The interaction between a rotating, spherical shell of matter and a central black hole

1978 ◽  
Vol 362 (1711) ◽  
pp. 469-492
Keyword(s):  
Black Hole ◽  
Spherical Shell ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Leading Order ◽  
Multipole Moments ◽  
Matter Distribution ◽  
Central Black Hole ◽  
Magnetic Components ◽  
Axis Of Rotation

A method due to Chrzanowski, involving horizon multipole moments, is applied to the problem of a black hole perturbed by an enclosing, distant, spinning, spherical shell of matter. The hole, of mass M and angular momentum J = aM , is at the centre of the shell, their respective axes of rotation differing by an angle ξ. The matter-distribution on the shell is axisymmetric about its axis of rotation, but otherwise arbitrary, except that the total mass of the shell is small in comparison with M . The energy-momentum tensor of such a shell has been previously found by Bass & Pirani. Using their expression, we calculate the spin-down law for the black hole, correct to leading order in the inverse of the shell’s radius, and to second order in its angular velocity. The solution may be expressed in terms of the ‘electric’ and ‘magnetic’ components E αβ and B αβ of the Weyl tensor C ijkl , as calculated at the centre of the shell, in the absence of the black hole. For, denoting by J ∥ and J ⊥ the components of J parallel and perpendicular, respectively, to the direction of spin of the shell, we have always d J ∥ /d t = 0 and 1/ J ⊥ d J ⊥ /d t =–4/15 M 3 ( E αβ E αβ + B αβ B αβ ) (1–3/4ã 2 +15/4ã 2 sin 2 ξ), where ã = a / M . This law is of theoretical interest. It shows points both of similarity to, and of difference from, the known laws describing the response of a black hole to (uniform) scalar and electromagnetic fields.

scholarly journals The thermodynamic theory of black holes

1977 ◽  
Vol 353 (1675) ◽  
pp. 499-521 ◽  
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Energy Momentum Tensor ◽  
Heat Bath ◽  
Naked Singularity ◽  
Momentum Tensor ◽  
Thermodynamic Theory ◽  
Model Systems ◽  
Quantum Energy ◽  
Third Law Of Thermodynamics

The thermodynamic theory underlying black hole processes is developed in detail and applied to model systems. I t is found that Kerr-Newman black holes undergo a phase transition at a = 0.68 M or Q = 0.86 M , where the heat capacity has an infinite discontinuity. Above the transition values the specific heat is positive, permitting isothermal equilibrium with a surrounding heat bath. Simple processes and stability criteria for various black hole situations are investigated. The limits for entropieally favoured black hole formation are found. The Nernst conditions for the third law of thermodynamics are not satisfied fully for black holes. There is no obvious thermodynamic reason why a black hole may not be cooled down below absolute zero and converted into a naked singularity. Quantum energy-momentum tensor calculations for uncharged black holes are extended to the Reissner-Nordstrom case, and found to be fully consistent with the thermodynamic picture for Q < M . For Q > M the model predicts that ‘naked’ collapse also produces radiation, with such intensity that the collapsing matter is entirely evaporated away before a naked singularity can form.

UNUSUAL HYDRODYNAMICS

1987 ◽  
Vol 02 (05) ◽  
pp. 1591-1615 ◽  
Author(s):  
V.A. BEREZIN
Keyword(s):  
Black Hole ◽  
Cosmological Model ◽  
Production Process ◽  
Particle Production ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Point Of View ◽  
Modified Equations ◽  
Nonsingular Cosmological Model

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

scholarly journals A NEAR HORIZON CFT DUAL FOR KERR–NEWMAN AdS

2011 ◽  
Vol 26 (18) ◽  
pp. 3077-3090 ◽  
Author(s):  
BRADLY K. BUTTON ◽  
LEO RODRIGUEZ ◽  
CATHERINE A. WHITING ◽  
TUNA YILDIRIM
Keyword(s):  
Black Hole ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
S Wave ◽  
One Dimensional ◽  
Conformal Field ◽  
Asymptotic Symmetries

We show that the near horizon regime of a Kerr–Newman AdS (KNAdS) black hole, given by its two-dimensional analogue a là Robinson and Wilczek (Phys. Rev. Lett.95, 011303 (2005)), is asymptotically AdS2 and dual to a one-dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy–momentum tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein–Hawking entropy via Cardy's formula. Our derived central charge also agrees with the near extremal Kerr/CFT correspondence (Phys. Rev. D80, 124008 (2009)) in the appropriate limits. We also compute the Hawking temperature of the KNAdS black hole by coupling its Robinson and Wilczek two-dimensional analogue (RW2DA) to conformal matter.

On the origin of black hole evaporation radiation

1976 ◽  
Vol 351 (1664) ◽  
pp. 129-139 ◽  
Keyword(s):  
Black Hole ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Static Vacuum ◽  
Black Hole Evaporation ◽  
A Value ◽  
Special Case ◽  
Collapse Process

The physical basis underlying the black hole evaporation process is clarified by a calculation of the expectation value of the energy-momentum tensor for a massless scalar field in a completely general two dimensional collapse scenario. It is found that radiation is produced inside the collapsing matter which propagates both inwards and outwards. The ingoing com­ponent eventually emerges from the star after travelling through the centre. The outgoing energy flux appears at infinity as the evaporation radiation discovered by Hawking. At late times, outside the star, the former component fades out exponentially, and the latter component approaches a value which is independent of the details of the collapse process. In the special case of a collapsing hollow, thin shell of matter, all the radiation is produced at the shell. These results are independent of regularization ambiguities, which enter only the static vacuum polariza­tion terms in the energy-momentum tensor. The significance of an earlier remark about black hole explosions is discussed in the light of these results.

scholarly journals A regular scale-dependent black hole solution

2018 ◽  
Vol 27 (03) ◽  
pp. 1850032 ◽  
Author(s):  
Ernesto Contreras ◽  
Ángel Rincón ◽  
Benjamin Koch ◽  
Pedro Bargueño
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Black Hole Solution ◽  
Energy Momentum Tensor ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Scale Dependence ◽  
Weak Energy Condition ◽  
Effective Energy ◽  
Regular Black Hole

In this work, we present a regular black hole solution, in the context of scale-dependent General Relativity, satisfying the weak energy condition. The source of this solution is an anisotropic effective energy–momentum tensor which appears when the scale dependence of the theory is turned-on. In this sense, the solution can be considered as a semiclassical extension of the Schwarzschild one.

scholarly journals A note on Reissner–Nordström black holes in the inverse electrodynamics model

2021 ◽  
pp. 2150155
Author(s):  
S. Habib Mazharimousavi
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
General Class ◽  
Black Hole Solution ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Nonlinear Electrodynamics ◽  
Nonlinear Electrodynamic ◽  
Electric And Magnetic Fields

Recently, the inverse electrodynamics model (IEM) was introduced and applied to find Reissner–Nordström black holes in the context of the general relativity coupled minimally with the nonlinear electrodynamics. The solution consists of both electric and magnetic fields as of the dyonic solutions. Here, in this note, we show that the IEM model belongs to a more general class of the nonlinear electrodynamics with [Formula: see text]. Here, [Formula: see text] is the energy momentum tensor of the nonlinear electrodynamic Lagrangian. Naturally, such a dyonic RN black hole solution is the solution for this general class.

scholarly journals Ideal Spin Hydrodynamics from the Wigner Function Approach

2021 ◽  
Vol 38 (11) ◽  
pp. 116701
Author(s):  
Hao-Hao Peng ◽  
Jun-Jie Zhang ◽  
Xin-Li Sheng ◽  
Qun Wang
Keyword(s):  
Wigner Function ◽  
Particle Number ◽  
Energy Momentum Tensor ◽  
Moment Tensor ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Momentum Tensor ◽  
Leading Order ◽  
Thermodynamical Parameters ◽  
Average Spin

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Kn and the average spin polarization χs have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Kn and χs .

Dynamics of extended bodies in general relativity - II. Moments of the charge-current vector

1970 ◽  
Vol 319 (1539) ◽  
pp. 509-547 ◽  
Keyword(s):  
Tensor Field ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The Body ◽  
Total Charge ◽  
Subsequent Paper ◽  
Multipole Moments ◽  
Current Vector ◽  
Charge Current ◽  
Infinite Set

The problem is considered of defining multipole moments for a tensor field given on a curved spacetime, with the aim of applying this to the energy-momentum tensor and charge-current vector of an extended body. Consequently, it is assumed that the support of the tensor field is bounded in spacelike directions. A definition is proposed for ‘a set of multipole moments’ of such a tensor field relative to an arbitrary bitensor propagator. This definition is not fully determinate, but any such set of moments completely determines the original tensor field. By imposing additional conditions on the moments in two different ways, two uniquely determined sets of moments are obtained for a vector field J α . The first set, the complete moments , always exists and agrees with moments defined less explicitly by Mathisson. If V α J α = 0, as is the case for the charge-current vector, these moments are interrelated by an infinite set of corresponding restrictions. The second set, the reduced moments , exists if and only if V α J α = 0. These avoid such an infinite set of interrelations, there being instead only one such restriction, the constancy of the total charge of the body. The energy-momentum tensor will be treated in a subsequent paper.

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