scholarly journals Noncommutative Reissner–Nordstrøm black hole

2018 ◽  
Vol 96 (12) ◽  
pp. 1259-1265 ◽  
Author(s):  
Carlos A. Soto-Campos ◽  
Susana Valdez-Alvarado
Keyword(s):  
Black Hole ◽  
Fourth Order ◽  
Riemannian Geometry ◽  
Deformation Parameter ◽  
Riemann Tensor ◽  
Quantum Level ◽  
Metric Tensor ◽  
Noncommutative Version ◽  
Curvature Tensors ◽  
Scalar Invariants

In this work we construct a deformed embedding of the Reissner–Nordstrøm (R-N) space–time within the framework of a noncommutative Riemannian geometry. We provide noncommutative corrections to the usual Riemannian expressions for the metric and curvature tensors. For the case of the metric tensor, the expression obtained possesses terms that are valid to all orders in the deformation parameter. Then we calculate the correction to the area of the event horizon of the corresponding noncommutative R-N black hole, obtaining an expression for the area of the black hole, which is correct up to fourth-order terms in the deformation parameter. Finally we include some comments on the noncommutative version on one of the second-order scalar invariants of the Riemann tensor, the so-called Kretschmann invariant, a quantity that is regularly used to extend gravity to the quantum level.

scholarly journals SECOND ORDER SCALAR INVARIANTS OF THE RIEMANN TENSOR: APPLICATIONS TO BLACK HOLE SPACETIMES

2002 ◽  
Vol 11 (06) ◽  
pp. 827-841 ◽  
Author(s):  
CHRISTIAN CHERUBINI ◽  
DONATO BINI ◽  
SALVATORE CAPOZZIELLO ◽  
REMO RUFFINI
Keyword(s):  
Black Hole ◽  
Riemann Tensor ◽  
Second Order ◽  
Black Hole Spacetimes ◽  
Definition Of ◽  
Scalar Invariants

We discuss the Kretschmann, Chern–Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman–Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr–Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.

scholarly journals Phase Transitions of the BTZ Black Hole in New Massive Gravity

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yun Soo Myung
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Phase Transitions ◽  
Fourth Order ◽  
Mass Parameter ◽  
Massive Gravity ◽  
Curvature Radius ◽  
Btz Black Hole

We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. Form2l2>1/2withm2being the mass parameter of fourth-order terms andl2AdS3curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. Form2l2<1/2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.

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.

On the existence of metric differential geometries based on the notion of area

1950 ◽  
Vol 46 (1) ◽  
pp. 67-72 ◽  
Author(s):  
F. Brickell
Keyword(s):  
Differential Geometry ◽  
Fourth Order ◽  
Homogeneous Function ◽  
Two Dimensional ◽  
Fundamental Function ◽  
Metric Tensor ◽  
Partial Derivatives ◽  
Dimensional Plane ◽  
Plane Element

The problem of constructing an n-dimensional metric differential geometry based on the idea of a two-dimensional area has given rise to several publications, notably by A. Kawaguchi and S. Hokari (1), E. T. Davies (2), and R. Debever (3). In this geometry the area of a two-dimensional plane element is defined by a fundamental function L(xi, uhk), where the xi are point coordinates and the uhk are the coordinates of the simple bivector representing the plane element. L is supposed to be a positive homogeneous function of the first degree with respect to the variables uij, and to possess continuous partial derivatives up to and including those of the fourth order. With these assumptions the problem of the construction of the metric differential geometry splits into two problems; the first of these is the problem of constructing a metric tensor gij(xr, uhk), and the second is the problem of constructing an affine connexion. We deal with the first problem only in this paper.

scholarly journals LUKEWARM BLACK HOLES IN QUADRATIC GRAVITY

2011 ◽  
Vol 26 (14) ◽  
pp. 999-1007 ◽  
Author(s):  
JERZY MATYJASEK ◽  
KATARZYNA ZWIERZCHOWSKA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Fourth Order ◽  
Spherically Symmetric ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Quadratic Gravity ◽  
De Sitter Universe ◽  
Electrically Charged

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.

scholarly journals A fourth-order indirect integration method for black hole perturbations: even modes

2011 ◽  
Vol 28 (13) ◽  
pp. 134012 ◽  
Author(s):  
Patxi Ritter ◽  
Alessandro D A M Spallicci ◽  
Sofiane Aoudia ◽  
Stéphane Cordier
Keyword(s):  
Black Hole ◽  
Fourth Order ◽  
Integration Method

scholarly journals Black hole and naked singularity geometries supported by three-form fields

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Bruno J. Barros ◽  
Bogdan Dǎnilǎ ◽  
Tiberiu Harko ◽  
Francisco S. N. Lobo
Keyword(s):  
Black Hole ◽  
Killing Vector ◽  
Field Potential ◽  
Naked Singularity ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Metric Tensor ◽  
Killing Horizon ◽  
Form Field

Abstract We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$Aαβγ, which is related to the field strength and a potential term. The field equations are obtained explicitly for a static and spherically symmetric geometry in vacuum. For a vanishing three-form field potential the gravitational field equations can be solved exactly. For arbitrary potentials numerical approaches are adopted in studying the behavior of the metric functions and of the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are studied in detail.

Effect of charge and deformation parameter on energy extraction in charged non-Kerr black holes

2019 ◽  
Vol 28 (16) ◽  
pp. 2040012
Author(s):  
Rehana Rahim ◽  
Khalid Saifullah
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Deformation Parameter ◽  
High Efficiency ◽  
Process Efficiency ◽  
Energy Extraction ◽  
Penrose Process ◽  
Kerr Black Holes ◽  
Very High

We analyze the charged Johannsen–Psaltis black hole for energy extraction via the Penrose process. Efficiency of the Penrose process is found to be dependent on the deformation parameter of the metric and charge. Doing the calculations numerically, we find that, in the nonextremal limit, presence of charge leads to lesser efficiency than the Kerr. In the extremal cases with negative deformation parameter, charge leads to a very high efficiency, higher than that of the Kerr and Johannsen–Psaltis black holes.

scholarly journals Hamiltonian expression of curvature tensors in the York canonical basis: (II) Weyl tensor, Weyl scalars, Weyl eigenvalues and the problem of the observables of the gravitational field

2014 ◽  
Vol 11 (06) ◽  
pp. 1450053 ◽  
Author(s):  
Luca Lusanna ◽  
Mattia Villani
Keyword(s):  
Gravitational Field ◽  
Weyl Tensor ◽  
Canonical Basis ◽  
Riemann Tensor ◽  
Space Time ◽  
Minkowskian Space ◽  
Canonical Gravity ◽  
The Family ◽  
Tetrad Gravity ◽  
Curvature Tensors

We find the Hamiltonian expression in the York basis of canonical ADM tetrad gravity of the 4-Weyl tensor of the asymptotically Minkowskian space-time. Like for the 4-Riemann tensor we find a radar tensor (whose components are 4-scalars due to the use of radar 4-coordinates), which coincides with the 4-Weyl tensor on-shell on the solutions of Einstein's equations. Then, by using the Hamiltonian null tetrads, we find the Hamiltonian expression of the Weyl scalars of the Newman–Penrose approach and of the four eigenvalues of the 4-Weyl tensor. After having introduced the Dirac observables (DOs) of canonical gravity, whose determination requires the solution of the super-Hamiltonian and super-momentum constraints, we discuss the connection of the DOs with the notion of 4-scalar Bergmann observables (BOs). Due to the use of radar 4-coordinates these two types of observables coincide in our formulation of canonical ADM tetrad gravity. However, contrary to Bergmann proposal, the Weyl eigenvalues are shown not to be BOs, so that their relevance is only in their use (first suggested by Bergmann and Komar) for giving a physical identification as point-events of the mathematical points of the space-time 4-manifold. Finally we give the expression of the Weyl scalars in the Hamiltonian post-Minkowskian linearization of canonical ADM tetrad gravity in the family of (non-harmonic) 3-orthogonal Schwinger time gauges.

scholarly journals Black hole shadows in fourth-order conformal Weyl gravity

2017 ◽  
Vol 95 (12) ◽  
pp. 1299-1306 ◽  
Author(s):  
Jonas R. Mureika ◽  
Gabriele U. Varieschi
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Fourth Order ◽  
Conformal Gravity ◽  
Weyl Gravity ◽  
General Relativistic

We calculate the characteristics of the “black hole shadow” for a rotating, neutral black hole in fourth-order conformal Weyl gravity. It is shown that the morphology is not significantly affected by the underlying framework, except for very large masses. Conformal gravity black hole shadows would also significantly differ from their general relativistic counterparts if the values of the main conformal gravity parameters, γ and κ, were increased by several orders of magnitude. Such increased values for γ and κ are currently ruled out by gravitational phenomenology. Therefore, it is unlikely that these differences in black hole shadows will be detected in future observations, carried out by the Event Horizon Telescope or other such experiments.

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