe with a Quantized Black Hole

2021 ◽  
Author(s):  
Sascha Kulas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dark Matter ◽  
Scalar Field ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Phenomenological Approach ◽  
The Other ◽  
Universe Model ◽  
Energy Field

In cosmology dark energy and dark matter are included in the CDM model, but they are still completely unknown. On the other hand the trans-Planckian problem leads to unlikely high photon energies for black holes. We introduce a model with quantized black hole matter. This minimizes the trans- Planckian problem extremely and leads to a scalar field in the oscillating universe model. We show that the scalar field has the same characteristics as a vacuum energy field and leads to the same Casimir effect. Shortly after the beginning of the big bounce this field decays locally and leads to the production of dark matter. In this model no inflation theory is needed. We emphasize that this model is mainly a phenomenological approach with the aim of new impetus to the discussion.

scholarly journals Gravitational Radius in view of Existence and Uniqueness Theorem

2021 ◽  
Vol 2081 (1) ◽  
pp. 012026
Author(s):  
Boris E Meierovich
Keyword(s):  
Black Hole ◽  
Standard Model ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Total Mass ◽  
Einstein Equations ◽  
Existence And Uniqueness Theorem ◽  
Gravitational Radius ◽  
Metric Tensor ◽  
Klein Gordon

Abstract 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.

scholarly journals Static and dynamic charged black holes

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Hyat Huang ◽  
Zhong-Ying Fan ◽  
H. Lü
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Reverse Engineering ◽  
Electric Charge ◽  
Scalar Potential ◽  
Hole State ◽  
Minimal Coupling ◽  
Charged Black Holes ◽  
Static Solutions

AbstractWe consider a class of Einstein–Maxwell–dilaton theories in general dimensions and construct both static and dynamic charged black holes. We adopt the reverse engineering procedure and make a specific ansatz for the scalar field and then derive the necessary scalar potential and the non-minimal coupling function between the scalar and the Maxwell field. The resulting static black holes contain mass and electric charge as integration constants. We find that some of the static solutions can be promoted to become dynamical ones in the Eddington–Finkelstein-like coordinates. The collapse solutions describe the evolution from a smaller charged black hole to a larger black hole state, driven by the scalar field.

scholarly journals Scalar field effects on the orbit of S2 star

2019 ◽  
Vol 489 (4) ◽  
pp. 4606-4621 ◽  
Author(s):  
◽  
A Amorim ◽  
M Bauböck ◽  
M Benisty ◽  
J-P Berger ◽  
...  
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Scalar Field ◽  
Coupling Parameter ◽  
Kerr Black Hole ◽  
Compact Object ◽  
Relative Mass ◽  
Exact Nature ◽  
Main Effect ◽  
Open Debate

ABSTRACT Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region is well established, but its neighbouring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g. stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be a scalar field of toroidal distribution, associated with ultralight dark matter particles, surrounding the Kerr black hole. Such a field is a form of ‘hair’ expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.

scholarly journals Is a Bose–Einstein condensate a good candidate for dark matter? A test with galaxy rotation curves

2020 ◽  
Vol 29 (09) ◽  
pp. 2050063 ◽  
Author(s):  
Elías Castellanos ◽  
Celia Escamilla-Rivera ◽  
Jorge Mastache
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Einstein Condensate ◽  
Average Particle ◽  
Rotation Curves ◽  
Massive Scalar Field ◽  
Thomas Fermi ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Galaxy Rotation Curves

We analyze the rotation curves that correspond to a Bose–Einstein Condensate (BEC)-type halo surrounding a Schwarzschild-type black hole to confront predictions of the model upon observations of galaxy rotation curves. We model the halo as a BEC in terms of a massive scalar field that satisfies a Klein–Gordon equation with a self-interaction term. We also assume that the bosonic cloud is not self-gravitating. To model the halo, we apply a simple form of the Thomas–Fermi approximation that allows us to extract relevant results with a simple and concise procedure. Using galaxy data from a subsample of SPARC data base, we find the best fits of the BEC model by using the Thomas–Fermi approximation and perform a Bayesian statistics analysis to compare the obtained BEC’s scenarios with the Navarro–Frenk–White (NFW) model as pivot model. We find that in the centre of galaxies, we must have a supermassive compact central object, i.e. supermassive black hole, in the range of [Formula: see text] which condensate a boson cloud with average particle mass [Formula: see text] eV and a self-interaction coupling constant [Formula: see text], i.e. the system behaves as a weakly interacting BEC. We compare the BEC model with NFW concluding that in general the BEC model using the Thomas–Fermi approximation is strong enough compared with the NFW fittings. Moreover, we show that BECs still well-fit the galaxy rotation curves and, more importantly, could lead to an understanding of the dark matter nature from first principles.

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