scholarly journals A black hole inside dark matter and the rotation curves of galaxies

2020 ◽  
Vol 29 (15) ◽  
pp. 2050107
Author(s):  
Fateen Haddad ◽  
Nidal Haddad
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Rotation Curves ◽  
Relativistic Regime ◽  
Matter System ◽  
Symmetric Black Hole ◽  
Fisher Relation

In this paper, we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian limit, the rotation curves of galaxies, including the flat region and the baryonic Tully–Fisher relation, and which has a regular horizon. We obtain as well the energy–momentum tensor of the dark matter sourcing this spacetime and it turns, in special, to satisfy the four energy conditions (dominant, weak, null and strong) everywhere outside the horizon. This black-hole-dark-matter system represents a successful simplified model for galaxies, opens a new area for exploring the relativistic regime of dark matter, and shows that the theory of General Relativity together with dark matter can account for the rotation curves of galaxies.

scholarly journals Fuzzy dark matter black holes and droplets

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
D. Batic ◽  
D. Asem Abuhejleh ◽  
M. Nowakowski
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dark Matter ◽  
Black Hole Solution ◽  
Mass Parameter ◽  
Radial Pressure ◽  
Momentum Tensor ◽  
Anisotropic Fluid ◽  
De Sitter ◽  
Hole Model

AbstractWe consider the possibility of having Dark Matter (DM) black holes motivated by the Einasto density profile. This generalizes both the noncommutative mini black hole model and allows DM to enter as the matter constituent which makes up the black hole. We show that it is possible to construct a black hole solution for each value of the Einasto index and for different values of the mass parameter, provided that the we work with the energy–momentum tensor of an anisotropic fluid. In particular, we achieve that by first considering the equation of state (EOS) $$p_r=-\rho $$ p r = - ρ . It turns out that the corresponding black hole solution exhibits a horizon structure similar to that of a Reissner–Nordström black hole and the central singularity is replaced by a regular de Sitter core. We also show that if the previous EOS is replaced by a nonlocal one, it is possible to construct a self-gravitating fuzzy DM droplet but also in this case, the radial pressure is negative. Finally, we contemplate scenarios of different dark matter black holes with moderate mass values which could have formed in galaxies. In particular, we probe the possibility whether such black holes could also be the central galactic objects.

scholarly journals Tractor Beams, Pressor Beams and Stressor Beams in General Relativity

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 271
Author(s):  
Jessica Santiago ◽  
Sebastian Schuster ◽  
Matt Visser
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Frequent Use ◽  
Advanced Civilization

The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these into the Einstein equations. This latter approach has found frequent use when confronted with creative input from fiction, wormholes and warp drives being the most famous examples. In this paper, we again take inspiration from fiction and see what general relativity can tell us about the possibility of a gravitationally induced tractor beam. We base our construction on warp drives and show how versatile this ansatz alone proves to be. Not only can we easily find tractor beams (attracting objects), but repulsor/pressor beams are just as attainable, and a generalization to “stressor” beams is seen to present itself quite naturally. We show that all of these metrics would violate various energy conditions. This provides an opportunity to ruminate on the meaning of energy conditions as such and what we can learn about whether an arbitrarily advanced civilization might have access to such beams.

THEOREM TO GENERATE NON-SPHERICAL RADIATING BLACK HOLE SOLUTIONS

2008 ◽  
Vol 23 (15) ◽  
pp. 1115-1127
Author(s):  
V. S. MOROZOVA ◽  
S. G. GHOSH
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Type I ◽  
De Sitter ◽  
Sitter Background ◽  
Two Parameter ◽  
Black Hole Solutions

We prove a theorem that characterizes a two-parameter family of solutions to Einstein equations with a negative cosmological constant, representing, in general, non-spherical radiating black holes in an anti-de Sitter background. It is shown that the best known non-spherical radiating black hole solutions are particular cases and static non-spherical black hole solutions, for Type I fluid, are also retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.

scholarly journals Topological black holes in mimetic gravity

2021 ◽  
Author(s):  
Ahmad Sheykhi ◽  
Saskia Grunau
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dark Matter ◽  
Einstein Gravity ◽  
Rotation Curves ◽  
Negative Constant ◽  
Massive Particles ◽  
Bound Orbits ◽  
Mimetic Gravity ◽  
Black Hole Solutions

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

scholarly journals Fluid dynamics in the warp drive spacetime geometry

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Osvaldo L. Santos-Pereira ◽  
Everton M. C. Abreu ◽  
Marcelo B. Ribeiro
Keyword(s):  
Perfect Fluid ◽  
Massive Particle ◽  
Momentum Tensor ◽  
Matter Density ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Inviscid Fluid ◽  
Spacetime Geometry ◽  
Complex Forms ◽  
The Cost

AbstractThe Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called a warp bubble, where a massive particle inside it acquires global superluminal velocities, or warp speeds. This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. The energy–momentum tensor considered has two fluid contents, the perfect fluid and the parametrized perfect fluid (PPF), a tentative more flexible model whose aim is to explore the possibilities of warp drive solutions with positive matter density content. Santos-Pereira et al. (Eur Phys J C 80:786, 2020) already showed that the Alcubierre metric having dust as source connects this geometry to the Burgers equation, which describes shock waves moving through an inviscid fluid, but led the solutions back to vacuum. The same happened for two out of four solutions subcases for the perfect fluid. Other solutions for the perfect fluid indicate the possibility of warp drive with positive matter density, but at the cost of a complex solution for the warp drive regulating function. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. Weak, dominant, strong and null energy conditions were calculated for all studied subcases, being satisfied for the perfect fluid and creating constraints in the PPF quantities such that a positive matter density is also possible for creating a warp bubble. Summing up all results, energy–momentum tensors describing more complex forms of matter or field distributions generate solutions for the Einstein equations with the warp drive metric where a negative matter density might not be a strict precondition for attaining warp speeds.

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.

scholarly journals Gravity with Extra Dimensions and Dark Matter Interpretation: A Straightforward Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. H. Coimbra Araújo ◽  
Roldão da Rocha
Keyword(s):  
Dark Matter ◽  
Extra Dimensions ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Newtonian Potential ◽  
Density Profiles ◽  
Full Compliance ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
The Universe

Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor—from the Einstein-Hilbert action—and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration whose density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extradimensional components. A Miyamoto-Nagai ansatz is used to solve Einstein equations. The stable rotation curves associated with such system are computed, in full compliance with the observational data, without fitting techniques. The density profiles are reconstructed and compared to the ones obtained from the Newtonian potential.

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.

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.

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